Fuel Cell Engines

Fuel Cell Engines Matthew M. Mench

Copyright © 2008 by John Wiley & Sons, Inc.

Fuel Cell Engines

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Fuel Cell Engines Matthew M. Mench

JOHN WILEY & SONS, INC.

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∞ This book is printed on acid-free paper. 

C 2008 by John Wiley & Sons, Inc. All rights reserved Copyright 

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information about our other products and services, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our Web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Mench, Matthew. Fuel cell engines / by Matthew Mench. p. cm. Includes index. ISBN 978-0-471-68958-4 (cloth) 1. Fuel cells. I. Title. TK2931.M46 2008 621.31 2429–dc22

2007046855

Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

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Contents

Preface vii Acknowledgments

3.3 xi 3.4

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Introduction to Fuel Cells

Preliminary Remarks 1 Fuel Cells as Electrochemical Engines 3 Generic Fuel Cell and Stack 6 Classification of Fuel Cells 9 Potential Fuel Cell Applications and Markets 17 History of Fuel Cell Development 23 Summary 24

Application Study Problems 25 References 26

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7

3.1 3.2

3.5 3.6 3.7 3.8

Application Study Problems 116 References 119

96

116

24 4

Basic Electrochemical Principles

4.1 4.2 4.3 4.4 4.5 4.6 4.7

29

Electrochemical versus Chemical Reactions 29 Electrochemical Reaction 31 Scientific Units, Constants, and Basic Laws 35 Faraday’s Laws: Consumption and Production of Species 43 Measures of Reactant Utilization Efficiency 48 The Generic Fuel Cell 50 Summary 56

Application Study Problems 58 References 61

3

1

Determination of Change in Enthalpy for Nonreacting Species and Mixtures 78 Determination of Change in Enthalpy for Reacting Species and Mixtures 83 Psychrometrics: Thermodynamics of Moist Air Mixtures 91 Thermodynamic Efficiency of a Fuel Cell Maximum Expected Open-Circuit Voltage: Nernst Voltage 106 Summary 114

Physical Nature of Thermodynamic Variables 62 Heat of Formation, Sensible Enthalpy, and Latent Heat 74

Polarization Curve 121 Region I: Activation Polarization 126 Region II: Ohmic Polarization 157 Region III: Concentration Polarization 168 Region IV: Other Polarization Losses 175 Polarization Curve Model Summary 181 Summary 183

Application Study Problems 186 References 189 5 5.1 5.2 5.3 5.4 5.5

58

Thermodynamics of Fuel Cell Systems

Performance Characterization of Fuel Cell Systems 121

62

5.6 5.7

185

Transport in Fuel Cell Systems

191

Ion Transport in an Electrolyte 191 Electron Transport 209 Gas-Phase Mass Transport 210 Single-Phase Flow in Channels 233 Multiphase Mass Transport in Channels and Porous Media 239 Heat Generation and Transport 263 Summary 276

Application Study Problems 279 References 281

278

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Contents

6

Polymer Electrolyte Fuel Cells

6.1 6.2 6.3 6.4 6.5 6.6 6.7

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Hydrogen PEFC 285 Water Balance in PEFC 298 PEFC Flow Field Configurations and Stack Design 325 Direct Alcohol Polymer Electrolyte Cells PEFC Degradation 356 Multidimensional Effects 362 Summary 369

Application Study Problems 371 References 374

8

285

371

339

Hydrogen Storage, Generation, and Delivery 426

8.1 8.2 8.3 8.4

Modes of Storage 426 Modes of Generation 438 Hydrogen Delivery 443 Overall Hydrogen Infrastructure Development 446 Summary 448

8.5

Application Study Problems 449 References 450 9

Experimental Diagnostics and Diagnosis

9.1 7 7.1 7.2 7.3 7.4 7.5 7.6

Other Fuel Cells

380

Solid Oxide Fuel Cells 381 Molten Carbonate Fuel Cells 392 Phosphoric Acid Fuel Cells 398 Alkaline Fuel Cells 410 Biological and Other Fuel Cells 418 Summary 418

Application Study Problems 420 References 421

419

449

9.2 9.3 9.4

Electrochemical Methods to Understand Polarization Curve Losses 454 Physical Probes and Visualization 469 Degradation Measurements 478 Summary 478

Application Study Problems 480 References 481 Appendix Index

485 503

479

453

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Preface The field of fuel cell science and technology is undergoing a rapid expansion in both applied and fundamental studies. While the explosive growth of prototype systems for portable, stationary, and transportation applications garner most of the public attention, any textbook that tries to capture this aspect would be hopelessly outdated by the time of publication. One only has to read the bevy of press releases hailing the introduction of a real fuel cell product “in about a year” to realize that the landscape of product development is continually evolving and, in some cases, circling back on itself. Some still question if fuel cells will ever have a real impact on power generation at all. While I agree that fuel cells are not the panacea for every power need, I do believe that development has reached a stage of critical mass, where ubiquitous implementation and real product development in at least portable and stationary applications will eventually occur. This book is based on the need for a single textbook that combines the essential elements of the myriad disciplines required to understand fuel cells at a fundamental level. The purpose of this textbook is to prepare the engineering student with a timeless understanding of the fundamentals of fuel cell operation, so that as the specific applications change, the fundamental understanding can be applied. To that end, the book has been structured to be as fundamental as possible, to prepare the student without engineering bias. I have taught my courses and written this book not as an advocate of fuel cells but rather as an engineer and scientist that studies them with an open mind to the alternatives. Too often, the clouds of hope, fear, or funding obscure the light of good science. The subject matter in each chapter could easily be expanded to cover an entire separate textbook. For the sake of brevity, and based on the material I can reasonably cover in a semester, I have limited the material discussed to the undergraduate and some graduate lectures I have developed at Penn State over the course of the past seven years. A majority of the material in the text is based on a senior-level undergraduate technical elective class I have developed. I find that the course material in Chapters 1–4, 6, and 7 can be covered in a normal 45-lecture undergraduate course. The material in Chapters 5 and 9 are mostly from a graduate-level course I teach, although the undergraduate course definitely includes the more basic aspects of the transport theory described in Chapter 5. The textbook has been written for a senior-level undergraduate student but should also serve as a good introductory text and reference for graduate study. Where useful, I have included typical values for many of the parameters introduced but have intentionally tried to avoid topics that may shift in time where possible, so that the book will remain useful into the future as a fundamental principles reference. Chapter 1 presents a global perspective of the field of fuel cells so that the reader can grasp the practical significance and potential applications of the fuel cells they are about to study. The chapter presents a brief history of various types of fuel cell development (many people are unaware that actual fuel cell products have been developed and in use for years now), the basic functions of a fuel cell, and attempts to place the field in proper context

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Preface

as a multidisciplinary collection of engineering disciplines. The field of fuel cells truly is an exciting multidisciplinary arena, where electrical, mechanical, material, chemical, and industrial engineering merge. A new class of engineer educated in these areas is needed to further fuel cell development. Chapter 2 introduces the basic electrochemical principles and terminology needed to understand electrochemical cells, reactant consumption, and product generation. The chapter concludes with a discussion of the generic fuel cell, including the function and desirable qualities in each fuel cell component. I find that early in the semester, when the generic fuel cell concept is presented with a hands-on in-class demonstration of a fuel cell assembly and disassembly, the students begin with a strong understanding of the various internal processes and engineering trade-offs that occur in any fuel cell, which really helps later when the analytical descriptions are derived and the student needs to be able to visualize the various physical phenomena. This element is key to the future understanding they can achieve, and I suggest the professor accompany discussion of the generic fuel cell with a physical example of a fuel cell in class to help this process along. Notes cannot convey the understanding achieved from simply taking a small fuel cell apart. Chapter 3 is an especially detailed description of the fundamental thermodynamics involved in fuel cell science. Some will find this is overwritten, especially for a graduatelevel class. However, in many schools and between different departments, the curricula in thermodynamics have been thinned out so much that many of my undergraduate students were losing touch when the concept of a Nernst voltage or even relative humidity was presented. To address this issue and provide enough material to get all students on the same foundation, this chapter includes a fundamental description of the thermodynamic parameters involved and the thermodynamic concepts needed for fuel cell study. Not all of this material should be covered in class, but it serves as a reference for students who are struggling to follow the concepts presented and helps them keep up with the other students. Since I find many students lose their joy of engineering when it enters the microscale, where possible, I have tried to impart a physical meaning to the parameters that can help link the micro- and macroscales. Chapter 4 is the largest and most important chapter in the text and could easily be separated into several separate chapters. In this chapter, the entire polarization curve is presented and dissected. Starting with the maximum thermal voltage, each departure from this voltage is analyzed in detail. The culmination of the chapter is the development of a zerodimensional fuel cell performance model that includes detailed expressions for losses from kinetic, thermodynamic, ohmic, concentration, crossover, or short-circuit polarizations. I find that assigning a computer project that asks the student to integrate this fuel cell model into a spreadsheet is an extremely valuable way to help cement the physical parameters and concepts in the students’ minds. Although a zero-dimensional model cannot account for many of the more complex effects involved, it is extremely valuable as a qualitative teaching tool. The professor can extend this model to make it as complex as desired. For a graduatelevel class, including more advanced flooding concepts, an extension to an along-thechannel-l-D model can make a good term project. I find that through this modeling project approach, the students realize the limitations of the model and the trade-offs with design parameters such as electrolyte thickness or humidity and achieve a global understanding of the relative importance of the controlling parameters. Also included in Chapter 4 is a semiempirical modeling approach commonly used. Although less fundamental, it can be

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Preface

ix

useful to delineate the relative importance of the various losses and as a comparative tool and so is included here. Chapter 5 covers the especially broad area of mass and heat transport in fuel cells. This is another chapter that could easily be expanded to cover an entire book. Some of the basic transport processes discussed can be taught along with the concentration polarization discussion of Chapter 4. This is what I do in my undergraduate class. In fact, the professor may wish to reorder the presentation of this material to cover Chapter 5 first, to set up a more complete understanding for the presentation of the polarization curve. I have tried this in class but have found that the introduction of the polarization curve comes too late in the semester for a significant final project to be accomplished. At the graduate level, the entire chapter can be taught, including the extended discussion of multiphase flow and flooding in the porous media of polymer electrolyte fuel cells (PEFCs). To truly understand flooding in polymer electrolyte fuel cells, a deep understanding of multiphase flow in mixed wettability porous media, such as diffusion media, is necessary and is presented. This topic is far from complete science, and will certainly evolve in the future. Chapter 6 is devoted entirely to PEFC systems, including hydrogen- and direct alcoholbased applications, issues, and degradation concerns. The specific devotion to PEFCs is based on my personal expertise and the fact the PEFC is the most broadly studied system and most likely to have future ubiquitous application in various applications. From a student perspective, the automotive application tends to draw students into the class, so that the PEFC tends to be the system of greatest student interest. Additionally, multiphase management for PEFCs is especially complex compared to other systems where only single phase flow is present in the reactant and product mixture. Due to its importance in stability, performance, and durability, special attention is taken to detail the water balance and flooding in PEFCs. Chapter 7 is a summary chapter of other fuel cell systems, including solid oxide, phosphoric acid, alkaline, and molten carbonate systems. By this chapter, the reader should possess the background information required to integrate the material presented and understand the various design constraints and engineering trade-offs inherent in each system. An understanding of the particular material and degradation issues is also presented. Other types of fuel cells such as biological and microbial fuel cells are given cursory treatment here, but they certainly enjoy the potential for strong future development. Chapter 8 is included for completeness and to present the reader with a summary of perhaps the biggest challenges in achieving real fuel cell applications: the storage, generation, and delivery of hydrogen. While this chapter is less technical in detail than others, it has been written to present the reader with the options available and the implicit engineering trade-offs accompanying the various choices. As with the rest of the textbook, the information is presented, where possible, without deference to the myriad political and economic factors involved. However, the subject of this chapter is one area where debate certainly rages. As an important capstone, Chapter 9 is given to introduce the reader to some of the more common options available to actually measure the parameters of interest used in fuel cell modeling and delineate the different polarization losses from one another. It is by no means complete and again is an example where an entire book could easily be written. The reader is expected to use this chapter as a starting point and reference for available techniques. Successful laboratory implementation will require additional reading, however, from other focused resources. This chapter can be used to prepare students for a laboratory

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Preface

project and is divided into two main sections. The first includes a description of the basic experimental techniques needed to obtain the parameters needed to describe the polarization curve model of Chapter 4. The second includes an overview of some of the laboratorybased diagnostics and visualization techniques available to discern current, species, and temperature distributions that can be used for transport parameter determination or for closing the energy, current, and mass balance equations for detailed model validation. In my class, I typically follow Chapter 4 with a laboratory project that covers some of the basic concepts presented. Finally, there are many topics which are not included in this textbook for various reasons. These include economic and political issues, hydrogen safety and regulation, system components, dynamic operation and instability, and system control issues. This information was excluded for brevity because it is well covered in other texts or to preserve the fundamental nature of the material. Some of these issues may be incorporated into future editions of this text, as my publisher permits and readers request. I sincerely hope the educational goals of this book are achieved and welcome feedback from my colleagues in the field to help me present a more complete and precise picture in future editions. Matthew M. Mench University Park, PA June, 2007.

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Acknowledgments First and foremost, I owe whatever accomplishments I have in my life to my God. I also want to thank my wife, Laurel, and my children, Elizabeth Adeline and Michael, for their willingness to let me vaporize from existence to finish this book. I am in great debt also to all of my graduate students, past and present, who helped me to learn and teach what I know and who continue to make life enjoyable and exciting in the process. Dr. Rama Ramasamy and Dr. Emin Caglan Kumbur have been especially helpful in reviewing sections of the text and providing valuable suggestions. I am greatly appreciative of Ms. Elise Corbin, who provided a vast majority of the sketches in the text. I also want to thank my publisher and his editorial assistants, Robert L. Argentieri, Bob Hilbert, Evan Jones, and Daniel Magers, respectively, for the faith and patience they have showed in me. I am in debt to the hundreds of students in my classes who have provided immensely valuable feedback that I have tried to incorporate in all facets of the textbook. I am also in debt to my colleagues in the profession and research sponsors who have given me insights and challenging problems to study that have ultimately led me down this path. Professor C. Y. Wang gave me my initial opportunity in the field. Professor Sukkee Um of Hanyang University in South Korea has been a close friend and fuel cell expert to whom I owe a lot. I also which to thank Professor Peiwen Li of the University of Arizona, whose feedback has enhanced the quality of the book. I wish to thank my academic advisor Keneneth Kuo, who taught me that, many times, progress and insight comes from unrelenting tenacity and determination and who encouraged me to write this book. Finally, I am grateful to my parents, J. Larry and Noreen Mench, and in-laws, Larry and Arlene Tepke, who have taught me that true progress is much more than what you do at work.

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Fuel Cell Engines Matthew M. Mench

1

Copyright © 2008 by John Wiley & Sons, Inc.

Introduction to Fuel Cells The Stone Age didn’t end because they ran out of stones—but as a result of competition from the bronze tools, which better met people’s needs. I feel there’s something in the air—people are ready to say that this is something we should do. —Jeroen van der Veer, Chairman of Royal Dutch/Shell Group 2000

1.1 PRELIMINARY REMARKS The science and technology of fuel cell engines are both fascinating and continually evolving. This point is emphasized by Figure 1.1, which shows the registered fuel-cell-related patents in the United States, Canada, and the United Kingdom from 1975 through 2003. A similar acceleration of the patents granted in Japan and South Korea is also well underway, led by automotive manufacturers. The rapid acceleration in fuel cell development is not likely to wane in the near future, as the desire for decreased dependence on petroleum supplies, lower pollution, and potential for high efficiency are driving this trend toward an alternative power generation technology. Any attempt to bring the reader the state-of-the art of the applied technology of fuel cell engines in a texbook would be hopelessly antiquated by the time it was published. The designs, materials, and components of fuel cell systems are constantly being improved for increased efficiency, durability, and lower cost. At the heart of the ever-changing fuel cell technology, however, is an equally fascinating and rich multidisciplinary fundamental science drawn from various engineering disciplines. The fundamentals of fuel cell science, emphasized in this textbook, are shown schematically in Figure 1.2. It is obvious that fuel cell science is not solely the domain of the electrochemist and can encompass nearly all engineering disciplines. Electrochemistry, thermodynamics, reaction kinetics, heat and mass transfer, fluid mechanics, and material science all play integral roles in basic fuel cell design. Outside the basic science of an individual fuel cell lie system and component issues that include manufacturing, sensing and control, vibration, and a plethora of other technologies. The goal of this text is to provide a fundamental background on fuel cell science shown in Figure 1.2 to serve as an introduction to this captivating and rapidly expanding field. As discussed in Section 1.6, there have been several waves of concentrated fuel cell research and development, each driven by a somewhat different impetus. Throughout the

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Introduction to Fuel Cells 1200

1000 Number of patents issued

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United States United Kingdom Canada

800

600

400

200

0 1975

1980

1985

1990

1995

2000

2005

Year of issue

Figure 1.1 Timeline of worldwide patents in fuel cells for select countries based on data from U.S., U.K., and Canadian patent offices.

history of development, however, the fundamental advantages common to all fuel cell systems have included the following: 1. A potential for a relatively high operating efficiency, scalable to all size power plants. 2. If hydrogen is used as fuel, pollution emissions are strictly a result of the production process of the hydrogen.

Electrochemistry Materials

Thermodynamics

Fluid mechanics

Reaction kinetics

Heat/mass transfer

Specific FC phenomena

FC system components

Figure 1.2 Major engineering disciplines involved in fundamental fuel cell science.

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1.2

Fuel Cells as Electrochemical Engines

3

3. No moving parts, with the significant exception of pumps, compressors, and blowers to drive fuel and oxidizer. 4. Multiple choices of potential fuel feedstocks, from existing petroleum, natural gas, or coal reserves to renewable ethanol or biomass hydrogen production. 5. A nearly instantaneous recharge capability compared to batteries. It should be noted that fuel cells must not be seen as a panacea for every powergenerating application need in the world. There are many specific applications, however, where fuel cell use has great potential to have a major impact on future power generation. Before this conversion can occur, however, the following technical limitations common to all fuel cell systems must be overcome: 1. Alternative materials and construction methods must be developed to reduce fuel cell system cost to be competitive with the automotive combustion engine (∼$30/kW) and stationary power generation systems (∼$1000/kW). The cost of the catalyst no longer dominates the price of most fuel cell systems, although it is still significant. Manufacturing and mass production technology are now also key components to the commercial viability of fuel cell systems. 2. Suitable reliability and durability must be achieved. The performance of every fuel cell gradually degrades with time due to a variety of phenomena. The automotive fuel cell must withstand load cycling and freeze–thaw environmental swings with an acceptable level of degradation from the beginning-of-lifetime (BOL) performance over a lifetime of 5500 h (equivalent to 165,000 miles at 30 mph). A stationary fuel cell must withstand over 40,000 h of steady operation under vastly changing external temperature conditions. 3. Suitable system power density and specific power must be achieved. The U.S. Department of Energy year 2010 targets for system power density and specific power are 650 W/kg and 650 W/L for automotive (50-kW) applications, 150 W/kg and 170 W/L for auxiliary (5–10-kW peak) applications, and 100 W/kg and 100 W/L for portable (milliwatt to 50-W) power systems [1]. 4. Fuel storage, generation, and delivery technology must be advanced if pure hydrogen is to be used. Hydrogen storage and generation are discussed in Chapter 8. The hydrogen infrastructure and delivery are also addressed in ref. [2]. 5. Desired performance and longevity of system ancillary components must be achieved. New hardware (e.g., efficient transformers and high-volume blowers) must be developed to suit the needs of fuel cell power systems. 6. Sensors and online control systems for fuel cell systems are needed, especially for transient operation, where performance instability can become a major issue. The advantages and disadvantages of particular fuel cell systems are discussed in greater detail throughout this book.

1.2 FUEL CELLS AS ELECTROCHEMICAL ENGINES Fuel Cells versus Heat Engines The first question many people ask is “why are these systems called fuel cell engines?” An engine is a device that converts energy into useful

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Introduction to Fuel Cells Waste heat Heat engine

Thermal energy Power

Same initial chemical energy Power Electrochemical engine Waste heat

Figure 1.3 Conceptual comparison between heat engines and electrochemical engines.

work. While a combustion engine converts the chemical energy of the fuel and oxidizer into mechanical work (i.e., it moves some mass through space), a fuel cell engine converts the same initial chemical energy directly into electrical work (i.e., it moves electrons through a resistance). Thus, fuel cells and batteries can both be considered electrochemical engines. Figure 1.3 shows a conceptual comparison between a heat engine and an electrochemical engine. Both systems utilize a fuel and an oxidizer as reactants. Both systems derive the desired output of useful work from the chemical bond energy released via the oxidation of the fuel. For the same fuel and oxidizer, the overall chemical reaction and the potential energy released by the reaction are identical. At first glance, this fact may not seem obvious. The difference between the heat and electrochemical engines lies in the process of conversion of the enthalpy of reaction1 to useful work. In the heat engine, the fuel and oxidizer react via combustion to generate heat, which is then converted to useful work via some mechanical process. An internal combustion engine in a car is a good example. Combustion expands the gas in the combustion chamber, which moves the pistons and is converted to rotational motion in the drive train. This turns the wheels and propels the vehicle. Conversely, in an electrochemical engine, the same enthalpy of reaction is directly converted into electrical current via an electrochemical oxidation process. The direct conversion of energy from chemical to electrical energy has a profound impact on the maximum theoretical efficiency of electrochemical devices, as we shall see in greater detail in Chapter 2. Before presenting the equations to describe this, a simple thought experiment can be used to demonstrate the increased potential efficiency of a fuel cell compared to a combustion engine. Consider a conventional automobile and a hydrogen polymer electrolyte fuel cell stack, as shown in Figure 1.4. The combustion engine would be too hot to touch during operation without burning one’s hand. The heat given off by the engine to the environment is not used to propel the vehicle and is therefore a waste product of the chemical energy initially available from the reaction. Now, consider a hydrogen fuel cell stack, which operates at around 70–80◦ C, at the same useful power output. The fuel cell would be very warm to the touch but much cooler than the combustion engine. Thus, the waste heat given off as an inefficiency in the fuel cell is less than the combustion engine. A fuel cell is not always more

1 If the reader is unfamiliar with enthalpy of reaction, a review of an undergraduate-level thermodynamics textbook

is suggested.

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1.2

(a)

Fuel Cells as Electrochemical Engines

5

(b)

Figure 1.4 Conceptual comparison of efficiency of fuel cell versus combustion engine. (Fuel cell stack image courtesy of General Motors Corporation.)

efficient than a combustion engine, but it is in many practical cases, as we shall discuss in Chapter 2. Fuel Cells versus Batteries Consider a common battery with stored fuel and oxidizer. When used to power a particular application, the fuel and oxidizer react to generate current, chemical products of the reaction and heat. This continuously depletes the reactants during operation until performance becomes unacceptable. In the simplest analogy possible, a fuel cell is similar to a battery, except with constant flow of oxidizer (commonly air) and fuel (hydrogen, methanol, or other), as shown in Figure 1.5. Imagine creating a fuel cell by drilling holes in a battery to allow a flux of oxidizer and fuel in and products of the reaction out. Instead of having a sealed battery where stored fuel and oxidizer gradually deplete, a fuel cell has constantly flowing reactants and products. In this way, a fuel cell can operate as a true steady-state device. In fact, one can consider a fuel cell as an instantly rechargeable battery. A battery, which derives energy from stored reactants, can never achieve a strict steady-state operation. Unlike a fuel cell, a primary battery is nonrechargeable. A secondary battery is rechargeable, but the process or recharging involves controlled reversal of the electrochemical reactions and takes significantly longer than refilling the flow of oxidizer and fuel in a fuel cell. The difference between a battery and a fuel cell system can also be related to the definitions of a system and control volume taken from basic thermodynamics.2 In a thermodynamic system, no mass flux is permitted to cross the system boundaries (battery), 2 See,

for example, Fundamentals of Engineering Thermodynamics, M. S. Moran and H. N. Shapiro, John Wiley and Sons, 1995.

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Introduction to Fuel Cells

Battery e-

Depleting fuel and oxidizer

(a)

Depleted fuel and products out

Fuel in

Anode Cathode Depleted oxidizer and products out

Oxidizer in Fuel cell

(b)

Figure 1.5

Basic comparison of batteries to fuel cells: (a) battery; (b) fuel cell.

while in a thermodynamic control volume, mass flux is permitted across the boundaries (fuel cell).

1.3

GENERIC FUEL CELL AND STACK Basic Operating Principles Figure 1.6 shows a schematic of a generic fuel cell with components common to most fuel cell types shown. Referring to Figure 1.6, separate liquid- or gas-phase fuel and oxidizer streams enter through flow channels, separated by the electrolyte/electrode assembly. Reactants are transported by diffusion and/or convection to the catalyst layer (electrode), where electrochemical reactions take place to generate current. Some fuel cells have a porous (typical porosity ∼0.6–0.8) contact layer between the electrode and current collecting reactant flow channels that functions to transport electrons and species to and from the electrode surface. In polymer electrolyte fuel cells

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1.3 Generic Fuel Cell and Stack

Figure 1.6

7

Schematic of a generic fuel cell.

(PEFCs) discussed in Chapter 6, an electrically conductive carbon paper or cloth diffusion medium (DM) layer (also called gas diffusion layer, or GDL) serves this purpose, and a DM covers the anode and cathode catalyst layer. At the anode electrode, the electrochemical oxidation of the fuel produces electrons that flow through the bipolar plate (also called cell interconnect) to the external circuit, while the ions generated migrate through the electrolyte to complete the circuit. The electrons in the external circuit drive the load (e.g., electric moter or other device) and return to the cathode catalyst where they recombine with the oxidizer in the cathodic oxidizer reduction reaction (ORR). The products of the fuel cell are thus threefold: (1) chemical products, (2) waste heat, and (3) electrical power. Description of a Fuel Cell Stack A single fuel cell can theoretically achieve whatever current and power are required simply by increasing the size of the active electrode area and reactant flow rates. However, the output voltage of a single fuel cell is limited by the fundamental electrochemical potential of the reacting species involved and is always less than 1 V for realistic operating conditions. Therefore, to achieve a higher voltage and compact design, a fuel cell stack of several individual cells connected in series is utilized. Series-parallel combinations are also utilized in some systems as well. Figure 1.7 is a schematic of a generic planar fuel cell stack assembly without a flow manifold and shows the flow of current through the system. For a stack in series, the total current is proportional to the active electrode area of each cell in the stack and is the same through all cells in series. The total stack voltage is simply the sum of the individual cell voltages. For fuel cells in parallel, the current is additive and the voltage is the same in each cell. For applications that benefit from higher voltage output, such as automotive stacks, over 200 fuel cells in a single stack can be used. Other components necessary for fuel cell system operation include subsystems for fuel and oxidizer delivery, voltage regulation and electronic control, fuel and possibly oxidizer storage, fuel recirculation/consumption, stack temperature control, and system sensing of control parameters. For the PEFC, separate humidification systems are also needed to ensure optimal performance and stability. A battery is often used

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Introduction to Fuel Cells

Figure 1.7 Fuelcell stack in series. The total current is the same in each fuel cell; the voltage is additive for each fuel cell plate in series. Not all stack arrangements are totally in series, however, and a mixed series–parallel arrangement can be used.

to initiate reactant pumps/blowers during start-up. In many fuel cells operating at high temperature, such as a solid oxide fuel cell (SOFC) or molten carbonate fuel cell (MCFC), a preheating system is used to raise cell temperatures during start-up. This can be accomplished with a combustion chamber that burns fuel and oxidizer gases. Figure 1.8 shows a 5-kW hydrogen PEFC developed by United Technologies Corporation (UTC) in the trunk compartment of a BMW 7 series car for use as an auxiliary power unit for electronics and climate control.

Figure 1.8 UTC 5kW Hydrogen PEFC demonstrated in 1999 in the trunk compartment of a BMW 7 series car for use as an auxiliary power unit (APU) to control electronics and climate control. (Image Courtesy of UTC Power Corporation.)

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Classification of Fuel Cells

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In all commercial fuel cells, provision must be made for residual fuel effluent recovery. Fuel utilization is not 100% due to concentration polarization limitation on performance discussed in Chapters 3 and 4, so that unused fuel in the anode exhaust stream is always present and must be actively recycled, utilized, or converted prior to exhaust to the environment. Potential effluent management schemes include the use of recycling pumps, condensers (for liquid fuel), secondary burners, catalytic converters, or dead-end anode designs.

1.4 CLASSIFICATION OF FUEL CELLS A number of fuel cell varieties have been developed to differing degrees, and the most basic nomenclature to describe them is according to the electrolyte material utilized. For instance, a SOFC has a solid ceramic oxide electrolyte and a PEFC has a flexible polymer electrolyte.3 Additional subclassification of fuel cells beyond the basic nomenclature can be assigned in terms of fuel used (e.g., hydrogen PEFC or direct methanol PEFC) or the operating temperature range. Table 1.1 gives the operating temperatures, electrolyte material, and likely applications for the most common types of fuel cells. Each fuel cell variant has certain advantages that engender use for particular applications. Low-temperature fuel cells include alkaline fuel cells (AFCs) and PEFCs. The primary advantages of operating under low temperature include more rapid start-up and higher efficiency.4 However, low-temperature systems generally require more expensive catalysts and much larger heat exchangers to eliminate waste heat due to the low temperature difference with the environment. High-temperature fuel cells (e.g., SOFC, MCFC) have an advantage in raw material (catalyst) cost and the quality and ease of rejection of waste heat. Medium-temperature fuel cells [e.g., phosphoric acid fuel cell (PAFC)] have some of the advantages of both high- and low-temperature classifications. Classification of fuel cells by temperature is becoming more blurred, however, since a current SOFC research focus is lower temperature (<600◦ C) operation to improve start-up time, cost and durability, while a focus of PEFC research has been to increase operation temperature to >120◦ C to improve waste heat rejection and water management. The ideal temperature seems to be around 150–200◦ C which is where the PAFC typically operates. However, the PAFC has its own historical limitations which have hampered enthusiasm for its continued development. Hydrogen PEFC The hydrogen polymer electrolyte fuel cell (H2 PEFC) operates at 20–100◦ C and is envisioned by many as the most viable alternative to heat engines and for battery replacement in automotive, stationary, and portable power applications. It should be noted that in the past, PEFCs have also been referred to as solid polymer electrolyte (SPE) fuel cells and proton exchange or polymer electrolyte membrane (PEM) fuel cells. Following the accepted nomenclature that fuel cell systems are named according to the electrolyte used, the term polymer electrolyte fuel cell (PEFC) is most concise and correct, although the moniker “PEM fuel cell” retains popularity because it has been historically more prevalent and easier to say. Currently, the majority of fuel cell research and development for automotive and stationary applications are on the H2 PEFC. The H2 PEFC 3 An

exception to this nomenclature is biological process based fuel cells, which are identified as biological fuel cells, or microbial fuel cells, regardless to the electrolyte used. 4 This is opposite to the heat engine, where higher operating temperatures bring increased efficiency. More on this interesting trend in Chapter 2.

10

a Modern AFCs < 100◦ C. b Includes direct methanol

30–100

CO, Sulfur, metal ions, peroxide

fuel cell and direct alcohol fuel cells.

Flexible solid perPolymer fluorosulfonic electrolyte acid polymer fuel cellb

Molten alkali metal 600–800 (Li/K or Li/Na) carbonates in porous matrix

Molten carbonate fuel cell

Low-temperature operation, high efficiency, high H2 power density, relatively rapid start-up

CO tolerant, fuel flexible, high-quality waste heat, inexpensive catalyst

CO tolerant, fuel flexible, high-quality waste heat, inexpensive catalyst

Stationary power with cogeneration, continuous-power applications

Stationary power with cogeneration, continuous-power applications

Premium stationary power

Space applications with pure O2 /H2 available

Most Promising Applications

Expensive catalyst, Portable, durability of components automotive, and not yet sufficient, stationary poor-quality waste heat, applications Intolerance to CO, thermal and water manangement

Electrolyte dissolves cathode catalyst, extremely long start-up time, carbon dioxide must be injected to cathode, electrolyte maintenance

Long start-up time, durability under thermal cycling, inactivity of electrolyte below ∼600◦ C

Low power density, expensive, platinum catalyst used, slow start-up, loss of electrolyte

Must run on pure oxygen without CO2 contaminant

Disadvantages

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Sulfur

Sulfur

Yttria (Y2 O2 ) stabilized zirconia (ZrO2 )

Solid oxide fuel cell

1–2% CO tolerant, good-quality waste heat, demonstrated durability

High efficiency, low oxygen readuction reaction losses

Advantages

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600–1000

Sulfur, high levels of CO

Solution of 160–220 phosphoric acid in porous silicon carbide matrix

Phosphoric acid fuel cell

CO2

60–250a

Solution of potassium hydroxide in water

Alkaline fuel cell

Major Poison

Electrolyte Material

Operating Temperature (◦ C)

Fuel Cell Types, Descriptions, and Basic Data

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Table 1.1

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Figure 1.9 UTC Power supplies fuel cell bus powerplants for transit programs in the United States and Europe. The fuel economy of transit buses powered by a UTC Power PureMotionTM fuel cell system is two times better than a diesel-powered bus. Fuel cell-powered buses also emit no harmful tailpipe emissions and operate quietly. (Image Courtesy of UTC Power Corporation.)

is fueled either by pure hydrogen or from a diluted hydrogen mixture generated from a fuel reformation process. A stack power density of greater than 1.3 kW/L is typical. Since the operating temperature is from room temperature to ∼80◦ C, a noble metal platinum catalyst is typically used on the anode and cathode. Figure 1.9 is a picture of a PEFC engine developed by UTC Power for city bus applications. The H2 PEFC has many technical issues that complicate performance and control. Besides issues of manufacturing, ancillary system components, cost, and market acceptance, the main remaining technical challenges for the fuel cell itself include (1) water and heat management, (2) durability, and (3) freeze–thaw cycling and frozen-start capability.

Direct Methanol Fuel Cell The liquid-fed direct methanol fuel cell (DMFC) is generally seen as the most viable alternative to lithium ion batteries in portable applications because DMFC systems require less ancillary equipment and can therefore potentially be more simplified compared to an H2 PEFC. Additionally, the usc of a liquid fuel simplifies storage. The DMFCs can potentially compete favorably with advanced Li ion batteries (which currently power many wireless portable applications) in terms of gravimetric energy density of ∼120–160 Wh/kg and volumetric energy density of ∼230–270 Wh/L. While both H2 PEFCs and DMFCs are strictly PEFCs (both use the same flexible polymer electrolyte), the DMFC feeds a liquid solution of methanol and water to the anode as fuel. The additional complexities of the low-temperature methanol oxidation reaction prevent the DMFC from

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(a)

(b)

Figure 1.10 Photograph of (a) PDA/smart phone concept model and (b) a handheld entertainment system concept model. Both are powered by Mobionő fuel cell technology, which uses a direct methanol fuel cell for power. (Image Courtesy of Mechanical Technology, Inc. (MTI).)

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obtaining the same level of fuel cell power density as the H2 PEFC. Figure 1.10 is a picture of a portable DMFC developed by MTI Micro for hand-held power application. Four main technical issues affecting performance remain: (1) two-phase flow management in the anode and cathode, (2) methanol crossover, (3) poor catalyst activity, and (4) high catalyst loading. While significant progress has been made by various groups to develop optimized catalysts, total noble metal catalyst loading is still on the order of 10 mg/cm2 . Typically a platinum–ruthenium catalyst is utilized on the anode for methanol oxidation, and a platinum catalyst is utilized on the cathode as in the H2 PEFC [3]. The DMFC is discussed in greater detail in Chapter 6. Solid Oxide Fuel Cell The SOFC represents a high-temperature fuel cell system with a solid ceramic electrolyte. The historical operating temperature of SOFC systems is around 800–1000◦ C, although developing technology has demonstrated 500◦ C operation [4], where simplified system sealing and materials solutions are feasible. Due to the elevated operating temperature, the catalysts used are non–noble metal and other inexpensive raw materials. High electrolyte temperature is required to ensure adequate ionic conductivity (of O2− ) in the solid-phase ceramic electrolyte. Operating efficiencies as high as 60% have been attained for a 220-kW cogeneration system [5]. Figure 1.11 is a schematic of the Siemens Westinghouse 100-kW tubular SOFC system. It is interesting to realize that most of the volume of larger fuel cell systems is not in the fuel cell itself but in ancillary components, including fuel processing and power conditioning systems.

Figure 1.11 Siemens 100 kW tubular solid oxide fuel cell and cogeneration system. The system has a peak power of ∼140 kW, typically feeding 109 kW into the local grid and 64 kW of hot water into the local district heating system. at an electrical efficiency of 46% [6]. (Image courtesy Siemens Power Generation.)

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There has been much recent development in the United States on SOFC systems, incubated by the Department of Energy Solid State Energy Conversion Alliance (SECA) program. The 10-year goal of the SECA program (started in the fall of 1999) is to develop 3–10-kw SOFC units at <$400/kW with rated performance achievable over the lifetime of the application with less than 0.1% loss per 500 h operation by 2021 [7]. Besides manufacturing and economic issues, the main technical limitations of the SOFC include achieving a reduced operating temperature, controling start-up time, durability, and proper cell-sealing. The SOFC is discussed in depth in Chapter 7. Molten Carbonate Fuel Cell Molten carbonate fuel cells are commercially available from several companies, including a 250-kW unit from FuelCell Energy in the United States and several other companies in Japan. Some megawatt-sized demonstration units are installed worldwide based on natural gas or coal-based fuel sources which can be internally reformed within the anode of the MCFC. Figure 1.12 shows a picture of a 250-kWe net MCFC developed by FuelCell Energy and installed at Yale University. MCFCs operate at hightemperature (600–700◦ C) with a molten mixture of alkali metal carbonates (e.g., lithium and potassium) or lithium and sodium carbonates retained in a porous ceramic matrix through a delicate balance of gas-phase and capillary pressure forces. Technical details of the MCFC are discussed in detail in Chapter 7. A major advantage of the MCFC is the lack of precious metal catalysts, which greatly reduce the system raw material costs. Original development on the MCFC was mainly funded by the U.S. Army in the 1950s and 1960s.

Figure 1.12 FuelCell Energy’s DFCő 300A 250 kWe net molten carbonate fuel cell system installed at Yale University in Connecticut. (Image courtesy of FuelCell Energy, Inc.)

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The U.S. Army desired operation of power sources from logistic fuel already available, thus requiring high temperatures with internal fuel reformation that can be provided by the MCFC. During this period, significant advances of this liquid electrolyte alternative to the SOFC were made [8]. Development waned somewhat after this early development, but advances have continued and MCFC commercialization has been achieved. The main disadvantages of MCFCs include (1) complex electrolyte management and loss through finite vapor pressure, (2) extremely long start-up time (the MCFC is generally suitable only for continuous power operation), (3) durability, and (4) carbon dioxide injection into the anode is needed to maintain electrolyte stability. Phosphoric Acid Fuel Cell The PAFC was originally developed for commercial application in the 1960s. The PAFC has an acidic, mobile (liquid) electrolyte of high concentration phosphoric acid contained by a porous silicon carbide ceramic matrix and operates at around 160–220◦ C. A 200-kW PAFC array that powers the Verizon call routing center in New York is shown in Figure 1.13. Like the MCFC, the electrolyte is bound by capillary and gas pressure forces between porous electrode structures. The PAFC is in many ways similar to the PEFC, except the acid-based electrolyte is in liquid form and the operating temperature is slightly higher. Over two-hundred 200-kW commercial PAFC units were developed and sold by United Technologies Corporation through several different divisions and subsidiaries, and many are still in operation.

Figure 1.13 The Verizon call routing center in Garden City, New York, is home to the largest U.S. commercial fuel cell installation of its kind. The fuel cells from UTC Power generate 200 kilowatts each, providing a total of 1.4 megawatts of clean power to the center. (Image Courtesy of UTC Power Corporation.)

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However, ubiquitous commercial application has not been achieved, primarily due to the high cost of approximately $4500/kW, about five times greater than cost targets for conventional stationary applications [9]. The main advantages of the PAFC include (1) the high operating temperature allows operation with 1–2% CO in fuel stream, (2) the highly concentrated acid electrolyte does not need water for conductivity, making water management very simple compared to the PEFC, and (3) the demonstrated long life and commercial success for premium stationary power of the PAFC. Besides the high system cost, the main technical disadvantages of the PAFC include (1) a bulky, heavy system compared to PEFC with area-specific power less than half of the PEFC (0.2–0.3 W/cm2 [10], (2) continued use of platinum catalyst with nearly the same loading as PEFCs, (3) the relatively long warm-up time until the electrolyte is conductive at ∼160◦ C (although warm-up time is much less than the MCFC or SOFC), and (4) the liquid electrolyte has finite vapor pressure, resulting in continual loss of electrolyte in the vapor phase. Modern PAFC design includes cooling and condensation zones to mitigate this loss. The PAFC is discussed in greater detail in Chapter 7. Alkaline Fuel Cell Alkaline fuel cells utilize a solution of potassium hydroxide in water as an alkaline, mobile (liquid) electrolyte. Alkaline fuel cells were originally developed as an auxillary power unit APU for space applications by the Soviet Union and the United States in the 1950s and served on the Apollo program as well as the Space Shuttle orbiter. A 12-kW AFC used to provide power and potable water for astronauts in the Space Shuttle orbiter is shown in Figure 1.14. The AFCs were chosen for space applications for their high efficiency and robust operation. The AFC operates around 60–250◦ C with greatly varied design and operating conditions. Modern designs tend to operate at the lower range of temperature and pressure near ambient conditions. The primary advantages of the AFC are the lower cost of materials and electrolyte and high operating efficiency (60% demonstrated for space applications) due to use of an alkaline electrolyte.

Figure 1.14 12-kW fuel cell power plant for the Space Shuttle Orbiter. Three units power the orbiter while in space as well as provide the drinking water for the astronauts. (Image Courtesy of UTC Power Corporation.)

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Potential Fuel Cell Applications and Markets

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For alkaline electrolytes, the oxidizer reduction reaction (ORR) kinetics are more efficient than acid-based electrolytes (e.g., PEFC, PAFC). Many space applications utilize pure oxygen and hydrogen for chemical propulsion, so the AFC was well suited as an APU. However, the alkaline electrolyte suffers an intolerance to even small fractions of carbon dioxide (CO2 ) found in air which react to form potassium carbonate (K2 CO3 ) in the electrolyte, gravely reducing performance over time. For terrestrial applications, CO2 poisoning has limited lifetime of AFC systems to well below that required for commercial application, and filtration of CO2 has proven too expensive for practical use. Due to this limitation, relatively little commercial development of the AFC beyond space applications has been realized. Some recent development of alkaline-based solid polymer electrolytes is underway, however. The AFC is discussed in greater detail in Chapter 7. Other Fuel Cells Many other fuel cell systems exist, and new versions are constantly being developed. Many of these are simply existing fuel cell systems with a different fuel. For example, PEFCs based on a direct alcohol solution offer alternatives to DMFCs for portable power and include those based on formic acid [11], dimethyl ether [12], ethylene glycol, dimethyl oxalate, and other so-called direct alcohol fuel cells (DAFCs) [13, 14]. A completely different concept is the biologically based fuel cell. Biologically based fuel cells use biocatalysts for conversion of chemical to electrical energy and can be classified into two basic categories: (1) microbial fuel cells (MFCs) and (2) enzymebased fuel cells. In the MFC, electricity is generated by anerobic oxidation of organic material by bacteria. The catalytic activity and transport of protons are accomplished using biological enzymes or exogenous mediators [15–17]. Although performance is relatively quite low, on the order of 0.1–1 mA/cm2 , the potential for generating some power, or simply power-neutral decomposition and treatment of domestic waste matter, currently a multibillion-dollar cost to society, is potentially quite significant. The enzyme-based biological fuel cell has significantly greater power density (1–10 mA/cm2 ) than the microbial fuel cell, although power produced is still orders of magnitude lower than a conventional precious metal catalyzed H2 PEFC [17]. However, enzymatic fuel cells have distinct advantages in terms of potential cost and operation at ambient temperature in near-neutral-pH environments. Enzymatic fuel cells are envisioned as implantable power devices in humans or as using environmentally derived fuel from tree saps for long-term remote sensor applications [18]. While biologically based fuel cells are probably the least-developed fuel cell power source, the unique aspects of the catalytic process and potential for natural sugar-based power are intriging. Another potentially interesting application on which this author has pondered is a weight loss fuel cell where blood sugar would be used to power an external fuel cell device, effectively burning calories with no physical exercise required. The feasibility of this concept is further explored in Problem 22.

1.5 POTENTIAL FUEL CELL APPLICATIONS AND MARKETS Fuel cells have the potential to replace existing power sources for many applications. Figures 1.15 and 1.16 show the exponential progression of commercial stationary power fuel cell installations and hydrogen refueling stations worldwide. Although the trends look promising, they currently represent only an infinitesimal fraction of the fueling infrastructure

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Figure 1.15 Commercial large (>10-kW) stationary power fuel cell installations under operation versus year. (Data adapted from Ref. [19].)

required for practical widespread use. Fuel generation, storage, and delivery infrastructure are still major barriers that must be overcome. Hydrogen generation, storage, and delivery are discussed in Chapter 8. Hydrogen infrastructure is a vast and speculative subject, and various summaries can be found [20, 21]. The most likely consumer applications for fuel cells include portable (0–100-W), stationary (0–25-kW), and transportation (∼100-kW) applications. Each market has unique demands that tend to be more suited to a particular type of fuel cell. For portable applications, high system power density and simplicity are desired over efficiency and cost. For stationary applications, durability and high efficiency are higher priorities. For transportation applications, compact size, rapid start-up, robustness, and high efficiency are the primary technical goals.

Figure 1.16 Cumulative worldwide hydrogen fueling stations. Upper bars in 2005 and 2006 are anticipated station installations. (Data adapted from Ref. [22].)

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Potential Fuel Cell Applications and Markets

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Figure 1.17 Toshiba 100 mWe micro direct methanol fuel cell which weighing 8.5 g (0.3 oz) [23]. (Image Courtesy Toshiba Corporation.)

Portable Applications Perhaps where fuel cells show the most promise for ubiquitous near-term implementation is in portable power (0–100-W) applications, such as cell phones and laptop computers. Current battery technology has not yet provided the energy density required for long-term operation, and recharging is time consuming. Additionally, the cost of existing premium power battery systems is already on the same order as contemporary fuel cells, with additional development anticipated. With replaceable fuel cartridges, portable fuel cell systems have the additional advantage of instant and remote rechargeability that can never be matched with secondary battery systems. A hand-held DMFC for portable power developed by Toshiba is planned for production. The 8.5-g DMFC shown in Figure 1.17 is rated at 100 mW continuous power (up to 20 h) and measures 22 mm × 56 mm × 4.5 mm, including a maximum of 9.1 mm for the concentrated methanol fuel tank [24]. As the wireless economy progresses, demand for higher power, smaller, and instantly rechargeable technologies will undoubtedly continue to push forward development of portable fuel cells. Stationary and Distributed Power Applications Stationary (1–500-kW) applications include power units for homes or auxiliary and backup power generation units. Stationary applications are designed for nearly continuous use and therefore must have far greater lifetime than automotive units, although operation at a near-continuous steady state is advantageous for durability. Stationary devices typically range from 1 kW temporary or auxiliary power generator units, examples of which are the Ballard fuel cell generator units shown in Figure 1.18, to 100-kW systems for regular power of buildings. Unlike the portable fuel cell, where ancillary components are reduced as much as possible, the stationary fuel cell system is not similarly constrained, and typically has an array of components to achieve high-efficiency, durable operation. A plot showing the estimated number of demonstration and commercial units in the stationary power category from 1985 to 2002 is given in Figure 1.19. Not surprisingly, the exponential growth in the number of online units follows a similar qualitative trend to the available patents granted for various fuel cell technologies shown in Figure 1.1. The early rise in stationary units in 1997 was primarily a result of PAFC systems sold by United Technologies Corporation, although recently most additional units have been PEFCs from various manufacturers. Data are estimated from the best available compilation

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Figure 1.18 Three generations of Ballard Mark 1030 (1320 W rated power) technology. The Mark 1030 V3 (on left) is 40% lighter and 26% smaller than the previous generation of residential cogeneration fuel cell. (Image courtesy of Ballard Power Systems, Inc.)

available online at www.fuelcells.org, and some manufacturers do not advertise prototype demonstrations, so that the exact numbers in Fig. 1.19 are not precise, but the qualitative trend of explosive growth is clear. Distributed power plants are even larger than stationary systems and are designed for megawatt-level capacity. Several have been demonstrated to date, including, a 2-MW MCFC demonstrated by FuelCell Energy in California [25]. However, as the power is

s

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Figure 1.19 Estimated number of projects initiated to install stationary power sources for 1985– 2002 based on data from [26].

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Potential Fuel Cell Applications and Markets

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scaled up to megawatt levels, the efficiency advantages of fuel cells become less favorable compared to gas turbine based cogeneration units, which has limited development of fuel cells for megawatt distributed applications. Transportation Applications Perhaps the most exciting potential application for fuel cell power is in transportation. The potential for high efficiency with low pollution, and severing the umbilical cord between the oil industry and the world economy is a strong driver toward development of fuel cell vehicles. Even early fuel cell pioneers also dreamed of fuel cell vehicles, and some early prototypes were built, such as the alkaline fuel cell built by Kordesh shown in Figure 1.20. The bottles on the roof of the car are actually laboratory cylinders of hydrogen, an approach that is obviously not recommended for safety but was nevertheless successful. Hundreds of fuel-cell-powered prototype vehicles are now in the testing stage. In 2003, Toyota leased around 20 fuel cell Rav-4 vehicles for ∼ US$10,000 per month. Figure 1.21 shows a prototype fuel cell vehicle built by Hyundai and Kia Motor Company. Although the potential benefits to society are tremendous, fuel cells for transportation applications suffer the most daunting technological hurdles. The existing combustion engine technology market dominance will be difficult to usurp, considering its low comparative cost (∼$30/kW), high durability, high power density, suitability for rapid cold start, and high existing degree of optimization. Additionally, the success of high-efficiency hybrid electric/combustion engine technology adds another rapidly evolving target fuel cells must match. The lack of an existing hydrogen fuel infrastructure and other issues make it highly likely that initial introduction would be in the form of fleet vehicles such as buses, taxi cabs, or postal vehicles. In this case, a single refueling station would be needed, and driving cycles and maintenance could be controlled and measured. In fact, many such demonstration

Figure 1.20 Early 5-kW alkaline fuel cell car built and driven on public roads by K. Kordesch [27]. Tanks on the top are for hydrogen storage. (Reproduced with permission from Ref. [27].)

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Figure 1.21 UTC Power develops proton exchange membrane fuel cell technology for next generation automobiles and works with major automobile manufacturers, including Hyundai. (Image courtesy of UTC Power Corporation.)

projects exist. Fuel cell buses have been in operation in cities such as Vancouver, Canada, and Chicago, Illinois, for several years.

Other Niche Applications Any application requiring electrical power could potentially operate on fuel cells, although not all make practical sense. The military has a need for fuel cells for battery replacement and transportation applications. The heavy weight and cost of primary batteries make fuel cells attractive, even just for training purposes. Replacing some of the nonrechargeable batteries presently used with reusable fuel cells would represent a major reduction in waste. Additionally, the potential for stealth and long life wireless operation is attractive for military reconnaissance and remote-sensing applications. For military transportation, higher efficiency and longer ranges would be a great benefit, as some estimates put the cost of a gallon of fuel delivered to the battlefield at over $100. Regenerative fuel cells are especially suited for space applications, where cargo can cost up to $10,000 per pound to take to space. In a regenerative fuel cell powered by hydrogen and oxygen, the closed fuel cell vessel actually operates as a battery, producing current from stored oxygen and hydrogen when in the power mode. In the power mode, product water is generated from the electrochemical reactions. In the regeneration mode, the water is electrolyzed back into oxygen and hydrogen by reversal of the hydrogen oxidation and oxidizer reduction reactions. Through this cycle, the fuel and oxidizer are continually recycled and reused, reducing the weight of reactants required to be put into orbit for a chosen duty cycle. Of course, the second law of thermodynamics requires more electrical power is input into the electrolysis than is produced by power generating hydrogen oxidation

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1.6 History of Fuel Cell Development

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reaction.5 In regenerative fuel cells for space application, however, the additional input power can come from solar panels, which take advantage of the radiation from the sun.

1.6 HISTORY OF FUEL CELL DEVELOPMENT In 1839, Sir William Grove conducted the first known demonstration of the fuel cell [28]. It operated with separate platinum electrodes in oxygen and hydrogen gas, submerged in a dilute sulfuric acid electrolyte solution, essentially reversing a water electrolysis reaction. Early development of fuel cells focused on use of plentiful coal for fuel, but poisons formed by the coal gasification limited the fuel cell usefulness and lifetime [29]. High-temperature SOFCs began with Nernst’s 1899 demonstration of the still-used yttria-stabilized zirconia solid-state ionic conductor, but significant practical application was not realized [30]. The MCFC was first studied for application as a direct coal fuel cell in the 1930s [31]. In 1933, Sir Francis Bacon began development of an AFC that achieved a short-term power density of 0.66 W/cm2 —high even for today’s standards. However, little additional practical development of fuel cells occurred until the late 1950s, when the space race between the United States and the Soviet Union catalyzed development of fuel cells for auxiliary power applications. Low-temperature PEFCs were first invented by William Grubb at General Electric in 1955 and generated power for NASA’s Gemini space program. However, short operational lifetime and high catalyst loading contributed to a shift to AFCs during the NASA Apollo program, and AFCs still serve as APUs for the Space Shuttle orbiter. After the early space-related applications, development of fuel cells went into relative abeyance until the 1980s, when rising energy costs fueled development. The PAFC built by United Technologies Company (UTC) became the first fuel cell system to reach commercialization in 1991. Although only produced in small quantities of twenty to forty 200-kW units per year, UTC has installed and operated over two hundred forty-five 200-kW units similar to that shown in Figure 1.13 in 19 countries worldwide. As of 2002, these units have successfully logged over five million hours of operation with 95% fleet availability [29]. Led by researchers at Los Alamos National Laboratory in the mid 1980s, resurgent interest in PEFCs was spawned through the development of an electrode assembly technique that enabled an-order-of-magnitude reduction in noble metal catalyst loading [29]. This major breakthrough and ongoing environmental concerns, combined with availability of a non-hydrocarbon-based electrolyte with substantially greater longevity than those used in the Gemini program, instigated a resurrection of research and development of PEFCs that continues today. Research and development toward commercialization of high-temperature fuel cells including MCFC and SOFC systems have also grown considerably since 1980, with a bevy of demonstration units in operation and commercial sales of MCFC systems. Figure 1.22 shows the estimated number of fuel cell systems built for all applications (excluding educational kits) per year. In 2004, the cumulative number of independent power-generating systems topped 11,000, with 10,000 of those units built in the preceding decade. Currently, the PEFC and SOFC are the most promising candidates for conventional power system replacement, with the MCFC also under continued development. The PAFC and AFC have all but ceased development efforts, with the exception of niche applications. Based on the continued market drivers of devinding petroleum resources, environmental 5 If

this were not so, we could make a perpetual-motion device, which is impossible.

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Portable Fuel Cell Systems

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Figure 1.22 Estimated cumulative number of portable fuel cell systems built (excluding educational kits) by year. (Based on data adapted from Ref. [32].)

concerns, and wireless technology needs, it is evident that, despite the lingering technical challenges, continued development of a variety of fuel cell systems will evolve toward implementation in many, but certainly not all, potential applications. In some cases, improvement of existing or other alternative power sources or the exiting technical barriers will ultimately doom ubiquitous application of fuel cells, while some applications are likely to enjoy commercial success.

1.7

SUMMARY The goal of this chapter was to introduce the reader to the wide variety of fuel cell engine technologies available and begin to dissect them in terms of operating parameters, strengths and limitations, and potential applications. The basic nomenclature of fuel cells was introduced, along with the various methods for classification of the various systems under development. Fuel cell implementation in portable, stationary, and transportation applications, is highly likely to occur during this century, although the pace is limited by some technological, safety, and infrastructural hurdles. Some fuel cell systems, such as the PAFC and MCFC, have already made it to the commercialization stage, although not yet on a major scale. Other fuel cell systems were heavily developed in the past but development has been nearly ceased due to certain technical or cost limitations. In the end, fuel cells are not a panacea that will solve every power generation need, but they do have significant potential advantages that engender their long-term implementation in many applications.

APPLICATION STUDY: SOCIOECONOMIC IMPACT OF FUEL CELL IMPLEMENTATION Imagine that fuel cells are implemented on a worldwide basis in consumer automotive vehicles in the next 20 years. On the one hand, the possible elimination of petroleum

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Problems

25

as a primary fuel source seems incredibly attractive: Middle Eastern instability and the growing Chinese and Indian economies threaten to increase oil prices and stifle worldwide economic growth and development. On the other hand, automotive fuel cells would require hydrogen, which is not a readily available resource and must be produced in an energy-intensive process that is still many times more expensive per unit of energy than petroleum. Additionally, the most likely automotive power plant replacement is the PEFC, which requires platinum catalyst. Platinum is a precious metal and ironically less readily available than the petroleum it replaces. The question posed is this: Are the worldwide platinum resources readily available or not? That is, if fuel cells do replace a significant number of automotive combustion engines over the coming years, will the market for platinum be as precarious as the future market for petroleum? The answer to this question is quite complex and varies depending on the source of information. For this assignment, you must investigate the available resources and make some engineering estimates to come to your own conclusion. Answer the following question in a short written report and include the websites and resources you consulted. Do you think replacing 50% of the cars on the road with fuel cells would affect world platinum markets? You will need to estimate the automotive power plants required worldwide, the amount of platinum per fuel cell, the average power of the fuel cell used, and several other things. The point of this exercise is to look beyond the text to find reliable Internet and other resources and use engineering logic to come to a reasonable scientific conclusion. It is likely that not every person will come to the same conclusion, but your conclusion should be justified with reasonable assumptions. Hint: You can use the numbers in Problem 18 to get started.

PROBLEMS Calculation/Short Answer Problems 1.1 Go online and try to find 10 reliable fuel cell information websites. There are good general sites as well as industrial sites with reliable information available. There are also dozens in not hundreds of sites with questionable accuracy. 1.2 Go online and identify companies that currently are developing each fuel cell technology listed in Table 1.1. Which technologies have the most/least current developers? 1.3 Go online to the U.S. Patent and Trade Office and determine how many fuel-cell-related patents were granted for the latest year available. How does it compare to Figure 1.1? 1.4 Describe the differences between a battery and a fuel cell. 1.5 List the relative advantages and disadvantages of the PAFC, SOFC, MCFC, AFC, H2 PEFC, and DMFC. List one potential power application well suited for each type of fuel cell.

1.6 List some potential niche applications for fuel cells. 1.7 Why do you think AFCs have been successfully implemented in space applications? 1.8 Why don’t fuel cell manufacturers simply use one large fuel cell plate to obtain the required power output instead of stacking many fuel cell plates? 1.9 Why would a stack be aligned in series or parallel and what specific advantages can you think of where a combination of series and parallel would be useful? 1.10 Find a market price for hydrogen gas and normalize the energy content compared to the current local price of gasoline. Using octane as an approximation for gasoline energy content, compare the cost per kilojoule of energy of hydrogen to gasoline. What cost per liter of gasoline do you think must be reached before the hydrogen fuel source is economically competitive? 1.11 Estimate the current approximate cost per kilowatt of power from a standard automotive combustion engine.

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(Hint: You can find this information if you do an internet search of “crate engines.”) This is the cost target for fuel cell systems. 1.12 Estimate the current approximate cost per kilowatt of power from a standard laptop computer and cell phone battery. This is the cost target for portable cell systems. 1.13 Estimate the current approximate cost per kilowatt of power from a standard stationary power generator system. This is the cost target for stationary cell systems. 1.14 Estimate the power density of a combustion engine on a volume basis, that is, kilowatts per liter. Compare this to a power density for PEFCs of 1.3 kW/L. 1.15 Make a plot of the volume of gas-phase hydrogen required to contain the equivalent energy in a gallon of gasoline as a function of pressure of 0–10,000 psig. (Hint: Assume the ideal gas law is valid.) 1.16 List the three products of reaction from an operating fuel cell and discuss how each can be utilized in a fuel cell system. 1.17 Consider an automotive application where nominally 300 V is required to operate the electric motors powering the wheels. If the fuel cells operate at an average cell voltage of 0.6 V, 1.1 A/cm2 , how many cells in series will the stack have? If the cells are 300 cm2 active area each, what is the total current out of the stack? If the stack is now arranged with the individual cells in parallel, rather than in series, what is the current and voltage output of the stack? Is there a difference in power output (Pe = IV) of the two designs (parallel vs. series)? Why would we choose one design over the other in a practical application?

Open-Ended Problems 1.18 Consider that, at present, about 0.8 mg/cm2 total of platinum is used to make a hydrogen fuel cell that can operate at around 0.65 W/cm2 . Calculate how much platinum would be needed to replace 50% of the cars on the road in the United States alone with fuel cells. Do you

think this would affect world platinum markets? Note: You will have to go outside the textbook to answer this question as well as make some reasonable estimates to enable calculation. Although it is clear that a great reduction in the precious metal loading of a hydrogen fuel cell would be desirable to achieve ubiquitous implementation, there are differing views about the effect that such a conversion would have. Do you think platinum recycling would be neccessary? 1.19 List some potential power source applications where a fuel cell could potentially replace a battery and discuss the relative advantages and disadvantages of this. Use Table 1.1 to help you decide which fuel cell would be most appropriate for each application. 1.20 List some potential power source applications where a fuel cell could potentially replace a combustion-based power source and discuss the relative advantages and disadvantages of this. Use Table 1.1 to help you decide which fuel cell would be most appropriate for each application. 1.21 For a hydrogen-based economy, a large supply of hydrogen will be needed. There are many ways in which hydrogen generation can be achieved. Do some research and discuss the various potential sources of hydrogen and comment on the advantages and drawbacks of each source. You can start in Chapter 8 of this text, but there are many more resources you can find. 1.22 Consider development of a fuel cell for weight loss. That is, a fuel cell would be attached to the human body and be fueled from the glucose in the bloodstream, effectively burning calories from the user’s blood effortlessly. Consider a current biological glucose-burning fuel cell current density of 5 mA/cm2 at 0.4 V and a fuel cell stack mounted next to the person with 100 cm2 per plate and 3 mm total per plate. Calculate the approximate volume of a weight loss fuel cell stack to burn 500 food calories (e.g., 500,000 thermodynamic calories) in an hour of use. Is this practicals? What current density would make this approach feasible?

REFERENCES 1. U.S. Department of Energy 2003 Multi-Year Research, Development and Demonstration Plan for Fuel Cells, http://www.eere.energy.gov/hydrogenandfuelcells/mypp/pdfs/3.4 fuelcells.pdf. 2. D. Sperling, and J. S. Cannon, The Hydrogen Energy Transition: Moving Toward the Post Petroleum Age in Transportation, Academic, 2004.

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References

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3. J. M¨uller, G. Frank, K. Colbow, and D. Wilkinson, “Transport/Kinetic Limitations and Efficiency Losses,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 847–855. 4. R. Doshi, V. L. Richards, J. D. Carter, X. Wang, and M. Krumpelt, “Development of Solid-Oxide Fuel Cells that Operate at 500◦ C,” J. Electrochem. Soc., Vol. 146, No. 4, pp. 1273–1278, 1999. 5. R. F. Service, “New Tigers in the Fuel Cell Tank,” Science, Vol. 288, pp. 1955–1957, 2000. 6. http://www.siemenswestinghouse.com/en/fuelcells/hybrids/index.cfm. 7. U.S. Department of Energy SECA Program, http://www.netl.doe.gov/seca/, 2006. 8. B. S. Baker, Ed., Hydrocarbon Fuel Cell Technology, Academic, New York, 1965. 9. J. M. King, and H. R. Kunz, “Phosphoric Acid Electrolyte Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 287–300. 10. Fuel Cell Handbook, 5th Ed., EG&G Services Parsons, Science Applications International Corporation, San Diego, CA, 2000. 11. M. Zhao, C. Rice, R. I. Masel, P. Waszczuk, and A. Wieckowski, “Kinetic Study of ElectroOxidation of Formic Acid on Spontaneously-Deposited Pt/Pd Nanoparticles—CO Tolerant Fuel Cell Chemistry,” J. Electrochem. Soc., Vol. 151, No. 1, pp. A131–A136, 2004. 12. M. M. Mench, H. M. Chance, and C. Y. Wang “Dimethyl Ether Polymer Electrolyte Fuel Cells for Portable Applications” J. Electrochem. Soc., Vol. 151, pp. A149–A150, 2004. 13. E. Peled, T. Duvdevani, A. Aharon, and A. Melman, “New Fuels as Alternatives to Methanol for Direct Oxidation Fuel Cells,” Electrochem. Solid-State Lett., Vol. 4, No. 4, pp. A38–A41, 2001. 14. C. Lamy and E. M. Belgsir, “Other Direct-Alcohol Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 323–334. 15. H. Liu, R. Narayanan, and B. Logan, “Production of Electricity during Wastewater Treatment Using a Single Chamber Microbial Fuel Cell,” Environ. Sci. Technol., Vol. 38, pp. 2281–2285, 2004. 16. T. Chen, S. Calabrese Barton, G. Binyamin, Z. Gao, Y. Zhang, H.-H. Kim, and A. Heller, “A Miniature Biofuel Cell,” J. Am. Chem. Soc. Vol. 123, pp. 8630–8631, 2001. 17. E. Katz, A. N. Shipway, and I. Willner, “Biochemcial Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 355–381. 18. S. C. Barton, J. Gallaway, and P. Atanassov, “Enzymatic Biofuel Cells for Implantable and Microscale Devices,” Chem. Rev., Vol. 104, pp. 4867–4886, 2004. 19. A. Baker and K.-A. Adamson, “Fuel Cell Today Market Study: Large Stationary Applications,” www.fuelcelltoday.com, article 1046, accessed September 28, 2005. 20. D. Sperling and J. S. Cannon, The Hydrogen Energy Transition: Cutting Carbon from Transportation, Elsevier, 2004. 21. Committee on Alternatives and Strategies for Future Hydrogen Production and Use Board on Energy and Environmental Systems, Division on Engineering and Physical Sciences, The Hydrogen Economy: Opportunities, Costs, Barriers, and R&D Needs, National Research Council and National Academy of Engineering of the National Academies, The National Academies Press, Washington, DC, 2003. 22. A. Baker, “Fuel Cell Market Survey: Automotive Hydrogen Infrastructure,” http://www .fuelcelltoday.com, article 988, May 25, 2005. 23. Toshiba’s Methanol Fuel Cell, Digital Photography Review, June 24, 2004.

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Introduction to Fuel Cells 24. Toshiba Press Release, June 24, 2004, http://www.toshiba.com/taec/press/dmfc 04 222.shtml. 25. Y. Mugikura, “Stack Materials and Stack Design,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 907–920. 26. www.fuelcells.org, March 2006. 27. M. Cifrain and K. Kordesch, “Hydrogen/Oxygen (Air) Fuel Cells with Alkaline Electrolyte,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, 2003, pp. 267–280. 28. W. R. Grove, On Voltaic Series and Combination of gases by Platinum, Phil. Mag., Vol. 14, pp. 127–130, 1839. 29. M. L. Perry and T. F. Fuller, “A Historical Perspective of Fuel Cell Technology in the 20th Century,” J. Electrochem. Soc., Vol. 149, No. 7, pp. S59–S67, 2002. ¨ 30. W. Nernst, “Uber die elektrolytische Leitung fester K¨orper bei sehr hohen Temperaturen,” Z. Elektrochem., No. 6, pp. 41–43, 1899. 31. E. Baur and J. Tobler, Z. Elektrochem. Angew. Phys. Chem., Vol. 39. p. 180, 1933. 32. A. Baker, D. Jollie, and K.-A. Adamson, “Fuel Cell Today Market Study: Portable Applications,” September 2005, http://www.fuelcelltoday.com, article 1034, accessed September 28, 2005.

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Fuel Cell Engines Matthew M. Mench

2

Copyright © 2008 by John Wiley & Sons, Inc.

Basic Electrochemical Principles The most urgent, long-term security requirement for the United States is to reduce our dependence on imported oil by developing clean, safe, renewable energy systems, and energy conservation programs. —Rear Admiral Eugene Carroll, U.S. Navy, Retired, Deputy Director, Center for Defense Information

2.1 ELECTROCHEMICAL VERSUS CHEMICAL REACTIONS In chemical or power production, we often have a choice of obtaining a desired result by either an electrochemical reaction or a purely chemical reaction. An example is electricity. To generate electrical power, purely chemical combustion of a fuel and oxidizer can be used to generate heat, which is converted into motion (e.g., in a piston), then converted into electrical power through a generator. There is also an option to obtain electrical power directly through an electrochemical reaction of the fuel and oxidizer, which produces current. There are many reasons why one option is chosen over another in practice, including convenience, quality, safety, and cost. Whether chemical or electrochemical, the overall reaction of the same fuel and oxidizer begins with the same chemical energy stored in the bonds of the reactants and releases the same chemical energy per mole of reactant. The difference lies in the form of the chemical energy released. Electrochemical reactions, such as in a battery or fuel cell, provide a direct conversion of chemical energy stored in bonds between atoms into electrical energy (i.e., current and voltage), whereas a chemical reaction converts this chemical energy into heat. Thus, a heat engine is limited in thermal efficiency by the Carnot cycle,1 and an electrochemical reaction engine is not. The thermal efficiency of a Carnot cycle, which is the measure of the maximum thermal efficiency of a chemical reaction heat engine, is ηth,carnot = 1 −

TL TH

(2.1)

1 It

is suggested that the reader consult with an undergraduate thermodynamics textbook if unfamiliar with the Carnot cycle.

29

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Basic Electrochemical Principles

where TL and TH are the heat rejection and heat addition reservoir temperatures, respectively. As a result, when the difference between the ambient and operating temperature is low, heat engines are inefficient. Although an electrochemical reaction engine is not subject to Carnot limitations, it is important to understand that this does not mean the following: (a) An electrochemical reaction has no limits on efficiency (we will discuss this in Chapter 3). (b) An electrochemical reaction always has greater thermodynamic efficiency than its chemical analog. Indeed, depending on the operating conditions, a chemically based cycle can be more efficient than an electrochemically based cycle. Many electrochemical reactions do have the potential to be much more efficient and operate at lower temperatures compared to a chemical reaction. There are many examples where electrochemical processes are more common than mechanical or chemical alternatives, including the following: 1. Chemical or Material Production From the early 1800s to around 1900, aluminum was typically produced through a chemical reduction of aluminum chloride. Aluminum was a rare and expensive material produced this way and was treated as a precious metal. A 2.8-kg pyramid, one of the largest casts of aluminum at the time, was used to cap the Washington Monument in 1884 [1]. The electrochemical route, known as the Hall–Heroult process of 1886, greatly reduced cost and ease of production. The process of recovering aluminum by high-temperature electrolysis of alumina dissolved in a molten salt bath was named after C. M. Hall and P. L. Heroult, who nearly simultaneously patented the process in the United States and France, respectively. Considering the importance of aluminum in aviation, it is doubtful commercial airline travel would be feasible without this electrochemical process for aluminum production. Other important examples of electrochemical production include chlorine, hydrogen, oxygen, and other gas-phase species. 2. Batteries According to a 2005 study, over 70 billion batteries are produced a year with a value of over $38 billion and growing [2]. Although actually small in comparison to aluminum production, this value should continually increase as the need for portable and wireless power grows. 3. Electroplating This important electrolytic process includes not only jewelry and other aesthetic applications but also electrical contacts and coatings for protection from corrosion (Figure 2.1). Electroplating alone was already a $10 billion market in 1991. 4. Sensors and Measurement Devices There are many sensors based on electrochemical reactions. A common example is the thermocouple, which exploits the thermodynamically governed relationship between temperature and voltage between the junction of two dissimilar metals. Other electrochemical-based sensors for physical parameters, species detection, or other uses are common. New developments in electrochemical processes continue to occur at a fast pace, and the field is always expanding. The Electrochemical Society (ECS) is one of the oldest technical societies in America, dating back to 1902. Members of the ECS have included H. H. Dow

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Electrochemical Reaction

31

Figure 2.1 The purification of copper sheets by electrolysis. Pure copper sheets act as the cathode and are spaced between impure copper sheets in an electrolyte bath. The process results in growth of the pure copper sheet. (Image from D. D. Ebbing, General Chemistry, Third Edition, Houghton Mifflin Company, Boston, 1990.)

(Founder of Dow Chemicals), C. M. Hall, and Thomas Edison. The need for electrochemical expertise and development, including fuel cells, will continue for the foreseeable future.

2.2

ELECTROCHEMICAL REACTION As discussed in Chapter 1, when an electrochemical reaction occurs, the overall global reaction and thus the chemical energy difference between the beginning and end states of the reactants and products are identical to the analogous chemical reaction. However, an electrochemical reaction circulates current through a continuous circuit to complete the reaction, while a purely chemical reaction does not. Current is strictly defined as motion of a charged specie and can be in the form of anions (negatively charged species such as O2− ), cations (positively charged species such as H+ ), or negatively charged electrons. An electrochemical reaction also has more requirements than a purely chemical one. Shown in Figure 2.2 is a basic electrochemical reaction cell. For an electrochemical reaction to take place, there are several necessary components: 1. Anode and Cathode Electrode The electrochemical reactions occur on the electrode surfaces. Oxidation occurs at the anode and reduction at the cathode. The reduction reaction is accompanied by the oxidation reaction, and the pair is often referred to as a redox reaction. Electrochemical reduction occurs in a reaction that consumes electrons, reducing the valence state. Electrochemical oxidation results in the loss of electrons and an increase in the valence state.2 2 The

valence state of an element is a measure of the electrons required to reach a filled outer electron shell.

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Basic Electrochemical Principles

Figure 2.2

Basic reaction circuit.

2. Electrolyte The main function of the electrolyte is to conduct ions from one electrode to the other. The electrolyte can be a liquid or a solid, and also serves to physically separate the fuel and the oxidizer and prevent electron short-circuiting between the electrodes. This is fundamentally different from a chemical reaction where the fuel and oxidizer react together. 3. External Connection between Electrodes for Current Flow If this connection is broken, the continuous circulation of current cannot flow and the circuit is open. When all components are in place, a complete circuit is formed, and continuous flowing current of ions and electrons can be maintained under the proper conditions. If any of these components are not present, the circuit is open, and no flow of current will occur. An example of this is a battery sitting on the shelf at a store. Since the system is missing an external connection, there is no continuous reaction. It is important to emphasize that current is not only the flow of electrons in the external connection between electrodes but also the flow of ions from one electrode to the other through the electrolyte and overall, the sum of the charges is conserved in the reaction. Global versus Elementary Reaction An important distinction between reaction steps, which is needed to understand the material presented in the rest of the book, is the concept of a global and elementary reaction. Consider the overall fuel cell reaction: H2 + 12 O2 → H2 O

(2.2)

We know that in a fuel cell the hydrogen and oxygen are separated by the electrolyte, so this reaction cannot possibly occur in one step as shown. This is the global hydrogen–oxygen redox reaction. Next, if we focus on just one electrode, the anode, we also have a global anodic reaction. For example, consider hydrogen oxidation for an acid electrolyte (PAFC and PEFC): H2 → 2H+ + 2e−

(2.3)

This looks very simple, but in reality it is still very unlikely to occur in a single step as shown. Equation (2.3) is the global hydrogen electrochemical oxidation mechanism. The

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Electrochemical Reaction

33

following elementary steps are believed to be mainly responsible for this overall oxidation mechanism in an acid electrolyte: H2 ⇔ 2(H − M)ad

(2.4)

(H − M)ad ⇔ H+ + e−

(2.5)

In these equations, M represents the nonreacting catalyst surface. The first step is the hydrogen dissociative chemisorption step, referred to as the Tafel reaction. In this step, the hydrogen bond is broken and a layer of atomic hydrogen is adsorbed on the catalyst surface. The second reaction step is responsible for the actual charge transfer and current generation and is referred to as the Volmer reaction. As a rule, the intermediate reactions must sum to the overall global mechanism. So even for the simple hydrogen oxidation reaction, there are multiple reaction steps. For the oxygen reduction reaction, the reaction is much more complex, can involve dozens of potential reaction steps, and is still a subject of research. We can, however, summarize the global oxidation and reduction reactions that occur at the anode and cathode of fuel cells with acid or alkaline electrolytes: For acid aqueous electrolytes that transport positive ions through the electrolyte (e.g. PEFC, PAFC): (2.6) Anode global hydrogen oxidation reaction (HOR): H2 → 2H+ + 2e− + − Cathode global oxygen reduction reaction (ORR): O2 + 4H + 4e → 2H2 O (2.7) For alkaline aqueous electrolytes that transport negative ions through the electrolyte (e.g. AFC, MCFC, SOFC): Anode HOR: H2 + 2OH− → 2H2 O + 2e− Cathode ORR: O2 + 2H2 O + 4e− → 4OH−

(2.8) (2.9)

It should be noted that many alternative pathways also exist to describe the oxygen reduction reaction, and more advanced publications should be consulted for current understanding in this evolving area. Conservation of Charge An excess of charge cannot be maintained in equilibrium. Conservation of charge is perhaps more difficult to grasp than conservation of energy or mass, but upon careful consideration, it is just as obvious a physical law. Since electrons and ions that carry current are discrete physical entities, the units of charge carried are also discrete. Consider the independent anodic and cathodic reactions of the fuel cell shown in Eq. (2.10): H2 → 2H+ + 2e−

Anode: Cathode: Overall:

2H+ + 2e− + 12 O2 → H2 O H2 +

1 O 2 2

(2.10)

→ H2 O

Although the anode and cathode reactions are independent, they are clearly coupled to each other by the necessity to balance the overall reaction, so that the electrons produced in the HOR are consumed in the ORR. Note that the overall balanced chemical equation has no stray charged species and is identical to the chemical combustion of hydrogen in air. However, in the electrochemical reaction, the anode oxidation and cathode reduction reactions are separate and produce or consume the charged species that make up the current.

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Basic Electrochemical Principles

When the products of an electrochemical reaction are at a lower chemical energy state than the reactants, the reaction is thermodynamically favorable, and the reaction will generate current, a flow of electrons or ions. Such a reaction is termed galvanic. Thermodynamics, discussed in detail in Chapter 3, can be used to determine if a given electrochemical reaction is thermodynamically favorable but cannot determine the rate of reaction. In fact, even a highly thermodynamically favorable reaction may proceed so slowly that no appreciable current can be detected. Discussion of the determination of rates of reaction described by electrochemical kinetics is given in Chapter 4. A fuel cell, a battery, and corrosion are examples of galvanic electrochemical reactions. Galvanic reactions occur without external input when the proper conditions are met, including all components necessary for the basic circuit shown in Figure 2.2. In comparison, some reactions require energy input to occur, and the products are at a higher chemical energy state than the reactants. Electrical-energy-consuming electrochemical reactions are termed electrolytic. The generation of hydrogen and oxygen by electrolysis of water is an example of an electrolytic process. Many industrial processes are also electrolytic, such as gold plating and production of certain chemicals such as aluminum. As an example, compare the galvanic HOR of a common fuel cell (Eq. 2.2) and the electrolytic water electrolysis reaction: Anode: Cathode: Overall:

OH− → 12 O2 + H2 O + 2e− H2 O + e− → 12 H2 + OH−

(2.11)

H2 O → H2 + 1/2O2

The fact that the galvanic HOR of Eq. (2.2) can be reversed is remarkable but is a typical feature of electrochemical reactions. Consider being able to reverse chemical combustion and produce gasoline from the tailpipe exhaust of an automobile. Of course, the energy required to electrolytically return the product water to its reactant state of hydrogen and oxygen is greater than the chemical energy released in the galvanic process or an unlimited supply of energy would be possible. However, the fact that the products of reaction can be returned to the initial chemical state is utilized in some fuel cell applications. In a reversible fuel cell system, the galvanic reactions of Eq. (2.10) provide power until the fuel and oxidizer are expended. Then, external power is required for the electrolysis of water to generate oxygen and hydrogen through the mechanism shown in Eq. (2.11). Thus, the fuel and oxidizer compartment can be sealed, and no refueling is needed. The reversible fuel cell system is ideal for space applications, where the cost of delivering weight into orbit can reach $5000/kg. During orbit, for example, the reversible fuel cell provides power when solar energy is unavailable, and solar panels provide power to electrolyze water when solar energy is available. A commercially available portable reversible fuel cell demonstration, unit is illustrated in Figure 2.3. A few general conventions are useful to remember considering electrochemical reactions. 1. Current is the flow of charged species through the electrolyte (ions) and through the external circuit (electrons). 2. Current is defined as the flow of positive charge and is thus movement in a direction opposite to the electron flow (although this convention is not universal). 3. For both galvanic and electrolytic reactions, electrons are conducted from the anode, through the external circuit, and to cathode.

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35

Figure 2.3 Reversible fuel cell demonstration kit from Eco Soul of Tustin, California.

4. For both galvanic and electrolytic reactions, oxidation occurs at the anode and reduction occurs at the cathode. Thus, in a hydrogen fuel cell, the hydrogen is being oxidized while the oxygen is being reduced. 5. The sign of the electrode depends on type of cell. For a galvanic reaction, reduction occurs at a higher voltage potential than oxidation and thus the cathode is designated as the positive electrode. For an electrolytic cell, the opposite is true and the anode is the positive electrode. In an automotive battery, the cathode is the positive (+), red-labeled electrode (Figure 2.4).

2.3

SCIENTIFIC UNITS, CONSTANTS, AND BASIC LAWS Although the reader is assumed to have at least a cursory knowledge of basic chemistry and electrical engineering concepts, a summary of some of the most basic relations, constants, and units common to electrochemistry is included to provide an understanding of the physical meaning of the commonly used parameters and allow us to make some basic calculations.

2.3.1

Electrical Charge, Current, Voltage, and Resistance Current and Charge The electricity that powers electric motors, radios, and so on, is really a flow of current. The flow of electrical current through a circuit, powering an electrical motor or other device, is analogous to the flow of water in a pipe, powering a

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Basic Electrochemical Principles

Figure 2.4 Cut-away illustration of car battery. (Adapted from http://www.tiscali.co.uk/reference/ encyclopaedia/hutchinson/m0016566.html.)

water wheel and providing mechanical energy, as depicted in Figure 2.5. The electrical current (I) is the rate of the flow of charged species and is analogous to the mass flow rate of water in the pipe. The total charge passed is analogous to the total mass of fluid passed over a given time:

dm dt = m˙ dt Pipe: Total mass passed = m = dt (2.12)

dc dt = I dt Wire: Total charge passed = q = dt The International System (SI) unit of current (I) is the ampere, named after the French mathematician and physicist Andr´e-Marie Amp`ere (1775–1836) [3]. Note from Figure 2.5 that the electron flow is shown moving in the direction opposite to the current because the direction of current is defined as the flow of positive charge and thus moves in a direction opposite to the negatively charged electron flow (although this convention is not universal). The total electrical charge passed (C) is designated with the SI unit of the coulomb, after the French physicist Charles Augustin Coulomb (1736–1806). A coulomb is the conventional unit of charge passed through the circuit and is equivalent to the total charge passed by the flow of an ampere of electrons in one second: 1 C = 6.28 × 1018 electrons passed = 1 As

(2.13)

Current conductor or water pipe

e

Figure 2.5

I

˙ m

Flow through a pipe or a wire is analogous.

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2.3 Scientific Units, Constants, and Basic Laws

37

Thus, the charge on a single electron is only −1.6 × 10−19 C. Since a coulomb is approximately equal to 6.28 × 1018 elementary charges, one ampere is equivalent to 6.28 × 1018 elementary charges moving through a surface in one second, or 1 C/s. Sometimes, it is more convenient to describe total charge passed in units of amperehour (Ah). While this can seem confusing at first, examining the units reveals it is simply a unit of total charge passed: 1 Ah = (C/s) · h × 3600 s/h = 3600 C

(2.14)

Total energy is often also expressed in a similar fashion. A look at an electric bill or a laptop computer battery will show the measure often used to define total energy as a watt-hour, even though it is really equivalent to a joule. 1 Wh = (1 Jh/s)(3600 s/h) = 3600 J

(2.15)

Voltage A volt (V) is a measure of the potential to do electrical work. Mechanical work is done when a weight is moved through a distance, and electrical work is done when current flows through a resistance. The volt (V) is named after Italian physicist Alessandro Volta (1745–1827), who demonstrated the first electrochemical battery in 1800 [4]. The higher the voltage, the greater the potential there is to do electrical work. Science students are familiar with the joule as the standard SI unit of energy. Voltage potential is derived from the same thermodynamic origin of energy difference between the chemical bonds of the reactants and products. In this context, we can convert to units appropriate for electrochemical work. The volt is defined as the measure of potential to do electrical work: 1 V = 1 J/C

(2.16)

A volt is thus a measure of the work required to conduct one coulomb of charge. The higher the voltage, the higher the potential is available to move this charge. The words potential and volt in fact are often synonymous with one another. Figure 2.6 illustrates a waterfall analogy to help understanding. The potential for the water flowing over the waterfall to do work is proportional to the difference in height between the top and the bottom of the waterfall and the flow rate of the water. The greater the difference in height between the top and the bottom, the more work a hydraulic turbine could extract from the same flow. Similarly, the electrodes in an electrochemical reaction are like the top and the bottom of the waterfall. The potential to convert chemical bond energy into electrical power is proportional to the difference in the potential (voltage) between the electrodes, not the absolute value of the electrodes (imagine if the bottom of the waterfall was only 1 m below the top—not much of a waterfall). The current is of course analogous to the mass flow rate of the water going down the waterfall (a trickle of water is not going to generate much power), and the total charge is analogous to the integration of the mass flow rate over time, or the total mass passed through the waterfall. Just as the mechanical power generated by the turbine scales directly with water flow rate and height of the falls, the electrical power scales directly with current and voltage: Pe = IV = IEcell

(2.17)

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Basic Electrochemical Principles Flow rate over the falls—current Ecathode

Ecell = Ecathode – Eanode

Eanode

Standard reference: standard hydrogen electrode (SHE = 0.0 V)

Figure 2.6

Waterfall analogy to voltage potential. E represents the voltage potential.

Since the voltage of a given reaction is a measure of the potential energy for the reaction, it must be referenced to some standard datum, selected as an arbitrary zero-voltage point. The standard commonly used in electrochemistry is the so-called standard hydrogen electrode (SHE). The SHE is the voltage of a platinum sheet electrode immersed in an aqueous electrolyte solution, with unit H+ ion activity i.e., 1 M concentration in contact with hydrogen gas at 1 atm hydrogen pressure [6]. The SHE is arbitrarily assigned to 0 V. Thus, other electrodes have an oxidation (negative) or reduction (positive) potential relative to the SHE. Since most fuel cells operate on hydrogen, the result is that the anode potential is around 0 V. In practice, the SHE is not always convenient, and many other reference electrodes with easily reproducible potentials have been devised and can be used instead of the SHE. The theoretical electrode voltage can be determined based on thermodynamic considerations, discussed in Chapter 3. The standard electrochemical reduction half-cell reaction series is shown in Table 2.1 and shows the reduction potential of the given half reaction relative to the SHE for the reactions shown. The oxidation potential of the reverse reaction is simply the same value with opposite sign. For a complete cell redox reaction, the standard cell voltage Ecell is simply the sum of the oxidation and reduction potentials: E cell = E anode + E cathode

(2.18)

If positive, the reaction is galvanic. If the cell voltage (Ecell ) is negative, this is the minimum applied voltage required to initiate the electrolytic reaction. As an example, consider a redox couple of the oxidation of zinc and the reduction of hydrogen: Anode (oxidation): Zn → 2e− + Zn2+ Cathode (reduction): 2e− + 2H+ → H2 Overall: Zn + 2H+ → Zn2+ + H2 From Table 2.1, the reduction potential of the zinc reaction is −0.76 V, so that oxidation of zinc relative to the SHE at standard conditions is 0.76 V. The cathode is the SHE, so the

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2.3 Scientific Units, Constants, and Basic Laws Table 2.1

39

Partial Electrochemical Reduction Potential Series at 298◦ C

Half Reaction − Ag+ aq + e → Ags AgBrs + e− → Ags + Br− aq AgCls + e− → Ags + Cl− aq HClOaq + H+ + e− → 12 Cl2,g + H2 Ol − Cu2+ aq + 2e → Cus 2+ − Feaq + 2e → Fes − Fe3+ aq + 3e → Fes + − 2Haq + 2e → H2,g 2H2 Ol + 2e− → H2,g + 2OH− aq − − HO− 2aq + H2 Ol + 2e → 3OHaq + − H2 O2,aq + 2H aq + 2e → 2H2 Ol − K+ aq + e → Ks + Liaq + e− → Lis − Mg2+ aq + 2e → Mgs N2,g + 4H2 Ol + 4e− → 4OH− aq + N2 H4,aq − − N2,g + 5H+ aq + 4e → N2 H5,aq + − NO− 3aq + 4Haq + 3e → NOg + 2H2 Ol + − Naaq + e → Nas − Na2+ aq + 2e → Nis 2+ − Znaq + 2e → Zn − O2,g + 4H+ aq + 4e → 2H2 Ol − + 2e → H2 O2,aq O2,g + 2H+ aq − O2,g + 2H2 Ol + 4e → 4OH− aq − O3,g + 2H+ aq + 2e → O2,g + H2 Ol − Ss + 2H+ aq + 2e → H2 Sg + H2 SO3,aq + 4Haq + 4e− → S(s) +3H2 Ol + − HSO− 4,aq + 4Haq + 2e → H2SO3,aq + H2 Ol

Voltage E◦ (V) +0.799 +0.095 +0.222 +1.63 +0.337 −0.440 +0.771 0.000 −0.830 +0.880 +1.776 −2.925 −3.05 −2.37 −1.16 −0.23 +0.96 −2.71 −0.28 −0.76 +1.23 +0.68 +0.40 +2.07 +0.141 +0.450 +0.170

Source: From [5].

voltage is 0.0 V. Overall, then, the voltage of the cell illustrated in Figure 2.7 at standard conditions is 0.76 V. Individual Electrode Behavior In Figure 2.6, a waterfall is shown to illustrate the voltage potential for the overall reaction. At each electrode, there is an independent half-cell global reaction coupled with the other electrode reaction only through conservation of mass and charge. Just as the potential for work from the waterfall is a result of the difference in location between the top and the bottom, the overall electrochemical cell voltage is a result of the difference in potential between the anodic and cathodic reactions, not the voltage of the individual reactions themselves. Consider a hydrogen-filled cathode and anode from Table 2.1. This electrochemical reaction circuit would have no overall potential for reaction, since there would be no potential difference between the two electrodes. This also illustrates the function of the electrode to separate fuel and oxidizer. If the electrolyte permits passage of reactants through it, they will mix at the electrodes and reduce voltage potential.

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Basic Electrochemical Principles e-

e-

Voltmeter Switch

Zn anode NO3-

H2(g)

Na+

Anode compartment Zn

NO3-

Zn(s)

NO3-

2+

Cathode compartment

Zn 2+ (aq) + 2e

H+

2H+(aq) + 2e-

H2(g)

Figure 2.7 The SHE used to reference a zinc oxidation reaction. (Adapted from Ref. [5].)

In a galvanic reaction, the potential difference between the cathode and the anode is positive, and the anode is at a lower potential compared to the cathode. As discussed, this voltage difference is a measure of the thermodynamic potential for reaction and is related to the chemical energy difference between products and reactants. The majority of fuel cells operate with oxygen in air at the cathode and hydrogen fuel at the anode. Thus, at open-circuit conditions the anode is nearly at SHE conditions and is therefore at around 0 V. The cathode potential is analogous to the top of the waterfall in Figure 2.6. Using Table 2.1, the overall cell voltage is simply the difference in the reduction potential between the cathode and anode: E cell = E cathode,red − E anode,red

(2.19)

There is a minus sign in Eq. (2.19) since both half-cell reactions are taken as reduction reactions whereas Eq. (2.18) uses one reduction and one oxidation reaction. At standard conditions (pure oxygen and hydrogen, 1 atm pressure, and 298 K), we expect an opencircuit cell voltage of 1.23 V. Resistance and Conductance Electrical resistance measured in ohms (), is a measure of the potential loss associated with moving a rate of charge. Put another way, in order to move a given rate of charge through a conductor, some voltage potential is lost. It is important to realize the energy is not lost. Indeed, conservation of energy still applies. Instead, the potential to do electrical work is lost and is dissipated into heat. The greater voltage potential lost per rate of charge passed, the greater the resistance. Resistance can be defined as R = V/A = (J/C)/(C/s) = Js/C2

(2.20)

One joule-second per coulomb squared is defined as one ohm, and its inverse (i.e., 1/) is defined, quite directly, as a mho. A mho is the unit of conductance, also known as a siemen

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2.3 Scientific Units, Constants, and Basic Laws ρ=

RA = Ω-m l

41

A = Cross-sectional area

l = Linear path of ion travel

Figure 2.8 Illustration of current through a wire.

(S). The siemen is named after Werner von Siemens (1816–1892), a German electrical engineer and businessman [7]. Electrical resistance is analogous to flow potential losses in a pipe. A small-diameter pipe has greater resistance to flow than a large-diameter pipe and suffers greater pressure loss per length for a given flow rate. Similarly, a material with high electrical resistance will have greater voltage potential loss per length for a given current. From experience and common sense, we know that fluid flow pressure losses through a pipe are a function of the geometry of the pipe, and the pressure loss is not an intrinsic property of all pipes. Similarly, electrical resistance is not an intrinsic property of a wire. Consider Figure 2.8, which shows a cylindrical wire axially conducting current. The resistance to current (which is physically a measure of the resistance to the flow of electrons) is proportional to the cross-sectional area A and inversely proportional to the length of travel. Obviously, the longer the wire, the greater the loss of voltage potential. An exceptionally thin wire has more electron interaction with the wire surface, leading to increased resistance to flow compared to a larger diameter wire. Resistivity ρ (m) is an intrinsic property of a material because it normalizes the resistance of the material for cross-sectional area (A) and length (l), removing geometric factors: ρ=

RA l

R=ρ

l l = A σA

(2.21)

Some resistivities of common materials are given in Table 2.2. The inverse of resistivity, 1/ρ, is the conductivity σ [(m)−1 ]. Generally, the conductivity of a material is used if the purpose is to conduct charged species, and its resistivity is used if it is an insulating material, although either choice is appropriate. Metals are generally good electron conductors. Gasphase conductivity is negligible except at extreme temperatures where significant gas ionization can occur. Electrolytes are designed to be excellent ionic conductors and poor electron conductors. Dependence of Conductivity on Operational Parameters The conductivity of various substances, and in particular fuel cell materials, can depend strongly on operating parameters. For example, the electron conductivity of solid materials such as graphite and steel decreases with increasing temperature due to increased molecular collision frequency. However, the ionic conductivity of the SOFC and PEFC electrolyte is a positively related function of temperature. In the PEFC, water saturation in the electrolyte also plays a major role. These functional dependencies are highly material specific and are discussed in later chapters.

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Basic Electrochemical Principles Table 2.2

Electrical and Ionic Resistivities of Selected Materials

Electron conductors

Electron Resistivity at 293 K (m)

Gold Aluminum Copper Silver Stainless steel Platinum Ruthenium Palladium Carbon Water (deionized) Polytetrafluoroethylene (Teflon)

2.44 × 10−8 2.28 × 10−8 1.7 × 10−8 1.6 × 10−8 7.2 × 10−7 1.1 × 10−7 7.1 × 10−8 10 × 10−8 3.5 × 10−5a 2.5 × 105 1016 –1017

Ionic Conductors

Ionic Resistivity (m)

Nafion PEFC electrolyte by DuPont, fully humidified SOFC electrolyte Liquid electrolytes

∼10 at 353 K 0.1–1 at 600–1000 K Highly concentration, temperature, and ion dependent

a Dependent

2.3.2

17:26

on direction and molecular structure.

Ohm’s Law Ohm’s law is named after the work of Georg Simon Ohm (1789–1854), a Bavarian mathematician and teacher. The basic form of Ohm’s law can be shown as V = IR

(2.22)

It is important to note that in liquid solutions Ohm’s law is true only for electrolytes without ionic concentration gradients, which may not always be strictly accurate [8, 9], but can be considered to be true for most fuel cell studies. Often, students have difficulty following the units involved in this simple relationship since they are often familiar with only volts, ohms, and amperes. Unit matching and conversion are critical components of any engineering analysis, and electrochemistry is no exception. If one breaks down the units of this relationship into units for energy, power, and so forth, we see that Ohm’s law is dimensionally consistent: V = IR V = A· J/C = (C/s)(Js/C2 ) = J/C

Ok!

Electrical Power Power is the rate of work, whether in mechanical, electrical, thermal, or other form. Electrical power (Pe ) can be expressed as Pe = IV W = (C/s)(J/C) = J/s = W

Ok!

(2.23)

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2.4

Faraday’s Laws: Consumption and Production of Species

43

If the voltage is the fuel cell voltage, the output is the electrical power from the fuel cell. If instead the voltage in Eq. (2.23) is the voltage potential lost due to resistance, the power generated is thermal dissipation. The delineation between electrical power and heat dissipation rate will become clear in future chapters if it is not now. Thus, electrical power has units of watts (J/s), as expected. Ohm’s law can also be substituted into Eq. (2.17) to obtain alternate expressions for electrical power: Pe = IV = I · IR = I 2 R V2 V ·V = Pe = IV = R R

(2.24)

Since it is often the case that mechanical and electrical systems operate in conjunction with one another, it is imperative to be able to convert among the units used for electrical systems and thermo-mechanical systems. Example 2.1 Simple Electrical Calculations A given circuit has a continuous 5 A DC (direct current) and an overall resistance of 10 . Calculate (a) the potential loss, in volts, to maintain steady state; (b) the electrical power dissipated as heat during operation, in watts; and (c) the total heat dissipated in 2 h. SOLUTION (a) Potential loss is found via Ohm’s law for this circuit: V = IR = 50 V. (b) Electrical power dissipated as heat is Ph = IV = 250 W. (c) The total heat dissipated is given as
t Total heat Q =

Ph dt = (250 W)(2 h)[1 (J/s)/W](3600 s/h) = 1800 kJ 0

COMMENT: The resistance shown represents the resistance in a generic electric circuit not a fuel cell.

2.4

FARADAY’S LAWS: CONSUMPTION AND PRODUCTION OF SPECIES In this section we consider a fundamentally important question: How much mass of a given reactant is required to produce a given amount of current? Conversely, how much current is required to produce a certain amount of product? Clearly, the fundamental relationships should be based on conservation of mass and charge. We cannot produce mass from an electrochemical reaction, only rearrange it, and a given amount of reactant can produce a fixed number of charged species, based on the balanced chemical reaction. Consider 1 mol

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Basic Electrochemical Principles

of reactant in a generic electrochemical reaction: ν A A + ν B B → νC C + ν D D

(2.25)

where ν i is the molar (stoichiometric) coefficient required to balance each species i in the reaction equation. Consider the number of electron charges moved through the circuit to react with 1 mol of species A in a one-electron process (e.g., for every mole of A consumed, one electron is moved through the circuit). An example is given for the anodic portion of the silver redox reaction: − Ags → Ag+ aq + e

(2.26)

We know from common experience that the overall silver redox reaction will oxidize (tarnish) silver over time. In this oxidation process, 1 mol of electrons and 1 mol of silver cation is produced per mole of silver reacted. However, not every reaction is a 1 mol–one electron process. Faraday’s constant F represents the charge per mole of equivalent electrons, that is, F=

6.023 × 1023 electrons/mole equivalent = 96,485 C/eq 6.242 × 1018 electrons/C

(2.27)

Faraday’s constant can also be written in terms of ampere-hour: F = 96,485 C/eq = 26.8 Ah/eq 3600 C/Ah

(2.28)

The equivalent electrons (eq) is very important but is commonly omitted. Many electrochemical reactions do not exchange 1 mol of electrons for 1 mol of reactant, as in Eq. (2.26). For example, consider the ORR that occurs at the cathode of many fuel cells: 4e− + 4H+ + O2 → 2H2 O

(2.29)

Here, 4 mol of electrons react per mole of oxygen. In this case, the charge carried per mole of oxygen reacted would be 4F. The scaling factor n is defined as the number of electrons transferred per mole of species of interest. n=

number of electrons = eq/mol mole of species of interest

(2.30)

Thus, the combination of nF is the charge passed per mole of species of interest, and the units of nF are coulombs per mole. Note that the unit “mole” is specific to the chosen species. That is, it is really a mole of the species of interest. The choice of the species of interest makes a difference, and n simply permits determination of the relationship between charge passed and reactant consumption (or product generation) of any species chosen. For example, in Eq. (2.29), n is 4 eq electrons/mol O2 for oxygen consumption. Alternatively, considering water produced as the species of interest, the value of n is 2, and there are 2F coulombs passed per mole of H2 O produced. Now, consider the HOR that occurs at the anode of many fuel cells: H2 → 2e− + 2H+

(2.31)

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Faraday’s Laws: Consumption and Production of Species

45

Here, there are 2F coulombs passed per mole of H2 (n = 2 eq electrons/mol H2 ). Note that it is possible that some purely chemical reactions can also occur in parallel with electrochemical reactions. In this case, the purely chemical component of the reaction must also be known to determine the relationship between charge passed and consumption or generation in the overall multi-reaction process. Faraday’s Laws In the early 1830s, Michael Faraday reported that the quantity of species electrolytically separated was proportional to the total charge passed, establishing a link between the flow of charge and mass [9]. This became the basis for Faraday’s first law of electrolysis: 1. For a specific charge passed, the mass of the products formed are proportional to the electrochemical equivalent weight of the products. Although Faraday’s results were purely experimental, the important implication from this proportional relationship was that electrical current was a result of discrete particles we now understand to be ions and electrons that are conserved as part of an overall balanced reaction equation. This understanding enabled quantification of many electrical phenomena and helped reveal the nature of protons and electrons. In his work, Faraday also discovered that the mass of the product species was directly proportional to the charge passed. This law provides a connection between the charge passed and the mass generated or consumed in a reaction through the balanced electrochemical reaction equations. Faraday’s second law of electrolysis is stated as follows: 2. The amount of product formed or reactant consumed is directly proportional to the charge passed. The second law is the most important for fuel cell study. This result is what we could expect from modern common sense and conservation of mass; the current generated is proportional to the mass reacted or produced: m∝I

(2.32)

Considering a purely electrochemical reaction, with an understanding of the discrete nature of charged particles that carry current, it seems obvious that there is a proportional relationship between charge passed and consumption or production of the involved species. The proportionality is based on the balanced electrochemical reaction equation and can be written as n˙ x =

I iA = nF nF

Let us examine the parameters and units involved: n˙ x = rate of molar consumption or production of species x (mol of x/s) I = current (A) A = superficial electrode area (cm2 ) i = current density, = I /A (A/cm2 ) n = equivalent electrons per mole of reactant x (eq/mol) F = charge carried on one equivalent mole (C/eq)

(2.33)

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Basic Electrochemical Principles

The superficial (or geometric) electrode area A is the active area of the electrode as viewed from above. For a given electrochemical reaction, Eq. [2.33] can be used to determine the amount of reactant consumed to produce a given current and the amount of product formed for a known current. The actual amount of reactant delivered to an electrode can be greater than determined by Faraday’s law but can never be less. The actual amount of product produced in a given reaction will never be greater than predicted. Example 2.2 Faraday’s Law Calculations current output:

Consider a single hydrogen fuel cell at 4 A

Anode oxidation: H2 → 2e− + 2H+ Cathode reduction: 4e− + 4H+ + O2 → 2H2 O Global reaction: H2 + 12 O2 → H2 O (a) What is the molar rate of H2 consumed for the electrochemical reaction? (b) What is the molar rate of O2 consumed for the electrochemical reaction? (c) What is the minimum molar flow rate of air required for the electrochemical reaction? Assume air is a mixture of 21% oxygen and 79% nitrogen by volume. (d) What is the maximum molar flow rate of air delivered for the electrochemical reaction? (e) What is the rate of water generation at the cathode in grams per hour? The molecular weight of water is 18 g/mol. (f) Can the generation rate of water be greater or less than the value predicted in part (e)? SOLUTION (a) Consider the hydrogen as the “reactant of interest,” x in Faraday’s law. Also recall that 1 A = 1 C/s: H2 → 2H+ + 2e− n = 2 electron eq/mol H2 n˙ H2 =

4 C/s iA = = 2.072 × 10−5 mol H2 /s nF (2 e− eq/mol H2 )(96,485 C/eq)

(b) Here, we are looking for the molar oxygen flow rate of oxygen consumed, which is determined from the oxidation–reduction reaction: 2H+ + 2e− + 12 O2 → H2 O n = 4 electron eq/mol O2 n˙ O2 =

4 C/s iA = = 1.036 × 10−5 mol O2 /s − nF (4 e eq/mol O2 )(96,485 C/eq)

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Faraday’s Laws: Consumption and Production of Species

47

(c) Now we are concerned with determination of the minimum required molar flow rate of air, which contains 79% nitrogen. The only required reactant here is oxygen, and the molar flow rate of oxygen required was solved in part (b). To achieve the same flow rate of oxygen in air, we simply must divide by the mole fraction of reactant (oxygen) in the air mixture. Note that nitrogen flow is inert here and simply “goes along for the ride”: 4 C/s iA n˙ O2 = n˙ air = = = 4.94 × 10−5 mol O2 /s − 0.21 nF (0.21 × 4 e eq/mol O2 )(96,485 C/eq (d) There is no maximum of reactant supplied. The amount of reactant supplied is governed by, for example, the pumps and blowers that make up the system. Faraday’s law only imposes a minimum amount of mass required to generate a given current. (e) Here, we are to determine the rate of water generation in grams per hours, which will require some minor unit conversion. The first step is to solve for the molar rate of water generation, which occurs at the cathode: 2H+ + 2e− + 12 O2 → H2 O n = 2 electron eq/mol H2 O n˙ H2 O =

4 C/s iA = (96,485 C/eq) = 2.072 × 10−5 mol H2 O/s nF (2 e− eq/mol H2 O)

Now simply convert to the appropriate units using the molecular weight: 4 C/s iA × MW = (18 g/mol)(3600 s/h) nF (2 e− eq/mol H2 O)(96,485 C/eq) = 1.34 gH2 O /h

m˙ H2 O =

(f) The value for water produced cannot be greater for a given current, since this would violate conservation of mass. Normally, the products cannot be less than that predicted either, unless another electrochemical reaction (called a side reaction) takes place that consumes some of the charge passed. COMMENTS: Notice the small numbers when units of moles per second are used. Be sure to keep enough significant digits. Also note from part (e) that a hydrogen fuel cell is also a water generator. The water produced must be removed from the fuel cell to allow reactant to reach the catalyst layer. In high-temperature systems, the water product is vapor, while lower temperature fuel cell systems can produce liquid effluent, which complicates design. Example 2.3 Fuel Cell Stack Calculations Consider a 20-cell stack operating steadily in series with 100 cm2 active area per electrode, with a current density of 0.8 A/cm2 . The fuel cell nominal voltage is 0.6 V per plate. (a) Determine the water production in grams per hour for this stack. (b) Determine the stack voltage and electrical power output. SOLUTION (a) This example is quite similar to the previous one, but with an additional complication that this is now a stack of fuel cells. Since they are in series, each fuel cell

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Basic Electrochemical Principles

produces the same total current (0.8 A/cm2 × 100 cm2 = 80 A), and thus the total water produced is simply 20 times the rate of water generation of an individual fuel cell in the stack. Consider the ORR at the cathode: 4e− + 4H+ + O2 → 2H2 O For water production, n = 2 electron eq/mol H2 O (0.8 C/s · cm2 100 cm2 ) iA n˙ H2 O = = = 4.15 × 10−4 mol H2 O/s per fuel cell nF (2 e− eq/mol H2 O)(96,485 C/eq) Now simply scale for the entire stack and to the appropriate units using the molecular weight and number of plates in series: iA · MW nF = (20 cells)(4.15 × 10−4 mol H2 O/s per fuel cell)(18 g/mol)(3600 s/h)

m˙ H2 O,stack = 20

= 538 g H2 O/ h per stack (b) Since the plates are in series, the stack voltage is 20 cells × 0.6 V per fuel cell = 12 V per stack The cells are all in series and therefore all carry the same current of 80 A. The stack electric power is simply Pe = IV, or 960 W. COMMENTS: This works out to be about 538 cm3 of water per hour. Larger fuel cell engines have a significant amount of water production to manage. Consider that an automotive fuel cell engine should be on the order of 100 kW, and about 932 kg (around 2 lb) of water per minute would be produced! Much of this leaves the system as vapor, however.

2.5

MEASURES OF REACTANT UTILIZATION EFFICIENCY There are various metrics utilized to quantify the efficiency of different aspects of an electrochemical reaction. One type of efficiency for a purely electrochemical reaction is based on species consumption. For a galvanic process, there will be a minimum amount of reactant required for a given reaction, as calculated by Faraday’s law, Eq. [2.33]. In practice, we are not constrained to provide exactly the minimum amount of reactant. For a given current, there is a calculated minimum amount of reactant, but there is no maximum. The actual flow rate of reactants is a function of the pumps and blowers that are used for reactant delivery. Obviously, the more flow delivered, the higher the parasitic power required, so we generally seek to deliver something close to the minimum requirement. The Faradic efficiency is a measure of the percent utilization of reactant in a galvanic process: εf =

theoretical required rate of reactant supplied actual rate of reactant supplied

(2.34)

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2.5

Measures of Reactant Utilization Efficiency

49

Faradic efficiency is often called the fuel utilization efficiency (µf ) when applied to the fuel in a galvanic redox reaction: µf =

theoretical required rate of fuel supplied actual rate of fuel supplied

(2.35)

For an electrolytic process, some side reactions and inefficiencies may occur and result in less than complete conversion. The current efficiency is defined as: εc =

actual rate of species reacted or produced theoretical rate of species reacted or produced

(2.36)

Stoichiometric Ratio In fuel cell parlance, the term stoichiometry is defined as the inverse of the Faradic efficiency. Students may be confused with this terminology, since the stoichiometric condition typically describes a balanced chemical reaction equation with no excess oxidizer. Here, the term stoichiometry is used slightly differently, and its meaning is similar to the definition of equivalence ratio used in combustion. Unlike chemical reactions, the reduction and oxidation reactions are separated by electrolyte, so each electrode can have a discrete stoichiometry: The cathodic stoichiometry is defined as: λc =

1 actual rate of oxidizer delivered to cathode = ε f,c theoretical rate of oxidizer required

(2.37)

The anodic stoichiometry is defined as: λa =

1 actual rate of fuel delivered to anode = ε f,a theoretical rate of fuel required

(2.38)

To avoid confusion the reader should be aware that other symbols for stoichiometry, besides λ, are commonly used in the literature, including ζ and ξ . The theoretical rate of reactant required is calculated by Faraday’s law, and the actual rate of reactant delivered is a function of the fuel or oxidizer delivery system. One important point is worth mentioning: Fuel cells must always have an anode and cathode stoichiometry greater than 1. For a value less than unity, the current specified could not be produced. For reasons explained in Chapter 4, a stoichiometry of exactly 1 is not possible either, so that a Faradic efficiency of 100% is not possible on the anode or cathode for a single pass of reactant.3 Example 2.4 Stoichiometry and Utilization Consider a portable 20 cm2 active area fuel cell operating steadily at 0.75 V, 0.6 A/cm2 . The fuel utilization efficiency is 50%, and the cathode stoichiometry is 2.3. The fuel cell is expected to run for three days before being recharged. The cathode operates on ambient air, and the anode runs off of compressed hydrogen gas. (a) Determine the volume of the hydrogen fuel tank required if it is stored as a compressed gas at 200 atm (20.26 MPa), 298 K. (b) How large would a pure oxygen container be if it was used to provide the oxidizer? Consider 200 atm (20.26 MPa) storage pressure and 298 K average ambient temperature. 3 Fuel

recirculators can be used to increase the effective faradic efficiency to 100%, but we are talking about a single pass of reactant through the fuel cell here.

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Basic Electrochemical Principles

SOLUTION (a) First we need to solve for the total hydrogen required to provide three days of power: From Faraday’s law for the anode on pure hydrogen n˙ H2 = λa

iA (0.6A/cm2 )(20 cm2 ) = 2× nF (2 e− eq)/mol H2 )(96,485 C/eq) × (3600 s/h)(24 h/day)(3 days) = 32.25 mol H2 consumed

(32.25 mol)(2 g mol) = 64.5 g H2 From the ideal gas law PV = m

Ru T MW

For the hydrogen V=

mRu T · MW P

(64.5 g)[8.314 J/(mol · K)] = 2 g/mol



298 K 20,260,000 Pa

 = 0.0039 m3 = 3.9 L

(b) Following along the same methodology for the cathode side, (0.6 A/cm2 )(20 cm2 ) iA = 2.3 × nF (4 e− eq/mol O2 )(96,485 C/eq) ×(3600 s/h)(24 h/day)(3 day) = 18.51 mol O2 consumed (18.51 mol)(32 g/mol) = 592.2 g O2   298 K m Ru T (592.2 g)[8.314 J/(mol · K)] V = = MW P 32 g/mol 20,260,000 Pa n˙ O2 = λc

= 0.002265 m3 = 2.27 L COMMENTS: Note these results are for a very low power (9-W) system. Around 10–20 W is needed for many portable applications, so the storage volume would greatly increase. Three days of power without a recharge in a portable device is quite difficult to achieve. Storage volume could be improved with increased performance, higher pressure storage fuel recirculation, or alternate storage techniques, such as use of liquid fuel.

2.6

THE GENERIC FUEL CELL Now that the basics of electrochemical reactions are known, we can begin discussion of basic fuel cell operation. A generic fuel cell is shown in Figure 2.9 with regions labeled A to H. Each variety of fuel cell has unique materials, structure, and design features, but at a basic level, all can be reduced to this generic design. Note that the basic components are the same as shown in Figure 2.9. To reduce ionic and electronic resistive losses and increase power density, the components in a fuel cell are designed to have the smallest possible path length for ions and electrons.

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Figure 2.9 Generic fuel cell.

For a single cell, component A in Figure 2.9 is known as the anodic current collector when the flow is a fuel. In a normal stack arrangement, where the anode current collector is also the cathode current collector on the opposing side, this is also known as a bipolar plate or cell interconnect, since it connects the anode and cathode of adjacent cells in series. The current collector functions as follows: 1. Conducts electrons from anode B to the external circuit or to the adjacent cathode in a stack. 2. Delivers fuel (liquid or gas) flow through the flow channels labeled “B”. The fuel diffuses or convects4 to the anode electrode C, where fuel oxidation occurs. 3. Provides structural integrity of stack (in most, but not all, designs). 4. Dissipate waste heat generated by inefficiencies of the reaction to constant, often with a coolant flow through the current collector. Current collector materials for fuel cell stacks of all varieties must satisfy the following requirements: 1. 2. 3. 4. 5. 6. 7.

Lightweight, compact and highly robust. Low-cost raw material and manufacturing process. High electrical conductivity over the expected lifetime of operation. High corrosion resistance in oxidizing and reducing environments. Impermeability to fuel and oxidant flow. No disintegration of material or electrical degradation over lifetime of operation. Suitable thermal expansion properties, which is more of a concern for higher temperature fuel cells. 8. Capable of proper sealing of reactant flow to prevent leakage. This is often accomplished with gaskets around the periphery to the cell plate.

4 Diffusion

and convection are specific modes of mass transport. If the reader is unfamiliar with these, a quick survey of Chapter 5 or an undergraduate mass transfer textbook is recommended for review.

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Figure 2.10

Examples of various flow field designs. (Images courtesy of Soowhan Kim.)

Current collector material and manufacturing engineering are active areas of research and development. Presently, a variety of materials are used for bipolar plates in fuel cell stacks. Specially coated metals, graphite, and doped polymers have been used for low-temperature fuel cells. High-temperature fuel cells have primarily utilized ceramics for this purpose. Component B in Figure 2.9 is known as the anodic flow field, or fuel flow field. It is typically machined or formed directly in the current collector plate, although it can also be a discrete part. The anode flow field main functions are to 1. facilitate transport of fuel to the anode and 2. facilitate removal of products of reaction. For each variety of fuel cell, many different configurations for the flow fields have been used to optimize heat and mass transfer, current collection, and so on. Because of the highly coupled interaction between heat, mass, and electrochemical phenomena involved, flow field design is not a straightforward matter. Basic flow field patterns include a simple serpentine arrangement, a parallel arrangement, a parallel serpentine combination, and others, as shown in Figure 2.10. A great deal of the engineering at the individual cell level is based on obtaining the best possible flow field design to balance reactant and heat transport, product removal, pressure drop, and machinability. Each design has particular advantages and limitations that will be discussed in detail in later portions of this text. Component C in Figure 2.9 is the anode electrode. The anode contains a thin region of catalyst that greatly facilitates the electrochemical reaction. This region is often referred to as the catalyst layer, although the region is much more complex than this name implies. The anode is the location of the fuel oxidation reaction. The basic functions of the anode catalyst layer are to 1. 2. 3. 4.

Enable the fuel oxidation reaction via a catalyst. Conduct ions from the reaction site to the electrolyte region D. Conduct electrons from the reaction site to the anode current collector A. Facilitate reactant transport and product removal to and from the catalyst locations.

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Figure 2.11

53

Transmission electron micrograph of PEFC catalyst layer [10].

Notice that the catalyst layer must have high electrical and ionic conductivity. The catalyst enables the electrochemical reaction by providing a facilitated reaction site, and the fuel is said to be “galvanically burned” at the anode. The catalyst layer is typically quite thin but is porous and three-dimensional in nature, and is the only interface with reactant, catalyst, and ion and electron conductors that enables a reaction. Consider a microscopic view of the anode catalyst layer, labeled in Figure 2.9 as D and shown in Figure 2.11. As discussed, both the anode and the cathode (labeled F) must have a high degree of mixed ionic and electronic conductivity and porosity. To achieve this, the catalyst layers are a highly three-dimensional porous structure consisting of the catalyst, electrolyte, electron conductor, and voids for reactant transport. Note the high relative porosity of this layer, typically around 40 to 70% for most fuel cells. The reaction in this highly porous structure depends on the simultaneous presence of reactant, catalyst, an ionic conductor with a continuous path to the main electrolyte, and an electronic conductor with a continuous path to the current collector. This is shown schematically in Figure 2.12. Although we conveniently use the geometric, or planform,5 area of the electrode as the superficial active area of the electrode for calculation of current density, the true active area of the porous electrode available for reaction can be orders of magnitude larger due to the three dimensional nature of the surface. Traditionally, the highly porous nature of the electrodes is to maximize the concept of a triple-phase boundary where reaction can occur between (1) the open pore for the reactant, (2) the catalyst, and (3) the ionic conductor. Increasing the triple-phase boundary (TPB) within the porous electrode structure leads to increased reaction site density for a given superficial electrode area and therefore results in a higher performance electrode. In some solid-phase electrode systems, the TPB concept is directly applicable, but in many systems such as the PEFC, the concept of the TPB is not strictly accurate, because there is actually 5 The

planform (geometric) area is the above view area.

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Figure 2.12 The simultaneous presence of reactant, catalyst, an ionic conductor with a continuous path to the main electrolyte, and a continuous path of electrical conductivity is needed or a reaction will not take place at a catalyst site. A catalyst rendered inactive by these situations is called an “orphan” catalyst.

a thin film of electrolyte coating the catalyst structure that has a limited permeability to the reactant. Thus, reaction can occur below the thin-film surface and is not strictly limited to TPB locations. Nevertheless, the heuristic concept of a TPB is useful to understand the engineering trade-offs in an electrode. If there is too little catalyst, or too much catalyst isolated from the reactant (orphan catalyst), or insufficient pathways for ion or electron transport exists, not enough reaction sites will be active and performance will suffer. If the porosity is too low or the electrode is too thick, the reactant will not be as available and performance will also suffer. Major losses in the catalyst layer can occur from lack of electrical or ionic conductivity. Based on the parallel needs of high porosity and mixed ionic and electronic conductivity, it is easy to understand that the catalyst structure is highly complex, and there is a tenuous balance between the various phase distributions. Although the structure is microscopic in nature, because the catalyst layer is typically manufactured using macroscopic methods, such as tape casting, spray coating, or painting, there can be a high number of orphan catalysts. Proper catalyst selection is critical for optimal fuel cell performance. Low-temperature fuel cells typically must utilize expensive noble metal catalysts such as platinum, which has been an historical barrier in terms of cost. Since higher temperatures more readily enable electrochemical reaction, less expensive catalysts such as nickel can be utilized for high-temperature fuel cells such as the SOFC or MCFC. Consider a reaction coordinate plane for a given galvanic electrochemical reaction shown in Figure 2.13. Even though the overall reaction is galvanic and will release electrical energy in going from reactants to products, in order to proceed from an equilibrium state of reactants to another equilibrium state of products, some activation energy is required to initiate a significant reaction. This is somewhat similar to a purely chemical combustion reaction, where an ignition source is needed to initiate an exothermic reaction from an initial nonreacting state. For an electrochemical reaction, this activation energy

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Activation energy Energy

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Path with better catalyst

Energy released

Total exothermic release available for work (electrical or chemical)

Stage of reaction

Figure 2.13

Reaction plane for effective and ineffective catalysts.

lost is in the form of lost voltage potential. The more effective the catalyst, the lower the activation energy barrier for reaction and the lower the voltage penalty. This activation polarization loss is discussed in detail in Chapter 4. For now, consider this barrier as a measure of the quality of the electrode structure and materials in the promotion of the desired reaction. The catalyst layer must have a high degree of mixed conductivity for both electrons and ions as well as a highly porous structure to promote reactant and product transport. Ionic conduction in the catalyst layer is typically provided by addition of electrolyte in the catalyst layer. This enables transport of ions through the catalyst layer to the main electrolyte structure and to the opposing electrode. Without this ionically conductive material in the catalyst layer, the circuit would not be complete. Concomitantly, if there were nothing in the catalyst layer that conducted electrons, electron flow from the reaction site to the current collector would not be possible. Electron conductivity is generally through catalyst and other supporting materials. Several varieties of fuel cells use an electron-conducting porous DM as an interface between the catalyst layer and the current collectors. This DM is not shown in Figure 2.9, since it is not a universal feature of all fuel cells. For example, PEFCs use a carbon-based porous media for this purpose, as shown in Figure 2.14. Either a woven carbon cloth or a carbon fiber structure bonded with a graphitized thermoset resin is typically used for this purpose. Alkaline fuel cells also use a similar porous media to aid electron conduction between the porous electrodes and current collectors. The electrolyte in a fuel cell (E in Figure 2.9) has three main purposes: 1. To physically separate the reactants. 2. To conduct the charge carrying ions from one electrode to the other. 3. To prevent electronic conduction between the anode and cathode. The first purpose is unique to electrochemical reactions. The separation of reactants produces a thermodynamic activity difference between the anode and cathode that results in the voltage potential difference. If there was air on both the anode and the cathode, there would be no potential for reaction and no voltage difference between the two electrodes.

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Figure 2.14 Close-up scanning electron microscope images of (a) woven carbon cloth and (b) nonwoven carbon paper bound with graphitized thermoset resin diffusion media used in PEFCs.

The second purpose is obvious but also includes a high resistance to flow of electrons. From the basic circuit schematic of Figure 2.2, the electrolyte completes the flow of current by conducting ions. However, the electrolyte must also be a strong electron insulator, or the effect would be to short circuit the flow of electrons to the eternal circuit. The cathode catalyst layer (F in Figure 2.9) is essentially the same function and purpose as the anode catalyst layer; however the catalyst type and loading may be different than that of the anode, as it is designed to promote the ORR. Additionally, the cathode flow field and current collector, G and H, respectively, serve the same function on the cathode as the anode, although the design may be different from that of the anode for a variety of reasons discussed later in this text.

2.7

SUMMARY The purpose of this chapter was to introduce the reader to the basics of electrochemical reactions, provide a physical understanding of the basic parameters used in electrochemistry, and introduce the general operation of a fuel cell. Future chapters will use this groundwork to expand fundamental understanding and investigate the basic trade-offs in engineering design. For an electrochemical reaction to take place, there must be an anode, a cathode, an electrolyte, and an external connection. Reactions producing and consuming electrical

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2.7

Summary

57

energy are termed galvanic and electrolytic, respectively. Electrochemical reduction occurs in a reaction that consumes electrons and electrochemical oxidation results in loss of electrons from the reactant. The electrical current is the rate of the flow of charged species. The total electrical charge passed is designated with the SI unit of coulomb. The volt is defined as the work required to conduct one coulomb of charge. Electrical resistance, measured in ohms, is a measure of the potential losses associated with moving a rate of charge, and is not an intrinsic material property. Resistivity ρ and its inverse, conductivity, are intrinsic properties of a material: ρ=

1 RA = l σ

Current, voltage, and resistance can be related through Ohm’s law in the absence of significant concentration gradients: V = IR Electrical power can be expressed as Pe = IV Faraday’s constant F represents the charge per mole of equivalent electrons: F=

6.023 × 1023 electrons/mol eq = 96,485 C/eq 6.242 × 1018 electrons/C

The scaling factor n is defined as the number of electrons transferred per mole of species of interest: n=

number of electrons eq = mole of species of interest mol

Thus, the combination of nF is the charge passed per mole of specie of interest, and the units of nF are coulombs per mole. Faraday’s second law of electrolysis can be written as n˙ x =

I iA = nF nF

The Faradic efficiency is a measure of the percent utilization of reactant in a galvanic process εf =

theoretical required rate of reactant supplied actual rate of reactant supplied

Faradic efficiency is often called the fuel utilization efficiency (µf ) when applied to the fuel in a galvanic redox reaction. The anode and cathode stoichiometries are defined as follows: λc =

actual rate of oxidizer delivered to cathode theoretical rate of oxidizer required

λa =

actual rate of fuel delivered to anode theoretical rate of fuel required

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In this chapter, the basic components, requirements, and functions of a generic fuel cell were also discussed. The reader should be familiar with the functions of the current collectors (also known as a bipolar plate or cell interconnect), the flow fields, the anodic and cathode electrodes with the concept of the triple-phase boundary, and the electrolyte. The reader should also understand the flow of current (ionic and electronic) through these components.

APPLICATION STUDY: DESIGN OF FUEL CELL WITH STORAGE TANKS AND TYPICAL MATERIAL/PERFORMANCE PROPERTIES In this assignment, you will design and compare various fuel storage systems for an automotive fuel cell application. Assume you need 7 kg of hydrogen onboard to achieve the desired range. There are several options to store hydrogen, including: 1. 2. 3. 4.

Liquefied hydrogen Compressed gas-phase hydrogen Stored as methanol in liquid form and reformed into hydrogen on-board Stored in a metal hydride and released via heat addition

Find reliable sources online or in print and perform a feasibility study of the four options listed above. Discuss in your report: 1. The volume and weight of the storage tanks required 2. The advantages and disadvantages of each design 3. How refueling would be accomplished in each option Include the Internet resources consulted and copies of any reports or articles used in preparation. Note that hydrogen storage is also discussed in Chapter 8.

PROBLEMS Calculation/Short Answer Problems 2.1 Define the units of the following in terms of the most basic SI units: (a) Volt (b) Ampere (c) Ohm (d) Faraday’s constant (e) n (as in iA/nF) 2.2 Determine the theoretical open-circuit voltage of the following fuel cells and determine which reactant would be the oxidizer and which would be the fuel for a galvanic reaction. (a) Oxygen and hydrogen gas (b) Lithium and oxygen gas (c) Magnesium and oxygen gas

2.3 Determine the minimum theoretical open circuit voltage that would be required to generate hydrogen peroxide, H2 O2 , with hydrogen gas and air. 2.4 Besides the desired hydrogen oxidation and oxygen reduction reactions, there are several other potential reactions listed in Table 2.1 that can occur in a hydrogen/air fuel cell stack (e.g., they only involve atomic hydrogen, oxygen, and nitrogen species). List the potential reactions; then determine the theoretical voltage for these reactions and decide if they could occur in a fuel cell or not. Could any of these reactions occur normally? Note, the species besides H2 , O2 , N2 , and H2 O must be generated and balanced by the overall reaction, so you will have to combine some reactions to achieve this. Using your results, explain why the hydrogen oxidation and oxygen reduction reaction is in fact the

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reaction that occurs, rather than other reactions along the same potential series.

and a hydrogen flow rate through the stack of 0.2 g/s of hydrogen.

2.5 Demonstrate how Ohm’s law is consistent in units; for example, show V = IR is self-consistent in terms of units.

2.11 We desire a fuel utilization efficiency of >95% on the anode of a 300-plate, 100-cm2 -active-area stack. Determine the hydrogen mass flow rate required in the stack as a function of current density.

2.6 Consider a 10-plate fuel cell stack at an anode stoichiometry of 1.2 with 20 A current generated in the stack and a stack voltage of 6.0 V. As an engineer, you have a choice to install a recirculation pump to recycle the unused hydrogen from the anode exhaust back into the anode to increase the effective fuel utilization to 100%. However, the pump required 60 W of parasitic power to operate continuously. Is installation of the pump justified? Explain. At what value of parasitic power does the addition of the pump become unjustified? 2.7 Consider a 300-plate fuel cell stack with 150 cm2 active area per plate: (a) For an anode and a cathode stoichiometry of 1.4 and 2.5, respectively, determine the mass flow rate of hydrogen and air into the fuel cell per ampere of current. (b) If the nominal operating point is an average of 0.6 V per plate with 1.2 A/cm2 , determine the stack voltage and electrical power output. (c) How much total electrical work at 0.6 V per plate could be performed with a storage tank containing 5 kg of hydrogen and limitless air? How much more output could be achieved if the unused fuel were recycled so that the effective fuel utilization became 100%. (d) Determine how many plates the fuel cell would have to have at 0.6 V per plate, 1.2 A/cm2 , to generate 150 horsepower for an automotive application. 2.8 A given fuel cell has continuous 150 A DC, an operating voltage of 0.55 V, and an overall internal resistance of 3 m at 1.4 A/cm2 current density. Calculate: (a) The potential loss from ohmic resistance, in volts, at this condition. (b) The total electrical work produced in 2 h. (c) The rate of ohmic heat dissipation from the cell in watts. 2.9 Describe the concept of the TPB and how this is relevant to fuel cell performance. A sketch will help. 2.10 Determine the single-pass fuel utilization efficiency for a 150-plate fuel cell stack with 120 A current output

2.12 It is proposed to develop a fuel cell that runs directly on propane (C3 H8g ) at a propane stoichiometry (λC3 H8 ) of 2.5 and a cathode oxygen stoichiometry (λc ) of 2 [note the cathode is running on air (79% N2 , 21% O2 by volume]. The cell operates at 0.3 V at a current density of 0.1 A/cm2 . The superficial active area of the cell is 25 cm2 . The anode electrochemical reaction is (C3 H8 )g + 6 (H2 O)g → 20H+ + 20e− + 3CO2 The basic cathode electrochemical reaction is O2 + 4e− + 4H+ → 2H2 O The balanced overall electrochemical reaction is thus (C3 H8 )g + 5O2 → 4H2 O + 3CO2 with the following molecular weights: C3 H8 44 g/mol H2 0 18 g/mol O2 32 g/mol air 28.85 g/mol CO2 28 g/mol (a) Is the overall cell producing or consuming water— at what rate in moles per second? (b) What is the actual supply rate of air at the cathode in grams per hour? 2.13 Consider a direct methanol fuel cell with a liquid methanol and water solution in the anode and an air cathode. The anode electrochemical oxidation reaction is CH3 OH + H2 O → 6H+ + 6e− + CO2 The basic cathode electrochemical reduction reaction is O2 + 4e− + 4H+ → 2H2 O The balanced overall electrochemical reaction is CH3 OH + 32 O2 → 2H2 O + CO2

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where methanol density is 700 kg/m3 and methanol molecular weight is 32 g/mol. (a) Calculate the minimum volume (in cubic centimeters) of a pure methanol fuel tank required to run a soldier’s uniform equipment for three days. The nominal power is 20 W. There are 10 cells in the stack in series and the total stack voltage is 5 V. (b) What is the molar rate of water consumption at the anode? (c) What is the molar rate of water production at the cathode? (d) Is there a water flow rate required at the anode? (e) What is the net molar rate of water production per mole of methanol for the cell? (f) What is the minimum molar rate of air required for reaction? 2.14 Consider a dimethylether [DME, (CH3 )2 O] fuel cell stack running at a DME stoichiometry (λDME ) of 2.4 and a cathode oxygen Faradic efficiency (εf ) of 0.3. There are 15 cells (connected in series) in the stack, all operating at 0.4 V. The active area of all cells in the stack is 25 cm2 , and the current density of each cell is 0.1 A/cm2 . The anode electrochemical reaction is (CH3 )2 O + 3H2 O → 12H+ + 12e− + 2CO2 The cathode electrochemical reaction is O2 + 4e− + 4H+ → 2H2 O with the following molecular weights:

2.15 Consider the following reactions typical of many fuel cells: H2 → 2H+ + 2e− 4H+ + 4e− + O2 → 2H2 O (a) Which reaction occurs at the anode of the fuel cell and which reaction occurs at the cathode? (b) Is this a galvanic or electrolytic cell? (c) Which is the positive electrode? 2.16 Consider a 25-cell hydrogen/air PEM fuel cell stack producing a total of 2.0 kW at 10 V. (a) What is the total stack mass flow rate of hydrogen if the anode stoichiometry is 1.3? (b) What is the total stack rate of generation of water at the cathodes in grams per hour? (c) If the theoretical maximum voltage of a single cell is 1.23 V, what is the voltaic efficiency of a single cell. Assume all cells have the same voltage. 2.17 Consider an ideal fuel cell to be run on pure oxygen and hydrogen for a given length of time. Determine the ratio of the minimum size of fuel to oxidizer storage tanks, V fuel /V oxidizer , assuming they are stored as gases at the same pressure and the anode and cathode stoichiometries (λa and λc ) are 1.5 and 2.0, respectively. 2.18 Considering the concepts discussed for the generic fuel cell, list three reasons why the original fuel cells invented by Grove worked so poorly relative to modern fuel cells? The Grove fuel cell operated with the use of flatplate platinum electrodes in an aqueous dilute sulfuric acid electrolyte solution, as shown below:

DME 44 g/mol H2 O 18 g/mol O2 32 g/mol Air 28.85 g/mol (a) How many moles of water are created at the cathode per mole of DME? (b) What is the theoretical consumption rate of DME at the anode in grams per second? What is the actual supply rate in grams per second? (c) What is the theoretical consumption rate of H2 O at the anode in grams per second? (d) What is the actual supply rate of air at the cathode in grams per hour? (e) Would a DME fuel cell theoretically need a water storage tank? Explain your answer.

e-

O2 e-

H2 e-

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References

Open-Ended Problems 2.19 Consider the generic fuel cell of Figure 2.9. (a) List three to five qualities that each of the components shown should have. Note: For repeating units (e.g., cathode and anode catalyst layers) you can just say “same as the other.” (b) Using your intuition about the function of these components, describe a loss or limitation that can occur with (a) the electrodes and (b) the bipolar plates and how you would solve or improve it. Then discuss what limitations or other offshoot advantages you might face with your solution/improvement.

61

As an example the bipolar plate needs to be noncorrosive. So we could use some kind of plastic composite or coated metal. The limitations encountered could be that the plating is expensive or will not last or the plastic composite has high electrical resistance compared to the metal it replaced. Other advantages would be that it is potentially cheaper to produce, faster to machine, and much lighter. 2.20 Estimate how much weight savings in terms of fuel and oxidizer would be realized by replacing a 100 W, 20 A fuel cell stack designed for 4000 h service with a reversible fuel cell recharged by a solar panel for a space application. Because fuel and oxidizer are recycled, you can assume an effective stoichiometry of 1.0 for the anode and cathode in both cases.

REFERENCES 1. G. J. Binczewski, “The Point of a Monument: A History of the Aluminum Cap of the Washington Monument,” J. Met., Vol. 47, No. 11, pp. 20–25, 1995. 2. Battery and EV Industry Review, Business Communications Co, Formington, CT Distributed by Global Information, 2005. 3. J. R. Hofmann, Andr´e-Marie Amp`ere: Enlightenment and Electrodynamics, Cambridge University Press, New York, 1996. 4. G. Pancaldi, Volta: Science and Culture in the Age of Enlightenment, Princeton University Press, Princeton, NJ, 2005. 5. T. L. Brown and H. E. LeMay, Chemistry, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 1988. 6. A. J. Bard and L. R. Falkner, Electrochemical Methods, Fundamentals and Applications, 2nd ed., Wiley, New York, 2001. 7. W. Feldenkirchen, Werner Von Siemens: Inventor and International Entrepreneur, Ohio State University Press, Columbus, OH, 1994. 8. J. S. Newman, Electrochemical Systems, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1991. 9. G. Prentice, Electrochemical Engineering Principles, Prentice-Hall, Englewood Cliffs, NJ, 1991. 10. D. Thompsett, “Pt Alloys as Oxygen Reduction Catalysts,” in Handbook of Fuel Cells— Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 467–480.

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Fuel Cell Engines Matthew M. Mench

3

Copyright © 2008 by John Wiley & Sons, Inc.

Thermodynamics of Fuel Cell Systems I believe fuel cell vehicles will finally end the hundred-year reign of the internal combustion engine as the dominant source of power for personal transportation. It’s going to be a winning situation all the way around—consumers will get an efficient power source, communities will get zero emissions, and automakers will get another major business opportunity—a growth opportunity. —William C. Ford, Jr., Ford Chairman, International Auto Show, January 2000

3.1 PHYSICAL NATURE OF THERMODYNAMIC VARIABLES Thermodynamics is the study of equilibrium at a macroscopic level. When a system is in mechanical equilibrium, there is no net force imbalance that causes motion. Complete thermodynamic equilibrium is more extensive and requires not only mechanical equilibrium but also thermal, phase, and chemical equilibrium. We can use classical thermodynamics to analyze chemically reacting and nonequilibrium flows, such as those in fuel cells, but are restricted to only the quasi-equilibrium beginning and end states of the process, with no details of the reaction itself. Thermodynamics can tell us the potential for reaction and direction of spontaneous reaction, but not how fast the reaction will occur. Classical thermodynamics also assumes a continuous fluid, meaning that there are enough molecules of a substance to yield accurate values of thermodynamic variables like pressure and temperature. As such, classical thermodynamics is generally inappropriate for use with microscopic-level molecular charge transfer processes and electrochemical reactions. In this chapter, the fundamentals of classical thermodynamics as it applies to the study of fuel cells is introduced. Although the reader is assumed to have a background in basic thermodynamics, this chapter includes a review of the physical meaning of several parameters used frequently in electrochemistry and how calculations of their values can be made. This chapter concludes by applying the thermodynamic concepts presented to determine the maximum expected thermodynamic efficiency and open-circuit voltage expected for a fuel cell at a given condition.

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Physical Nature of Thermodynamic Variables

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Figure 3.1 Concept of temperature and a continuum: (a) continuum assumption not valid; (b) continuum assumption valid. CV = control volume.

3.1.1 Physical Meaning of Parameters Temperature (T) Temperature is a thermodynamic parameter that everyone has common experience with, yet many people have no concept of what temperature physically represents. Temperature is a measure of the mean kinetic energy of the continuum of molecules being measured. For an individual molecule, temperature has little physical meaning in a macroscopic sense (imagine trying to measure the temperature of an individual molecule). Consider a very small box representing the space of interest, as in Figure 3.1. When the box is very small (Figure 3.1a), only a few molecules travel in and out of it, and any measure of temperature would be erratic and unsteady, as the number of molecules in the box changes with time. Now consider that the box is large enough so that the average number of molecules in the box remains constant over time, which is the continuum assumption, illustrated in Figure 3.1b. In this case, a measurement of the average kinetic energy of the molecules is a meaningful quantity represented by the temperature. Pressure (P) Pressure is similar to temperature in that, from a macroscopic perspective, there is no physical meaning for pressure of an individual molecule. For a continuous mixture, pressure is a measure of the molecular momentum transfer from collision on the plane of measurement. Consider a balloon filled with helium, as in Figure 3.2. To expand the balloon against the restraining force of the elastic balloon material, there must be an internal pressure greater than the atmospheric pressure. At the balloon’s internal surface, the molecules are colliding and reflecting off of the wall. Since the internal pressure must

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Figure 3.2

Molecular collision and concept of pressure at a balloon wall.

be greater (or the balloon would not inflate), either there is a greater density of molecules colliding on the inside of the balloon than the outside, or the average momentum of the molecules inside is larger, which corresponds to a higher temperature. This also explains why pressure is linearly related to temperature and the number of moles in the ideal gas equation of state (EOS): PV = n Ru T

(3.1)

where n is the number of moles of the mixture, P is the absolute pressure, Ru is the universal gas constant (8.314 kJ/kmol·K), V is the system volume, and T is the absolute temperature. Nonideal behavior Although much of the thermodynamic state behavior for the gasphase species in fuel cells can be well approximated with the ideal gas law, it is important to realize that Eq. (3.1) is not a perfect representation of the true physics, and there are some applications pertinent to fuel cells where the assumption of ideal gas behavior is not accurate. The ideal gas law assumes that (1) there are no net intermolecular interaction forces and (2) the volume of the molecules is very small relative to the volume of the containment. While these assumptions are accurate at low pressure and high temperature (where density is low), they are not accurate at low temperature and high pressure, or near the critical point of a substance. Obviously, ideal gas behavior is not appropriate in a two-phase regime or to describe condensing or vaporizing water in a low-temperature fuel cell. Thermodynamic parameters for the water vapor in mixtures should generally be taken from thermodynamic steam tables, except at very low vapor pressure with no phase change where ideal gas behavior can sometimes be used. In fact, tabulated thermodynamic data are always preferred to empirical or semiempirical correlations or generalized charts. Another application where the assumption of the ideal gas law is not perfectly accurate is at the high pressures used for fuel or oxidizer storage, where the intermolecular interactions and finite molecular volume can become significant. There are many methods to correct for nonideal gas behavior, including use of empirically or semiempirically modified EOSs. Actually, hundreds of EOSs have been developed to describe the pressure–density–temperature relation for a wide variety of gas-, liquid-, and solid-phase substances. For additional background, the reader is referred to a fundamental thermodynamics textbook [e.g., 1]. An early attempt to improve the ideal gas EOS was

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proposed by Johannes Diderik van der Waals in 1873. Van der Waals was awarded the 1910 Nobel Prize in Physics for his work, which can also be applied to compressible fluids with modification. For gases, the van der Waals EOS is shown as P=

a Ru T − v − b v2

(3.2)

where v is the molar specific volume, V/n, and n is the number of moles. The van der Waals EOS achieves a higher accuracy than the ideal gas law because the two constants a and b correct for the main assumptions implicit in the ideal gas law. The positive constant a represents the net intermolecular attractive forces and therefore acts to reduce the effective pressure in Eq. (3.2). Theoretically, this constant can be shown to be [2] a=

27 Ru2 Tc2 64 Pc

(3.3)

where Tc and Pc are the critical temperature and pressure, respectively. The constant b accounts for the finite volume of the molecules; thus it is subtracted from the molar specific volume of the system. Theoretically, this can be shown to be [2] b=

Ru Tc 8 Pc

(3.4)

Table 3.1 provides some theoretical correction factors for the van der Waals EOS, calculated based on the critical-point data. Although inconvenient to use, improved accuracy can be achieved by using empirically derived correction factors, rather than the theoretical values determined from Eqs. (3.3) and (3.4). Such data are available for many species but are rarely, if ever, needed in the study of fuel cells. While the van der Waals EOS has improved accuracy compared to the ideal gas law and is historically quite important, it is not frequently utilized because more accurate approximations are now available, especially for behavior near the critical point. Other approaches include two or more parameters that are empirically defined by fitting experimental data, or the so-called virial EOSs, which have a series expansion form with coefficients based on molecular theory, statistical mechanics, or experimental data. Table 3.1 Van der Waals EOS Coefficients for Various Species Calculated from Critical-Point Data Species

Formula

Hydrogen Oxygen Water vapor Carbon dioxide Nitrogen Air Methanol Methane

H2 O2 H2 Og CO2 N2 Mixture property CH3 OH CH4

Force Parameter, a [kPa · (m3 /kmol)2 ]

Volume Parameter, b (m3 /kmol)

24.73 136.95 553.12 364.68 136.57 136.83 965.32 229.27

0.02654 0.03169 0.03045 0.04275 0.03863 0.03666 0.06706 0.04278

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Perhaps the simplest approach to EOS modification is that of a compressibility factor Z. Here, the ideal gas EOS is modified with a compressibility factor: Pv =Z n Ru T

(3.5)

Obviously, for a true ideal gas, Z = 1. Analytical expressions for Z can be derived as a function of various parameters, based on the van der Waals correction factors or those in various other EOS formulations. Compressibility charts for many species have been experimentally generated and can be used to estimate the compressibility factor. For a wide variety of gasphase species such as air and water vapor, the compressibility factor follows a consistent behavior when correlated by the reduced pressure (Pr ) and reduced temperature (Tr ): Pr =

P Pc

Tr =

T Tc

(3.6)

where Pc and Tc are the critical pressure and temperature, respectively. This behavior is known as the law of corresponding states, although it is not really a law of nature. Many species follow this relationship, and the ideal gas correction factor can be represented on a generalized compressibility chart. Figure 3.3 is a generalized compressibility chart that can be used in lieu of species-specific data and provides a good estimate of the compressibility factor. For hydrogen and some noble gases like helium, which do not follow the generalized compressibility chart trends well, a specific chart based on measured data should be used. Figure 3.4 is a hydrogen-specific compressibility chart. If a specific chart is not available, hydrogen and other noble gases can be approximated with a generalized compressibility

Figure 3.3 Generalized compressibility chart. (Reproduced from E. F. Obert, Concepts of Thermodynamics, McGraw-Hill, New York, 1960.)

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1.10

67

400 500 600 300 700 1000

1.05

500

0 400 50

350 300

1.00

300 250

1.0 Compressibility Factor, Z

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200

0.9

180

0.8

160

0.50

150

0.7

140

0.90

130

0.6 0.95

120

0.5

115

0.4

110 105

0.3

TR =100

0.1 0

0

0.5

1.0

1.5

2.0

2.5

3.0

4.5 5.0 3.5 4.0 Reduced Pressure, Pr

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

Figure 3.4 Experimentally measured hydrogen compressibility chart. (Reproduced with permission from [3]. Copyright American Chemical Society.)

chart if 8 K and 8 atm are added to the critical temperature and pressure used in Eq. (3.6) respectively. Although more accurate, this is a rather arbitrary empirical correction and only appropriate over a limited range [3]. Example 3.1 Hydrogen Storage Volume Consider a hydrogen tank storage system for a fuel cell automobile. Seven kilograms of hydrogen gas compressed to 68 MPa (approximately 10,000 psig) and stored at 20◦ C is required to provide a driving range of about 480 km (approximately 300 miles). Using the ideal gas law, the van der Waals EOS, and the generalized compressibility chart, determine the interior volume required for the hydrogen storage tanks. SOLUTION

(a) Ideal gas law EOS: V = =

m Ru T kg · N · m/kmol · K · K n Ru T ⇒V = = = m3 P MWH2 P kg/kmol · N/m2 7 × 8314 × 293 = 0.1254 m3 2 × 68,000,000

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(b) Van der Waals EOS: We first need to rearrange Eq (3.2) to suit the problem, which becomes a cubic expression in V:

  a  P Pb Ru T 3 2 V − ab = 0 + − − + V V n3 n2 n2 n where n is the number of moles, which in this case is 3.5 kmol. For hydrogen, we look up Tc = 33.2 K from the Appendix and Pc = 1.3 MPa. From Eq. (3.3)
 27 8,3142 33.22 27 Ru2 Tc2 (N · m/kmol · K) · K = = 24,725 N · m4 /kmol2 a= 2 64 Pc N/m 64 1,300,000 The constant b is defined in Eq. (3.4): b=

Ru Tc 8314 × 33.2 = = 0.02654 m3 /kmol 8 Pc 8 × 1,300,000

Solving the cubic expression we find V = 0.2064 m3 . This result is substantially higher than using the ideal gas assumption due to the intermolecular attractive forces and finite molecular volume effects. (c) Generalized compressibility chart: Here, we use the generalized compressibility chart with the 8 K and 8 atm correction for hydrogen along with some unit conversion (1 MPa = 9.869 atm): Pr =

671.1 atm = 32.21 12.83 atm + 8 atm

Tr =

T 293 K = 7.111 = Tc 33.2 K + 8 K

From the generalized compressibility chart, we see that Z ∼ 1.42. Then n Ru T m Ru T kg · N · m/kmol · K · K ⇒V =Z = P MWH2 P kg/kmol · N/m2 7 × 8314 × 293 = 0.178 m3 = 1.42 × 2 × 68,000,000

V =Z

If we had not used the correction, we would have found that Pr =

671.1 atm = 52.31 12.83 atm

Tr =

T 293 K = = 8.83 Tc 33.2 K

and we could extrapolate Z to be ∼1.58 from the generalized compressibility chart: V = 1.58 ×

(7 kg)(8314 N · m/kmol · K)(293 K) = 0.198 m3 (2 kg/kmol)(68,000,000 N/m2 )

The most accurate result would be from the hydrogen-specific compressibility chart in Figure 3.4. We would have found that Pr =

671.1 atm = 52.31 12.83 atm

Tr =

T 293 K = = 8.83 Tc 33.2 K

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Z ∼ 1.4 V = 1.4 ×

(7 kg)(8314 N · m/kmol · K)(293 K) = 0.176 m3 (2 kg/kmol)(68,000,000 N/m2 )

COMMENTS: Note that there is significant deviation for each approach. Of them, the hydrogen-specific compressibility chart should be the most accurate since it is based on directly measured experimental data. The corrected generalized compressibility chart values were also quite close. Considering the vehicle range is directly related to the mass of fuel that can be stored, use of the ideal gas law alone would greatly underestimate the storage volume required, by almost 30% in this case. If the hydrogen were stored in a liquid form, the tank volume could be decreased, but insulation would be needed to prevent excessive boil-off. The ideal gas law would definitely not be appropriate for liquid H2 storage, and direct saturated and liquid thermodynamic data tables for hydrogen would be appropriate. Internal Energy (U) We should first distinguish the nomenclature used in this text for the intensive (mass-related) variables, including internal energy. For these variables, a capital letter refers to the absolute value of the parameter of interest. For example, U, the internal energy, is taken to be in units of energy, or joules. A lowercase parameter represents a mass-intensive quantity. For example, u represents the internal energy per unit mass in kilojoules per kilogram. An overscored lowercase letter is representative of a molar specific quantity. Therefore u¯ represents the internal energy in kilojoules per kilomole. Internal energy U is a macroscopic measure of the total thermal energy stored in a thermodynamic system. Considering a closed container with gas as our system, we need to understand the way thermal energy can be stored in the gas-phase constituents to understand the concept of total internal energy. From the first law of thermodynamics for the system, the internal energy can be converted into potential energy or kinetic energy or transferred out of the system as heat or as work: dE = dKE + dPE + dU = δ Q − δW

(3.7)

Where dE is the change in energy of the system and dPE and dKE represent the change in potential and kinetic energy of the system, respectively. The internal energy U is a measure of the system total thermal energy stored in the individual, nonreacting species at the given temperature and pressure condition. In individual molecules, the internal energy can be stored in the following ways: Ĺ Translational Kinetic Energy This is different from the kinetic energy of the system in Eq. (3.7), which is a measure of the change in kinetic energy of the system as a whole. As an example, consider a stationary container of gas. There is no change in the kinetic energy of the system (it is zero); however, the individual molecules can store energy in the form of their translational motion. The thermodynamic measure of this form of energy is the temperature. Ĺ Vibrational Motion A molecule can store energy via the oscillation of the bond distance between atoms. The more bonds in a molecule, the greater the vibrational motion contribution to the total stored energy. A monatomic species such as argon has no bonds and therefore cannot store energy in this form.

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CV

Flow in

1

2 Flow out

Figure 3.5 Flow work at the flux boundaries of a control volume.

Ĺ Rotational Motion of Molecules Spinning molecules store energy in the form of rotational momentum. Similar to the vibrational modes of storage, for a more complex structure, the molecule has a greater number of rotational modes available. A monatomic species such as helium has no bonds and therefore cannot store energy in this form. Ĺ Atomic-Level Storage At the atomic level, energy is stored in the orbital states, intermolecular and interatomic forces, and nuclear spin states. Intermolecular forces become important for high-pressure gases, liquids, and solid states. Note that the stored internal energy does not contain the chemical energy that would be released or consumed for a reaction that converts the species into other molecules. This energy is a result of the reconfiguration of the bond structure and can be orders of magnitude greater in value compared to the energy stored in nonreacting species. Enthalpy (H) Enthalpy is a unique thermodynamic parameter that is defined based on the other thermodynamic quantities of internal energy, pressure, and density: H =U+

P = U + Pv ρ

(3.8)

where v is the specific volume. Enthalpy is a measure of the energy stored in a flowing fluid. It is therefore defined as the internal energy plus the flow work. The flow work is the energy required for flow of the fluid across the control volume boundary. Consider a basic control volume of a container with gas-phase flow in and out of the control surface, as shown in Figure 3.5. For a control volume, the first law of thermodynamics includes not only the flux of heat and work across the control surface but also the flux of energy across the control surfaces via mass flow in and out of the control volume. The first law for a control volume is written as1  
 
V2 dEcv V2 (3.9) m˙ i h i + i + gz i − m˙ e h e + e + gz e = Q˙ cv − W˙ cv + dt 2 2 e i 1 The

reader is referred to detailed texts on thermodynamics if a deeper explanation is needed.

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Here, E is energy, Q˙ is the rate of heat transfer across the control surface and is positive for heat added to the system, and W˙ is the rate of work across the control surface and is positive for work done by the system on the surroundings. The final two terms on the right-hand side of Eq. (3.9) represent the flux of energy into and out of the control volume in the form of enthalpy, kinetic energy, and potential energy carried by mass flux across the control surfaces. In order to cross into and out of the control surface, some flow work is done on the control volume (at the entrance) and on the environment (at the exit). For a compressible substance, this total flow energy is represented as h¯  u¯ + P v¯ (3.10) Internal energy

Flow work

For an ideal gas, we can also show that h¯ = u¯ + Ru T

(3.11)

Constant-Pressure Specific Heat (cp ) The constant-pressure specific heat is defined as the rate of change of enthalpy with temperature at constant pressure:  ∂ h¯  c¯ p (T, P) ≡ (3.12) ∂T p Constant-Volume Specific Heat (cv ) The constant-volume specific heat is defined as the rate of change of internal energy with temperature at constant volume:  ∂ u¯  c¯v (T, P) ≡ (3.13) ∂ T v The specific heats are a measure of the capacity for the internal energy storage, which can change with temperature. As the temperature changes, different rotational and vibrational modes of energy storage become active, and the specific heat values can change. For the same energy input to two substances, the substance with the larger specific heat will have a lower increase in temperature, since it has a relatively high capacity for thermal energy storage in other modes besides translational velocity. Figure 3.6 shows the constantpressure specific heats of a variety of gas-phase species as a function of temperature. Note the temperature independence of the monotomic species which can only store internal energy as translational and interatomic forces. As the molecular complexity increases (i.e., more bonds), the capacity to store energy increases, and the specific heat is generally higher. As the temperature is increased, more vibrational and rotational modes become active, increasing the specific heat to a limit, where all energy storage modes are fully occupied or the molecule disassociates into smaller fragments. Gas-Phase Specific Heat The specific heat of an ideal gas is solely a function of temperature, and even nonideal gases have an insignificant dependence on pressure. For most cases involving fuel cells except hydrogen storage, the conditions are such that an ideal gas

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Figure 3.6

Specific heat as function of temperature for several species.

model is valid over the operating range, and the partial derivatives of Eqs. (3.12) and (3.13) can be replaced with ordinary differentials:  d h¯  c¯ p (T ) = (3.14) dT  p  d u¯  c¯v (T ) = (3.15) dT v To determine the enthalpy or internal energy change for a temperature change for a nonreacting species, we integrate Eqs. (3.14) and (3.15): T2

T2 d h¯ =

T1

T1

T2

T2 d u¯ =

T1

c¯ p (T ) dT

(3.16)

c¯v (T ) dT

(3.17)

T1

The enthalpy change between two temperature states of a nonreacting substance is known as the sensible energy. Determination of the sensible enthalpy at a given temperature can be done in several ways with varying accuracy. If we can assume constant specific heats, for a nonreacting gas we can simplify Eqs. (3.16) and (3.17) as h¯ 2 − h¯ 1 = c¯ p (T2 − T1 )

(3.18)

u¯ 2 − u¯ 1 = c¯v (T2 − T1 )

(3.19)

To use constant specific heats, a suitable average temperature should be chosen to minimize inaccuracies in the result, since any nonmonatomic specie will have a functional dependence

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with temperature, as shown in Figure 3.6. This is generally acceptable for fuel cells since they tend to operate over a narrow temperature range. If we do not assume constant specific heats, we must integrate the specific heat curve-fit expression with respect to temperature. This is still a simple matter and more acurrate: T2 u¯ 2 − u¯ 1 =

c¯v (T ) dT

(3.20)

c¯ p (T ) dT

(3.21)

T1

T2 h¯ 2 − h¯ 1 = T1

where the proper polynomial expression for c¯ p (T ) or c¯v (T ) is inserted and integrated. The absolute specific internal energy and enthalpy at a given temperature T 2 is given by T2 ¯ 2) = u(T

c¯v (T ) dT

(3.22)

c¯ p (T ) dT

(3.23)

T,ref

T2 ¯ 2) = h(T T,ref

where 298 K is typically chosen as the standard reference temperature. Specific heat values have been measured for a wide variety of gases and can be used to determine the internal energy and enthalpy. Specific heat relationships are generally modeled with a high-order polynomial, such as those listed below for common fuel cell gases, valid in the range of 300–1000 K [1]: c¯ p (T )H2 = 3.057 + 2.677 × 10−3 T − 5.810 × 10−6 T 2 Ru + 5.521 × 10−9 T 3 − 1.812 × 10−12 T 4

(3.24)

c¯ p (T )O2 = 3.626 − 1.878 × 10−3 T + 7.055 × 10−6 T 2 Ru − 6.764 × 10−9 T 3 + 2.156 × 10−12 T 4

(3.25)

c¯ p (T )N2 = 3.675 − 1.208 × 10−3 T + 2.324 × 10−6 T 2 Ru − 0.632 × 10−9 T 3 − 0.226 × 10−12 T 4

(3.26)

c¯ p (T )Air = 3.653 − 1.337 × 10−3 T + 3.294 × 10−6 T 2 Ru − 1.913 × 10−9 T 3 + 0.2763 × 10−12 T 4

(3.27)

c¯ p (T )H2 O = 4.070 − 1.108 × 10−3 T + 4.152 × 10−6 T 2 Ru − 2.964 × 10−9 T 3 + 0.807 × 10−12 T 4

(3.28)

c¯ p (T )monatomic gas = 2.5 Ru where T is in kelvins.

(3.29)

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Liquid- and Solid-Phase Specific Heat is constant, so that

For an incompressible liquid or solid, the density

   d h¯  d u¯  dP/ρ¯  d u¯ ¯ ) = c¯v (T ) = c(T c¯ p (T ) = = +  =   dT p dT p dT  dT

(3.30)

p

Solids and liquid have no distinction between constant-pressure or constant-volume specific heats, and a single specific heat value is appropriate. The specific heat of most incompressible substances varies only slightly with temperature and can generally be considered constant over a limited temperature range of interest to fuel cell studies. For example, the mass specific heat of liquid water at 25◦ C is 4.179 kJ/kg · K, while at 100◦ C, the specific heat of the liquid phase is 4.218 kJ/kg · K, only about 1% higher.

3.2

HEAT OF FORMATION, SENSIBLE ENTHALPY, AND LATENT HEAT Enthalpy of Formation The enthalpy of a given component is an important parameter, as it is a measure of the internal energy and flow energy potentially available for conversion into other forms of energy and work. In order to determine the relative thermal energy exchange between states, we need to define an arbitrary baseline from which the differences are measured. Consider any species at standard temperature and pressure (STP; 298 K, 1 atm). This is our chosen baseline state. The enthalpy of the substance at this state is termed the enthalpy of formation or the heat of formation: h ◦f = heat of formation

(3.31)

Heats of formation for some fuel cell species are given in Table 3.2. Others can be found in thermodynamics references or online. For an element in its stable state, for example diatomic hydrogen or monotonic helium, no energy is required or released to achieve a stable state at STP. Therefore, the heat of formation of atomic species in their stable state at STP is defined as zero. For a compound like water, which is a product of an exothermic Table 3.2 Heats of Formation of Common Fuel Cell Species at 1 atm, 298 K Species

Formula

h¯ ◦f (kJ/kmol)

Water vapor Liquid water Carbon dioxide Carbon monoxide Methanol vapor Liquid methanol Methane Nitrogen Oxygen Hydrogen

H2 Og H2 Ol CO2 CO CH3 OHg CH3 OHl CH4,g N2 O2 H2

−241,820 −285,830 −393,520 −110,530 −200,890 −238,810 −74,850 0 0 0

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qout = h°f 25°C 1 atm O2 Combustion

25°C 1 atm

25°C 1 atm

H2O

H2

Figure 3.7 Heat of formation.

reaction between O2 and H2 , however, thermal energy must be exchanged to achieve a stable compound at STP, resulting in a nonzero heat of formation. Consider Figure 3.7, in which a steady flow of oxygen and hydrogen at 1 atm, 25◦ C, is mixed and completely burned in a flow reactor to form a water vapor stream that exits the reactor at 25◦ C, 1 atm. We know from experience with combustion that the reaction is exothermic and heat would be released by the reaction. In this example, heat must be removed from the reactor to cool the product water vapor to its exit condition of 1 atm, 25◦ C. The heat removed to achieve this is equivalent to the heat of formation of the water vapor. From this example, we see that for a water molecule to exist at STP some thermal energy conversion (and therefore a nonzero heat of formation) is required. In this case, thermal energy is released, so that the chemical energy state of the product water is lower than the initial reactants. Therefore, the heat of formation for the water vapor is negative, as is the case for any exothermic reaction. Note from Figure 3.7 that there is a difference between the heat of formation of water in a liquid or vapor state. This is due to the latent energy required for vaporization and is discussed in the following section. If we were to take the reactor in Figure 3.7 and produce liquid-phase exhaust, additional heat would have to be removed to condense the vapor. Sensible Enthalpy Consider a water vapor stream exiting the reaction chamber in Figure 3.7 at 25◦ C, 1 atm. In order to change this stream from 25◦ C to some other temperature T without additional reaction, some heat transfer is required. This energy required is called sensible enthalpy: ¯ ) − h¯ (Tref ) h¯ s = sensible enthalpy = h(T

(3.32)

where the reference temperature is 25◦ C. Latent Heat When a substance is undergoing a phase change, the temperature is generally constant, but there is still a thermal energy exchange when the molecular structure is reordered to a different phase. This thermal energy difference between the molecular structures of the two phases is termed latent heat: LH = latent heat

(3.33)

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m˙ vap

˙ vap h fg = Q˙ in m

Figure 3.8

t = t2

t = t1

Schematic of evaporating droplet.

Consider a droplet evaporating at ambient pressure, as shown in Figure 3.8. At this pressure, the boiling point (where the liquid will undergo phase change) is 100◦ C. The energy required to boil off the water is termed the latent heat of vaporization, hlv . The latent heat of vaporization for water at 100◦ C is 2257 kJ/kg. Besides vaporization, there is also a latent heat released when vapor condenses and reforms into a liquid at a lower molecular energy state. The enthalpy of condensation is simply the additive inverse, −2257 kJ/kg. This concept is a little more difficult to conceptualize, but a droplet condensing on a surface will release thermal energy and actually heat the surface. This latent heat release is what can cause severe burns when people are exposed to steam. Thermal energy is also released when a substance freezes. To take advantage of this effect, some citrus fruit farmers spray crops with water when freezing temperatures are expected, a technique known as irrigational frost protection [4]. When the water freezes, it releases 334 kJ/kg and forms a thermal barrier for heat loss, protecting the fruit from damage. Overall, latent heat is required for melting, boiling, and sublimation and is released for condensation, freezing, and desublimation. Example 3.2 Latent Heat of Vaporization Consider a 1-mg droplet of liquid water at l atm pressure. Determine the sensible enthalpy required to heat the droplet from 25 to 100◦ C, and the total energy required for complete vaporization. SOLUTION

The latent heat required for vaporization is:


E = mh lv = (1 mg)(2257 kJ/kg)

 1 kg (1000 J/kJ) = 2.257 J 1,000,000 mg

The liquid droplet enthalpy values can be determined using a constant liquid specific heat of water of 4.182 kJ/kg · K. The sensible enthalpy required to get the same droplet from 25◦ C to the boiling point of 100◦ C is: H2 − H1 = m[h s (T2 ) − h s (T1 )] = m[h(100) − h(25)] = mc(T2 − T1 ). (1 mg)c(100 − 20) = (4.182 kJ/kg · K)(80) = 0.335 J COMMENTS: The latent heat of vaporization is actually quite large compared to the sensible enthalpy required to increase the droplet temperature. This is why it takes a relatively long time to actually boil water into vapor, compared to the time required to heat

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the water to the boiling temperature on the stove. The energy difference between phases can be an important part of the overall energy in a fuel cell, especially for low-temperature PEFCs where phase change processes are common. Total Enthalpy Putting it all together, for a substance that deviates from the reference state at some state A, the mass specific enthalpy can be written as h A = h °f + h s + LH (3.34) Enthalpy at some state A

Enthalpy of formation

Sensible enthalpy

Latent heat for any phase change

At any temperature, the enthalpy is the heat of formation required to arrive at STP plus the sensible enthalpy required to heat (or cool) the substance to depart from STP plus whatever latent heat is required to achieve the phase state at the given temperature. If there is no phase change from the formation state, the LH term is obviously zero. Example 3.3 Determination of Enthalpy of a Single Species per unit mass of water vapor at 600 K, 1 atm.

Determine the enthalpy

SOLUTION In order to get water vapor at 600 K, there is an enthalpy of formation required to obtain liquid water at 298 K. Next, there is a sensible enthalpy required to heat from 298 K to the boiling point in liquid form, at 373 K. Then, there is a latent heat of vaporization required at 373 K to boil the water at 1 atm. Finally, there is a sensible enthalpy input required to raise the water vapor temperature from 373 to 600 K. We can write all of this as Increase to boiling temperature

h = h °f + h s,l + LH + hs,v

Get to 298 K

Boil

Go from 393 K to 600 K

From Table 3.2, at 298 K, 1 atm, the liquid water h¯ ◦f = −285,830 kJ/kmol, which equals −15,879 kJ/kg. The sensible enthalpy to heat the water to its boiling point at 373 K is h s,l = h(373) − h(293) ≈ cH2 O,l (80) ≈ (4.182 kJ/kg · K)(80 K) = 336 kJ/kg

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The latent heat of vaporization of water is 2257 kJ/kg. Finally, the vapor-phase water must be heated from 373 to 600 K via another sensible enthalpy change: h s,v = h(600) − h(373) ≈ c p,ave,H2 O,v × 227 = 18 kg/kmol/35.06 kJ/kmol · K × 227 K = 442 kJ/kg where an average vapor-phase water specific heat has been used for convenience, although a more precise value can be obtained from integration of Eq. (3.28). Since the total amount of sensible enthalpy contribution is quite small compared to the latent heat required for vaporization, the error with using an average value of specific heat is small. Now, in total, we have h = h ◦f + h s,L + LH + h s,v = −15,879 + 336 + 2257 + 442 = −12,844 kJ/kg COMMENTS: Note the small contribution from sensible enthalpy relative to the heat of formation or heat of vaporization. Also note that we could have also started with vapor at 293 K by using the heat of formation of vapor-phase water. This would have eliminated the need to calculate the latent heat term since it is included in the heat of formation, and we would only have to calculate the sensible enthalpy of the gas phase to go from 293 to 600 K.

3.3

DETERMINATION OF CHANGE IN ENTHALPY FOR NONREACTING SPECIES AND MIXTURES Nonreacting Species Calculation Consider a single nonreacting ideal gas with a temperature change. For example, consider preheating hydrogen in a SOFC cathode intake from 300 to 600 K. To determine the change in enthalpy from a state at T 1 to a state at T 2 with no phase change, we can follow Eq. (3.34): h °f,1 = h °f,2

LH1 = LH2 (3.35)

h2 − h1 =

h °f

+ h s + LH

2

−

h °f

+ h s + LH

1

For a nonreacting species with no phase change, the heat of formation and LH terms cancel out, and what is left is the change in sensible enthalpy. So, for a nonreacting gas we can show that h 2 (T2 ) − h 1 (T1 ) = h s,2 − h s,1 = [h (T2 ) − h (Tref )] − [h (T1 ) − h (Tref )] h s,2

(3.36)

h s,1

For an enthalpy change between two temperature states of a nonreacting species, the reference temperature enthalpy terms cancel out. This will not be the case for reacting mixtures but simplifies things here. There are several ways to solve Eq. (3.36) for the

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sensible enthalpy change: 1. For many species there are tables available to look up the enthalpy values. 2. We can integrate the specific heat expressions in Eqs. (3.24)–(3.29). 3. We can assume constant specific heats at an appropriate average temperature and solve Eq. (3.18). The assumption of constant specific heats is generally the easiest to implement and is also justified in most cases for fuel cells, as we shall see in Example 3.4. Example 3.4 Calculation of Enthalpy for Nonreacting Species Consider water vapor entering a SOFC. Determine the molar and mass specific enthalpy change required to heat the water vapor from a 298 K inlet temperature to 1073 K using (a) constant specific heats at an average temperature and (b) evaluation of the integration of the proper polynomial expression for the specific heat. SOLUTION

(a) For water vapor the proper polynomial expression is Eq. (3.28):

c¯ p (T )H2 O = Ru (4.070 − 1.108 × 10−3 T + 4.152 × 10−6 T 2 − 2.964 × 10−9 T 3 + 0.807 × 10−12 T 4 ) At an average temperature of 685 K, the above expression reduces to c¯ p,ave,H2 O = 37.3 kJ/(kmol · K) h¯ 2 − h¯ 1 = c¯ p,ave,H2 O (1073 − 298) = 28,894 kJ/kmol (b) The evaluation of the integral with Eq. (3.28) yields h¯ 2 − h¯ 1 =

1073  c¯ p (T )H2 O dT = 29,029 kJ/kmol 298

COMMENTS: Although the integrated solution is shown quite compactly, integration of a fourth-order polynomial is a very tedious exercise if done by hand. Note that for even a large temperature change of around 700 K there is little difference (0.5%) in the result; it is often not worth the additional effort for simple calculations. Nonreacting Ideal Gas Mixture Calculation In many cases relevant to fuel cells, we must deal with mixtures rather than pure gases. Thermodynamic properties of mixtures can be easily calculated based on the mole or mass fractions of the constituents. A good example of this is air, which is a nonreacting mixture of mostly nitrogen and oxygen. For these mixtures, we can assume each species in the mixture is occupying the total volume but at a partial pressure in the mixture, where the partial pressure is defined as Pi = yi P

(3.37)

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Here, P is the total mixture pressure and yi is the mole fraction of constituent i, defined as yi =

ni n˙ i = n˙ total n total

(3.38)

where ni is the number of moles of species i and ntotal is the total number of moles in the mixture. The n˙ i and n˙ total terms represent the molar flow rates of species i and the mixture, respectively. The sum of the partial pressures equals the total mixture pressure and the sum of the mole fractions equals 1: 

Pi = P



and

yi = 1

(3.39)

Because it is so common, thermodynamic tables have been developed to describe most of the thermodynamic properties for air. However, for other gas mixtures, one usually has to calculate the mixture properties. For molar specific properties, the mixture value is based on an average value among the constituents, weighted by the relative mole fractions: x¯mix =

n 

yi x¯i

(3.40)

i=1

Here, x¯ is the molar intensive thermodynamic parameter of interest (e.g., enthalpy and internal energy) and x¯i is the molar intensive parameter for species i. Example 3.5 Determination of Nonreacting Ideal Gas Mixture Properties Given a mixture of air (21% oxygen and 79% nitrogen by volume) at 2 atm pressure and 350 K, find (a) the partial pressures of each species and (b) the mixture molar specific heat. SOLUTION (a) Since we know the mole fractions are yO2 = 0.21 and yN2 = 0.79, we can easily determine the partial pressures of each constituent: PO2 = 0.21 × 2 atm = 0.42 atm PN2 = 0.79 × 2 atm = 1.58 atm  Pi = 2.0 atm = P (b) The mixture molar specific heat is calculated by first looking up the constituent specific heats at 350 K or calculated from Eqs. (3.25) and (3.26) and averaging them on a molar basis: c¯ p,mix =

n 

yi c¯ p,i = 0.21 c¯ p,O2 + 0.79 c¯ p,N2

i=1

= 0.21 × 29.7 kJ/(kmol O2 · K) + 0.79 × 29.2 kJ/(kmol N2 · K) = 29.3 kJ/(kmol mix · K)

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COMMENTS: Since air is commonly tabulated, we usually do not have to calculate its mixture properties. However, you can use air tables as a reference to make sure you understand the concepts here. In some cases, property values are tabulated in mass-specific units (e.g., enthalpy in kilojoules per kilogram). In this case, we can evaluate mixture properties on a mass basis:

xmix =

n 

M f i xi

(3.41)

i=1

where the mass fraction of each species is defined as Mfi =

mi m total

(3.42)

and the sum of the individual mass fractions equals 1: 

Mfi = 1

(3.43)

The mixture property on a mass basis can be converted to a molar basis by xmix · MWmix = x¯mix

(3.44)

where the molecular weight of the mixture, MWmix , can also be calculated based on an averaging technique as in Eq. (3.40). For a nonreacting mixture, determination of the change in enthalpy (or other thermodynamic properties) is the same as for a single ideal gas species, but follows ideal gas mixture property relations discussed in this section and exemplified in the following example. Example 3.6 Change in Properties for a Nonreacting Ideal Gas Mixture Find the change in absolute enthalpy for a 3-kg mixture of air (21% O2 , 79% N2 by volume) heated from 400 to 600 K. SOLUTION We are dealing with an ideal gas mixture. The mixture molecular weight (MWO2 = 32 kg/kmol, MWN2 = 28 kg/kmol) is first determined: MWmix =

n 

yi MWi = 0.79 · MWN2 + 0.21 · MWO2 = 28.85 kg/kmol

i=1

To determine the change in enthalpy, we use a molar average approach. Since the mixture is not reacting, the heats of formation cancel out and we are left with a simple calculation

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of the sensible enthalpy change of the mixture: From Eqs. (3.36) and (3.40) the change in enthalpy can be shown as  T  T1  2      h¯ mix = c¯ p,O2 dT − c¯ p,O2 dT − = 0.21 yi h¯ s,i yi h¯ s,i   T2 T1 Tref Tref  T  T1  2  + 0.79 c¯ p,N2 dT − c¯ p,N2 dT   Tref

Tref

To solve for the molar specific enthalpy change, we can integrate the expressions using the polynomials given in this chapter. If we assume constant specific heat, then this reduces to h¯ mix = 0.21 c¯ p,O2 (T2 − Tref ) − c¯ p,O2 (T1 − Tref ) + 0.79 c¯ p,N2 (T2 − Tref )

− c¯ p,N2 (T1 − Tref ) and h¯ mix = 0.21 c¯ p,O2 ,ave (T2 − T1 ) + 0.79 c¯ p,N2 ,ave (T2 − T1 ) Evaluating the specific heats of oxygen and nitrogen from Eqs. (3.25) and (3.26) at an average temperature of 500 K, we can show h¯ mix = 0.21 × 31.09 kJ/(kmol · K) (200 K) + 0.79 × 29.56 kJ/(kmol · K) (200 K) = 5976 kJ/kmol To find the absolute enthalpy change, we need to multiply the mixture molar specific enthalpy change by the total number of moles in the mixture: n mix =

3 kg 3 kg = 0.104 kmol = MWmix 28.85 kg/kmol

Finally, Hmix = n mix h¯ mix = (0.104 kmol) (5976 kJ/kmol) = 621.5 kJ COMMENTS: Note that the reference temperature enthalpy cancels out of the sensible enthalpy expression. In some thermodynamic tables, the reference point is chosen differently; therefore the absolute enthalpy calculated may be different. However, the enthalpy change between two states will always be the same. Also, there are several ways the air mixture properties could have been calculated. The mixture specific heat for air could have been used and c¯ p,mix (T2 − T1 ) would have given the molar specific enthalpy change. Also, since tables abound for air, we could have read the enthalpy changes directly from an ideal gas air table.

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3.4 DETERMINATION OF CHANGE IN ENTHALPY FOR REACTING SPECIES AND MIXTURES Consider a generic chemical or electrochemical reaction: νa A + νb B → νc C + νd D       Reactants

(3.45)

Products

where the ν’s represent the coefficients of the balanced electrochemical reaction. In order to determine the change in enthalpy for the reaction, we use the following relationship to account for the change in molar specific enthalpy between product and reactant states:       h¯ = h¯ P − h¯ R = v i,P h¯ i P − v i,R h¯ i R       = v j,P h¯ ◦f + h¯ s + LH P − v i,R h¯ ◦f + h¯ s + LH R

(3.46)

where R represents reactants and P represents products. To determine the total enthalpy change, simply multiply by the number of moles reacted of each species:  H P−R =

n 





−

n i h¯ i

i=1

m 

 n j h¯ j 

j=1

P

(3.47) R

Here we have assumed there is no latent heat term in the enthalpy expression, although it should be added as needed if not already accounted for in the heat of formation. Similar expressions can be written for the change in any intensive thermodynamic parameter of interest. For example, consider generic parameter x, where x can represent s, u, or g, that is, x¯ =  x¯ P − x¯ R  ¯ P− ¯ R = v i,P (x) v j,R (x)

(3.48)

and X P−R =

 n  i=1

  m  − n j x¯ j 

 n i x¯i

j=1

P

(3.49) R

Example 3.7 Change in Enthalpy for Reacting Gas-Phase Mixture Find the change in enthalpy per mole of hydrogen for combustion of a 50% hydrogen–50% oxygen mixture (by mole) at 298 K. The final product is water vapor and oxygen at 1000 K. SOLUTION

The chemical reaction can be written as H2 + O2 → H2 O +

1 2

O2

where the initial mixture was 50% oxygen, 50% hydrogen by volume (mole), so there is unreacted oxygen in the products by a simple species balance. The enthalpy per mole of

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hydrogen is simply the molar specific enthalpy change of the reaction, since there is one mole of hydrogen in the balanced chemical reaction. h¯ =

 

     v j,R h¯ ◦f + h¯ s v i, p h¯ ◦f + h¯ s − 

 h¯ = 1.0 h¯ °f +



1000

c¯ p dT Tref

  0   − 1.0 h¯ °f +  





 h¯ = 1.0 h¯ °f +

 + 0.5 h¯ °f +

0 

c¯ p dT Tref

1000



0



H2 O,v

0

+ 1.0 h¯ °f + Tref



O2

    c¯ p dT  

298

H2

c¯ p dT 298

Tref

H2 O,v

298

   c¯ p dT 

1000

0

O2

   c¯ p dT 

1000

+ 0.5 h¯ °f + 298

O2

where the sensible enthalpy of the reactants is zero, based on a 298 K reference temperature, and the formation enthalpies of oxygen and hydrogen are zero by convention. Also, we will use the heat of formation for gas-phase water vapor to eliminate the need to include a separate latent-heat-of-vaporization term. We can integrate the sensible enthalpy terms using the polynomial expressions given in this chapter. If we evaluate the specific heat integrals using the polynomials given in Eqs. (3.25) and (3.28), after evaluation, this reduces to # " h¯ = 1.0 (−241,820 + 29,745)H2 O,v + 0.5 (0 + 22,712)O2 = −200,718 kJ/kmol H2 COMMENTS: We could have also come close using an average specific heat value, but in this case the polynomial approximating the specific heat behavior with temperature was integrated exactly. For reacting mixtures, since the products at state “P” are different from the reactants at state “R”, the mixture property mole fractions change for products and reactants and the reference temperature enthalpy in the sensible enthalpy term does not cancel out. In this case it is important that the reference temperature for the heat of formation is the same as the sensible enthalpy. Also, it is interesting to see the dominance of the enthalpy of formation compared to the sensible enthalpy. The energy released from an exothermic chemical or electrochemical reaction is typically an order of magnitude or more larger than the sensible enthalpy change. Entropy (S) The concept of entropy is typically more difficult to grasp than most other thermodynamic parameters, yet it is an important part of the science of fuel cells to

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understand. Often, students describe the entropy of a system as some nebulous measure of “randomness.” While a dorm room may indeed be a high-entropy environment, a more fundamental physical representation of the meaning of entropy can be obtained from statistical thermodynamics. From a statistical thermodynamic viewpoint, entropy is proportional to the number of quantum microstates available, consistent with the given system constraints and thermodynamic parameters [5]: S = k B ln 

(3.50)

where kB is Boltzmann’s constant (1.3807 × 10−23 J/K) and  is the number of thermodynamically available quantum microstates consistent within the macroscopic thermodynamic constraints of the system. One can heuristically envision the number of possible microstates available for the molecules to occupy as a set of available boxes in which to put marbles, as shown in Figure 3.9. The more boxes available, the more possible combinations the marbles could be distributed among, hence the randomness of the distribution is increased. From the second law of thermodynamics, a system in equilibrium will maximize the number of available microstates within a given set of macroscopic constraints and occupy the available microstates with an equal randomness. This representation also satisfies the fundamental principle of entropic maximization for a given system. Practically, we need an expression for calculating entropy in terms of regularly measurable thermodynamic quantities. We cannot inspect a system to determine the number of available quantum microstates or buy an entropy meter at the store like we can purchase

A

B

C

(a)

A

I

B

J

C

K

D

L

E

M

F

N

O

G

H

P

(b) Figure 3.9

Heuristic representation of available microstates. (a) lower entropy; (b) higher entropy.

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a temperature or pressure sensor. Therefore, we seek to derive an expression relating the change in entropy to things we can easily measure like temperature and pressure. Consider the first law of thermodynamics for a simple compressible system in an internally reversible process with no changes in potential or kinetic energy: dU = δ Q − δW

(3.51)

From the second law of thermodynamics and the definition of compression work for this system, we can show that (δ Q)rev = T dS (δW )rev = P dV

(3.52) (3.53)

Plugging Eqs. (3.52) and (3.53) into Eq. (3.51) yields dU = T dS − P dV

(3.54)

From the definition of enthalpy we can show that H = U + PV dH = dU + P dV + V dP dH = T dS + V dP

(3.55) (3.56) (3.57)

Rearranging these equations and dividing by temperature and mass, we can show that v dP dh − T T du P dv ds = + T T ds =

(3.58) (3.59)

These are the entropy equations we seek, which relate the entropy to properties such as enthalpy, temperature, and pressure, which we can already measure or solve for. This was derived considering a reversible process but is applicable for any process, since entropy is a thermodynamic state property which does not depend on the path taken to arrive at the final equilibrium state. Determination of Entropy for Ideal Gas For a nonreacting ideal gas, enthalpy and internal energy are functions of temperature only, and the ideal gas EOS can be used to relate the P, V, and T variables together. Using the ideal gas law along with the definitions of specific heat, we can simplify Eq. (3.58) on a molar intensive basis as follows: d s¯ =

c¯ p (T ) dT dP − Ru T P

(3.60)

Note that an analogous expression could be derived unsing the constant-volume specific heat and Eq. (3.59), but working with pressure is often more intuitive than volumes, so we will use this relationship from here.

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For a change from a reference state 1 to some other state 2 for a nonreacting system, we can integrate: T2

c¯ p (T ) dT P2 − Ru ln T Pref

s¯2 − s¯ref =

(3.61)

Tref 1

or 0 T2

s¯2 = s¯ref + At 0 K

c¯ p (T ) dT P2 − Ru ln T Pref

Tref 1

(3.62)

P departure T departure

This is analogous to Eq. (3.34) for the absolute enthalpy except the reference temperature chosen is different and there is a temperature and pressure dependence. Because entropy is a measure of the number of possible microstates available, it is only zero at absolute zero, where there is no molecular motion. Thus, the reference point of the entropy of every substance is 0 K, 1 atm. The absolute entropy at some state 2 is the entropy caused by departure from 0 K and 1 atm. Evaluation of the integral in Eq. (3.61) has been done for many ideal gas substances and has been tabulated as a function of temperature: ◦

T

s¯ (T ) =

c¯ p (T ) dT T

(3.63)

0

For gases that have a variable specific heat, the appropriate specific heat polynomial can be integrated. If we are to determine the entropy change for a nonreacting ideal gas from state 1 to state 2, we can show P2 s¯2 (T2 , P2 ) − s¯1 (T1 , P1 ) = s¯ ◦ (T2 ) − s¯ ◦ (T1 ) − Ru ln P      1 f (T )

(3.64)

f (P)

Thus, the entropy change can be broken down into temperature-dependent and pressuredependent portions. Tabulated values for the temperature-dependent s¯ ◦ term for various common fuel cell species are given in the Appendix. Because this is a tabulation of the more precise integration of the specific heat function, it is more accurate than assuming constant specific heats. Determination of Entropy for Nonreacting Liquids and Solids For liquids and solids, one can safely assume incompressibility over any pressure range common to fuel cells so that the pressure dependence of entropy is negligible. Additionally, the specific heat of liquids and solids varies little over a wide temperature range. Using these simplifications,

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the entropy change for a liquid or a solid between two states can be determined to be s¯2 − s¯1 = c¯ ln

T2 T1

(3.65)

Determination of Change in Entropy for Nonreacting Gas Mixture mixture we have s¯ (T )i = s¯ ◦ (T, Pref )i − Ru ln

Pi Pref

For a species in a

(3.66)

and the reference partial pressure is still 1 atm. Note that species i now has a mixture partial pressure, calculated with Eq. (3.37). The entropy of a mixture can be evaluated using a molar or mass averaging among the constituents in the mixture, as in Eq. (3.40). Determination of Change in Entropy for Reacting Gas Mixture The change in entropy for a reacting mixture can be determined in an analogous fashion to the change in enthalpy (of any other intensive parameter of interest) for a reacting mixture. For the generic chemical or electrochemical reaction ν A + ν B → νc C + νd D a  b     Reactants

(3.67)

Products

The entropy change between products and reactants can be evaluated as   ¯s = s¯ P − s¯ R = v i,P (¯si ) P − v j,R (¯si ) R

   Pi Pi ◦ ◦ = v i,P s¯ (T, Pref )i − Ru ln − v j,R s¯ (T, Pref )i − Ru ln Pref P Pref R (3.68) For the total entropy change, we can write S P−R =

n 

n i (¯si ) P −

n 

i=1

  n j s¯ j R

(3.69)

j=1

Gibbs Function (G) The Gibbs function (G) is defined from other thermodynamic properties, enthalpy and entropy, so that it is itself a thermodynamic property: G ≡ H − TS

(3.70)

The Gibbs function is a measure of the maximum work possible at a given state from a constant temperature and pressure reversible process. It can be shown from a combination of the first and second laws of thermodynamics for a simple compressible system that the Gibbs function of a system will always decrease or remain the same for a spontaneous process. Consider the differential of the Gibbs function: dG = dH − T dS − S dT

(3.71)

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From the first law for a simple compressible system at a given constant temperature (T) and pressure (P) with only compression work δ Q − δW = dU = δ Q − P dV

(3.72)

where the inexact differential of work and heat transfer are used because they are not properties but path functions. From the second law of thermodynamics, we know that dS ≥

δQ T

(3.73)

Combining these we can show that dU + P dV − T dS ≤ 0

(3.74)

Considering the differential of absolute enthalpy dH = dU + P dV + V dP

(3.75)

Rearranging, we can show that 0 dH

V dP

(3.76)

T dS ≤ 0

where the pressure differential is zero for this constant pressure and temperature process: 0 dG = dH

T dS

S dT

(3.77)

Plugging Eq. (3.76) into Eq. (3.77), we can show that dGT, p ≤ 0

(3.78)

In other words, the Gibbs function of a system will always be minimized in a spontaneous process (dG < 0). When the Gibbs energy reaches a local minima, where the change is zero (dG = 0), the reaction stops and local thermodynamic equilibrium is achieved, as illustrated in Figure 3.10. The term Gibbs free energy is often used synonymously with Gibbs function. The term free energy is often confusing to people but makes perfect sense in the context of a natural tendency to reduce the chemical energy of a system through a spontaneous reaction. For the Gibbs free energy to increase, external work must be applied to the system to increase the energy state of the system. The Gibbs free energy can also be thought of as the maximum energy available for conversion to useful work. The change in Gibbs energy for a reaction is calculated in the same fashion as other thermodynamic intensive parameters. The absolute molar intensive Gibbs function at a given temperature and pressure is written as g¯ = g¯ ◦f + h¯ − T s¯

(3.79)

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G Local thermodynamic equilibrium can be established

Reaction coordinate

Figure 3.10 Chemical equilibrium is achieved at a minimum in Gibbs function for given temperature and pressure.

For nonreacting mixtures, the change in the Gibbs function between two states will involve only the change in the sensible enthalpy and entropy, as the formation terms will cancel: g¯ 2 − g¯ 1 = g¯ = h¯ 2 − h¯ 1 − T (¯s2 − s¯1 )

(3.80)

For reacting mixtures where the products and reactants differ, the Gibbs formation energy to achieve STP conditions for a given species is required. The Gibbs energy of formation g¯ ◦f is calculated based on 298 K, 1 atm pressure and is chosen to be zero for stable species in their natural state, similar to the enthalpy of formation. For nonreacting mixtures, the Gibbs function is calculated using molar or mass averaging the constituents. For reacting mixtures, the methodology is the same as presented for enthalpy and entropy since the Gibbs function is a combination of them. One point of confusion is common. The Gibbs function of formation and enthalpy at a reference state of 298 K, 1 atm is chosen to be zero for all stable species in their natural state, yet the reference condition of zero entropy is 0 K. Therefore, every species has some entropy at 298 K, and the choice of a zero Gibbs function for a stable species at 298 K seems to conflict with the definition of the Gibbs function in Eq. (3.79). This is because the reference temperatures chosen for the Gibbs function and the entropy are different. However, since we are choosing a reference temperature for the Gibbs function of 298 K, what we actually evaluate in Eq. (3.79) is the change in the Gibbs function from 298 K, 1 atm, to some other state. Thus, we can expand Eq. (3.79) to be g¯ = g¯ ◦f + (h¯ − h¯ ref ) − T (¯s − s¯ref )

(3.81)

where the reference temperature for the enthalpy and entropy is 298 K. Since we are actually evaluating a difference in enthalpy and entropy, the absolute value of the Gibbs function will not be in conflict at reference conditions, despite the apparent discrepancy in the reference point temperatures. For reacting mixtures, the change in Gibbs function can be determined in an analogous fashion to the other parameters. For the generic reaction in Eq. (3.67).   v i,P (g¯ i ) P − v j,R (g¯ j ) R (3.82) g¯ = g¯ P − g¯ R =

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Psychrometrics: Thermodynamics of Moist Air Mixtures

91

Methods for calculating for nonreacting ideal gas mixtures, reacting ideal gas mixtures, liquids, and solids are based on determination of entropy and enthalpy changes in previous sections. Examples of the calculation are given in Section 3.6, where the Gibbs function is used to determine the expected open-circuit voltage (OCV) of a fuel cell.

3.5 PSYCHROMETRICS: THERMODYNAMICS OF MOIST AIR MIXTURES Psychrometrics is the study of nonreacting moist air mixtures and is critical to understand the water balance in low-temperature PEFCs. Nonreacting moist mixtures can be evaluated exactly like other nonreacting gas mixtures, but since engineering with moist air mixtures is so common, additional parameters and special charts have been developed to aid in calculation and analysis. In most fuel cells, water is produced as a product and must be removed from the fuel cell as part of the effluent mixture. In low-temperature PEFCs, the water balance is critical to maintain proper electrolyte conductivity while avoiding electrode flooding. To begin, we will first assume a two-gas mixture of water vapor and another ideal gas mixture, air. In this case, the total atmospheric pressure is the sum of the air and vapor partial pressures: P = Pa + Pv = ya P + yv P

(3.83)

It is important to realize there can be many other moist gas-phase mixtures besides air. Consider a humidified anode fuel mixture of CO2 , CO, H2 , and H2 O vapor. Then, P = PCO2 + PH2 + PCO + Pv

(3.84)

The humidity ratio is defined as the mass of moisture per mass of dry mixture and can also be defined as the rate of moisture mass flow per dry mass flow: ω=

mv m˙ v = m˙ dry m dry

(3.85)

where the dry mixture includes everything but the water vapor. Considering the mixture as an ideal gas (note the water vapor partial pressure is typically low enough that ideal gas behavior can be assumed with little error), we can show that ω=

mv Pv V · MWv /Ru MWv Pv = = · m dry Pdry V · MWdry /Ru MWdry Pdry

(3.86)

If the dry mixture is air, for instance, MWair = 28.85 kg/kmol, and the humidity ratio is defined as ω=

mv 18 Pv Pv Pv = = 0.622 = 0.622 m dry 28.85 Pa Pa P − Pv

(3.87)

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where P is the total pressure, Pv is the water vapor partial pressure, and Pa is the air partial pressure in the humidified mixture. The humidity ratio in a pure hydrogen humidified stream would be ω=

18 Pv Pv Pv mv = =9 =9 m dry 2 PH2 PH2 P − Pv

(3.88)

The relative humidity is a more common parameter known to anyone who has heard or seen a weather forecast. It is defined as the ratio of actual water vapor pressure, Pv , to the saturation water vapor pressure, Psat : RH =

Pv Psat (T )

(3.89)

Equations (3.88) and (3.89) can be related through the vapor pressure Pv . In equilibrium, the RH cannot exceed unity. The saturation pressure (Psat ) is the maximum possible vapor pressure that can be achieved in equilibrium and is solely a function of temperature and completely independent of other gas-phase species. Consider a closed container filled initially with liquid water and dry air, as shown in Figure 3.11. Some of the water molecules will have enough energy to break free of the liquid phase and enter the gas phase, and concomitantly, some of the gas-phase molecules will collide with and rejoin the liquid phase. Eventually, equilibrium will be established between the rate of liquid molecules entering the gas phase and the rate returning to the liquid state, with no net rate of transfer between phases. The vessel will thus have an equilibrium gas-phase mixture of air and vapor at fully saturated (RH = 1 where Pv = Psat ) conditions, given enough time. Now consider heating the vessel. The additional thermal input energy to the liquid will provide enough energy for evaporation of more liquid into the vapor phase, and, over time, a different equilibrium will be established. Several concepts are often misunderstood regarding equilibrium between a liquid and its vapor phase. The first is that every species has a unique saturation pressure relationship

Figure 3.11

Equilibrium between liquid and gas phases in a closed container.

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Figure 3.12

Psychrometrics: Thermodynamics of Moist Air Mixtures

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Saturation pressure versus temperature for water.

with temperature. Water will establish phase equilibrium between the liquid and gas phases that is a function of temperature only, and each species has a unique saturation vapor pressure–temperature relationship. For example, methane will have a different equilibrium vapor pressure at 30◦ C than water. The second major misunderstanding comes from the fact that the phase equilibrium is established between a liquid and its own vapor state. Any other gases present have no effect on the equilibrium saturation vapor pressure. That is, if the gas phase in the container in Figure 3.11 were hydrogen instead of air, the same equilibrium water vapor pressure would be established. If the container were initially evacuated, the final total system pressure established would be the saturation pressure at the system temperature. A plot of the saturation pressure–temperature relationship for water is shown in Figure 3.12. Finally, the saturation pressure can be conveniently curve fit, which is especially useful for modeling: Psat (T )(Pa) = −2846.4 + 411.24 T (◦ C) − 10.554 T (◦ C)2 + 0.16636 T (◦ C)3

(3.90)

This curve fit is accurate from 15◦ C to 100◦ C. Although a polynomial was chosen here, other fits are available [6], are easy to generate based on generally available thermodynamic values, and may have a more accurate fit in different temperature regions. A couple of points are worth noting from Figure 3.12. First, the slope of the change in Psat with temperature is very shallow at typical ambient conditions. Around 20◦ C, there is very little difference in the saturation vapor pressure for a few degrees change in temperature. In terms of fuel cell operation, this means the water present in the ambient air commonly used as the oxidizer actually has very little variation with ambient temperature or humidity conditions, compared to the water exchanged through various modes in an fuel cell operating at elevated temperatures >50◦ C. Although the change in saturation pressure with temperature is modest at room temperature (the typical operating temperature of

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PEFCs is 80◦ C), the saturation pressure is extremely sensitive to temperature. At 80◦ C and 1 atm total pressure, a 1◦ C change is about a 5% change in the saturation pressure. Therefore, for low-temperature PEFCs, heat and water management are major design considerations. For higher temperature fuel cells, the water generated is generally in the vapor state or part of the electrolyte. For operating temperatures above 100◦ C, water is not always in a vapor state. According to Eq. (3.89), if the total system pressure is increased, the RH can still be less than 1 for temperatures above the atmospheric pressure boiling point. This is the physical principle behind a pressure cooker. Since the container can be sealed and pressurized, the water inside will boil, and concomitantly cook the food, at a higher temperature. Example 3.8 Calculation of Maximum Water Uptake in a Flow Given a flow inlet to a 5-cm2 active area fuel cell at 3 atm, 50% RH at 80◦ C, and an anode stoichiometry of 3.0. Determine the maximum possible molar rate of water uptake from the incoming anode flow if the fuel cell is operating at a current density of 0.8 A/cm2 . You can assume the flow rate, pressure, and temperature are constant in the fuel cell. SOLUTION This problem integrates some of our understanding from the previous chapters as well. To achieve water balance, the vapor uptake into the anode and cathode streams plus any liquid water droplets removed from the system must equal the water produced by the reaction. First, we must solve for the molar flow rate of gas into the fuel cell anode. The flow rate of dry gas is given as n˙ H2 = λa

(0.8 A/cm2 )(5 cm2 ) iA =3× = 6.22 × 10−5 mol H2 /s − nF (2 e eq/mol H2 )(96,485 C/eq)

The water mole fraction of the incoming water vapor is RH =

0.5 × 47,684 Pa yv P RH · Psat (T ) ⇒ yv = = = 0.0784 Psat (T ) P 303,975 Pa

where the saturation pressure is found from Eq. (3.90). The maximum possible water uptake in this flow, at RH = 1, would be double the actual input value at RH = 50% (0.157). From the definition of mole fraction yv =

n˙ v n˙ v = n˙ total n˙ dry + n˙ v

Solving for the vapor flow rate input to the fuel cell anode gives n˙ v =

n˙ dry yv (6.22 × 10−5 mol/s) × 0.0784 = 5.291 × 10−6 mol/s = 1 − yv 1 − 0.0784

For the fully humidified maximum, this value is n˙ v =

n˙ dry yv (6.22 × 10−5 mol/s) × 0.157 = 1.158 × 10−5 mol/s = 1 − yv 1 − 0.157

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The maximum uptake is simply the difference in the maximum value in the flow at 100% RH and the actual value input: n˙ v,uptake,max = 5.291 × 10−6 mol/s − 1.158 × 10−5 mol/s = 6.289 × 10−6 mol/s COMMENTS: What we have solved for is the maximum possible uptake of water vapor into the anode flow stream, which may not actually be achieved. Depending on the design, it is quite possible that the flow residence time in the fuel cell is not long enough to achieve the equilibrium condition. We have also assumed constant pressure, temperature, and flow rate to simplify the problem. In reality, there are often variations in these values through the fuel cell, which can even be used to help control the water uptake in advanced designs. Finally, in this problem we only considered the anode, while the complete water balance must include the cathode as well. Evaporation and Condensation Equilibrium thermodynamics cannot predict the rate of phase change and can only be applied to the beginning and ending quasi-equilibrium states. The difference between the actual vapor pressure of the liquid in the gas phase and the maximum saturation pressure is the driving force for evaporation. This is similar to the temperature and voltage potential gradients being the driving forces for heat and ion transport, respectively. The higher the temperature and the dryer the gas phase, the faster the evaporation of the liquid into the gas phase. Conversely, if a moist mixture is suddenly cooled so that the vapor pressure exceeds the saturation pressure at the new temperature conditions, water will condense into liquid until the vapor pressure is equal to the maximum saturation pressure at the new temperature. The rapid cooling and droplet wise condensation of the moist air from our lungs are how we can see our breath on a cold day. It should be emphasized that evaporation and condensation are very complex nonequilibrium topics that are the source of many specialized textbooks. The processes of condensation and evaporation are related to physicochemical parameters, including temperature, vapor pressure, surface tension, surface energy and contact angle, surface impurities, homogeneity and roughness. Phase change is a local phenomenon, and some degree of local supersaturation is required to initiate condensation and desublimation. Note that there is a difference between boiling and evaporation. In boiling, the entire volume of liquid is brought to a temperature where the saturation pressure is at least equal to the atmospheric pressure. The appearance of vapor bubbles occurs volumetrically within the fluid. However, we also know from common experience that, if we leave a pan of water out, it will slowly evaporate into the air with no volumetric vapor bubbles formed, even though the temperature is far below the boiling point. The end result is the same, a dry pan, but the processes of evaporation and boiling are clearly different. The water in the pan will evaporate over time because the air around us is rarely fully humidified. As discussed, evaporation is a surface phenomenon related to the imbalance between the saturation vapor pressure and actual vapor pressure just above the liquid surface. If there is less than full humidification in the ambient gas, the imbalance between the saturation pressure and the actual vapor pressure acts as a driving force for evaporation. The imbalance will drive the vapor pressure above the liquid toward a thermodynamic equilibrium of full saturation. Some molecules in the liquid state at the gas–liquid interface will have enough stored energy to escape the surface and go into the gas phase, cooling the resulting liquid in a process known as evaporative cooling (this is a reason why you feel cold when you get out

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of a swimming pool on a hot day). The cooling liquid must then absorb heat from the surroundings in an amount equivalent to the latent heat of evaporation for the lost mass. Clearly, the volatility of a liquid is related to the intermolecular forces near the surface of the liquid. This can be affected by temperature, impurities, surface morphology, and other factors. If the gas in the room becomes fully saturated and the air is static, a dynamic equilibrium will be established and net evaporation will return to zero. If a saturated gas mixture is cooled, a net flux of gas-phase vapor molecules will condense into the liquid phase upon collision with the liquid surface until a new equilibrium is established at the cooler temperature. Upon condensation to a lower thermal energy state, the new liquid will release thermal energy and heat the droplet in an amount equivalent to the latent heat of fusion for the condensed mass.

3.6

THERMODYNAMIC EFFICIENCY OF A FUEL CELL The process of energy conversion in a fuel cell must satisfy the first law of thermodynamics and conserve energy. The initial chemical bond energy available as the difference between the enthalphy of the products and reactants in a galvanic process is conserved, but it is converted into electrical energy (i.e., current and voltage) and thermal energy (i.e., heat), as discussed in Chapter 2. Since the purpose of a fuel cell is to convert chemical energy into electrical energy, the thermodynamic efficiency of a fuel cell can be written as ηth =

actual electrical work maximum available work

(3.91)

The question to answer now is: What are the actual electrical work and maximum available work for a given process? Maximum Electrical Work for a Reversible Process Consider a generic reversible system with mechanical and electrical work and heat transfer at constant temperature. From the first law of thermodynamics for a simple compressible system dU = δ Q − δW

(3.92)

The work can be divided into mechanical expansion work and electrical work: δW = δW p + δWe = P dV + δWe

(3.93)

For a reversible system, the second law of thermodynamics can be written as δ Q = T dS

(3.94)

The differential change in the Gibbs free energy for a constant-temperature reaction is 0 dG = dH − T dS − S dT

(3.95)

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The differential change in enthalpy for a given reaction is dH = dU + P dV + V dP

(3.96)

dU = T dS − δWe − P dV

(3.97)

We can then show that

By substitution, we can show that −dG = δWe

(3.98)

Since this derivation was done for a reversible system, it is an expression of the maximum electrical work possible from a system. Therefore the change in Gibbs free energy is related to the maximum conversion of chemical to electrical energy for a given reaction. From Eq. (3.78) the direction of spontaneous reaction is that of decreasing free energy. Maximum Expected Voltage (E◦ ) Next, we will consider electrical work. It is generally easier for most people to envision the concept of classical mechanical work, that is, moving a weight through some distance. The concept of electrical work is similar if one considers electrical work to be the moving of an electron through a distance. Consider the energy (work) required to move a given charge: 


J C eq electrons (3.99) w¯ e = nFE = mol reactant eq electrons C       Charge to be passed in coulombs

Work to move a coulomb

Note that here E is not energy; it is voltage. The symbol E is commonly used to designate a voltage based on the concept of electromotive force (EMF). Combining Eqs. (3.98) and (3.99), an expression for the maximum possible reversible voltage of an electrochemical cell can be deduced and is shown as E◦ : −g¯ −G = E◦ = nF nF

for 1 mol oxidized

(3.100)

where E◦ is also called the reversible voltage, because it is the maximum possible voltage without any irreversible polarization losses. This is the maximum possible voltage of an electrochemical cell, since it is derived assuming a reversible process. If we are looking at the redox reaction on a per-mole-of-fuel basis, the absolute Gibbs function is equivalent to the molar specific value. All fuel cell losses are associated with departure from this maximum. Since F is a constant and n is constant for a particular global redox reaction, the functional dependence of the maximum possible voltage of an electrochemical cell is related strictly to the dependencies of the Gibbs free energy, namely temperature and pressure of the reactants and products. Thermal Voltage What if all the potential chemical energy for a reaction went into electrical work? If there were no heat transfer, there would be no entropy change; from Eq. (3.95), dG = dH. In this case, we can show that −H = E th = E ◦◦ nF

(3.101)

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E◦◦ (also shown as Eth ) is known as the thermal voltage for a reaction and is the maximum voltage for a reversible, adiabatic system. Since there is an entropy change associated with every real reaction process, this voltage is merely a limit representing the case of all chemical energy converted into electrochemical work, with no heat transfer or change in available microstates (entropy). The thermal voltage can be simply calculated using the concepts of this chapter. Since enthalpy is only a function of temperature for an ideal gas or liquid, calculation is a straightforward matter. The ratio of maximum expected voltage (E◦ ) to thermal voltage (E◦◦ ) represents the maximum electrical work to the total available potential electrical work, the maximum thermodynamic efficiency possible: ηt,max =

maximum electrical work H − T S −G/n F E◦ = = ◦◦ = maximum available work −H/n F E H (3.102)

Therefore, an expression of the maximum possible thermodynamic efficiency of a fuel cell can be written as ηt,max = 1 −

T S H

(3.103)

Table 3.3 shows some enthalpic, entropic, and Gibbs formation values for many fuel-cellrelated reactants and products at 25◦ C, 1 atm conditions to aid in calculation. Table 3.3 Enthalpy of Formation, Gibbs Energy of Formation, and Entropy Values at 298 K, 1 atm Species

Molecular Formula

Carbon Hydrogen Nitrogen Oxygen Carbon monoxide Carbon dioxide Water vapor Liquid water Hydrogen peroxide Ammonia Hydroxyl Methane Ethane Propane Octane vapor Octane liquid Benzene Methanol vapor Methanol liquid Ethanol vapor Ethanol liquid

Cs H2,g N2,g O2g COg CO2,g H2 Og H2 Ol H2 O2,g NH3,g OHg CH4,g C2 H6,g C3 H8,g C8 H18,g C8 H18,l C6 H6,g CH3 OHg CH3 OHl C2 H5 OHg C2 H5 OHl

Source: From [1].

h¯ ◦f (kJ/kmol)

g¯ ◦f (kJ/kmol)

s¯ ◦ (kJ/kmol · K)

0 0 0 0 −110,530 −393,520 −241,820 −285,830 −136,310 −46,190 39,460 −74,850 −84,680 −103,850 −208,450 −249,910 82,930 −200,890 −238,810 −235,310 −277,690

0 0 0 0 −137,150 −394,380 −228,590 −237,180 −105,600 −16,590 34,280 −50,790 −32,890 −23,490 17,320 6,610 129,660 −162,140 −166,290 −168,570 −174,890

5.74 130.57 191.50 205.03 197.54 213.69 188.72 69.95 232.63 192.33 183.75 186.16 229.49 269.91 463.67 360.79 269.20 239.70 126.80 282.59 160.70

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<

Figure 3.13 Comparison of maximum thermodynamic efficiency for heat engine (Carnot cycle) and fuel cell engine (hydrogen fuel cell, HHV assumed).

Chapter 1 discussed the advantages of the fuel cell in comparison with conventional heat engine technologies and noted the fuel cell (or battery) was not constrained to a Carnot efficiency. At the time it was noted that this does not mean a fuel cell can have unlimited efficiency. Recall from Chapter 2 that the natural limitation on the efficiency for an ideal Carnot cycle heat engine can be shown as ηt,max = 1 −

TL TH

(3.104)

where the TL and TH are the temperatures of heat rejection and heat addition, respectively. Figure 3.13 shows a comparison of the maximum thermodynamic efficiency of an ideal heat engine and an ideal hydrogen fuel cell with liquid water vapor as the exhaust. Several points concerning this plot are useful to keep in mind: 1. The plot shows that the maximum thermodynamic efficiency is not always greater for a fuel cell. At high temperatures, a heat engine can theoretically be more efficient. 2. The plot shows only the maximum possible efficiency, which will not be obtained in practice for the heat engine or fuel cell. For a fuel cell, the efficiency decreases with increasing electrical power, so that it only approaches the theoretical value at open-circuit conditions, where no useful electrical work is produced. 3. The hydrogen fuel cell shows a decreasing efficiency with temperature, but this is not a universal result and depends on the fuel used. Some types of fuels show almost no relationship to temperature, and some show an increasing trend with temperature. This is related to the entropy of reaction, as shown in Figure 3.13 and discussed in greater detail in the following section.

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Relating Temperature Change to Maximum Efficiency Recall the expression for maximum thermodynamic efficiency of a fuel cell, and noting that the enthalpy of reaction for a galvanic (exothermic) process is negative, we can show that ηt = 1 −

T S T S =1− ⇒ sign of ηt ∝ 1 + T S H negative

or ηt (T ) ∝ S

(3.105)

That is, since the absolute temperature is always positive, the dependence of the maximum efficiency varies with temperature, according to the sign of the change in entropy. There are three possibilities, as depicted in Figure 3.13: 1. The entropy change is quite small, and there is almost no variation of maximum thermodynamic efficiency with temperature. 2. The entropy change is significant, and the net change is positive (this would correspond to the presence of more thermodynamic microstates in the product compared to the reactant). In this case the maximum thermodynamic efficiency would increase with temperature. 3. The entropy change is significant, and the net change is negative (this would correspond to the presence of fewer thermodynamic microstates in the product compared to the reactant). In this case the maximum thermodynamic efficiency would decrease with temperature, as in a hydrogen fuel cell. The key to predicting the qualitative relationship between temperature and the maximum thermal efficiency is in the evaluation of the entropy change (number of microstates) between the products and reactants. Comparing the potential microstates available to a solid or liquid, a low-density gas-phase species has much greater entropy. Therefore, the number of microstates varies directly with the number of moles of gas-phase species, and the contribution of liquid- and solid-phase species is comparatively insignificant. This makes sense, because for an ideal gas the volume of a mole of gas at a given temperature and pressure is constant and thus a lower number of moles of gas results in a lower volume of gas and a correspondingly lower entropy. Consider the hydrogen fuel cell overall redox reaction: H2 + 1 O2 −−−−−−→ H2 Ol or g     2  1.5 mol gas

1 mol if gas phase or 0 mol if liquid

The S is proportional to the moles of gas-phase species of products and reactants: S ∝ (n g,P − n g,R )

(3.106)

Here, S is negative, because the product has fewer moles of gas than the reactants. From Eq. (3.105), we can qualitatively predict that the maximum thermodynamic efficiency will

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decrease with increasing operation temperature for this fuel cell, which correctly predicts the actual calculated relationship shown in Figure 3.13. As a second example, consider the direct methane fuel cell overall reaction: (CH4 )g + 2O2 −−−−→ CO2 + 2H2 Og       3.0 mol gas

3.0 mol gas

In this case S is nearly zero, since the moles of gas-phase species of reactants and products are equivalent. In this case, the entropy may be slightly positive or negative depending on the difference between the molecular structures of the products and reactants, but we can qualitatively predict from Eq. (3.105) that the maximum thermodynamic efficiency will be nearly invariant with temperature, which would correspond to the straight line shown in Figure 3.13. Finally, consider the direct formic acid fuel cell overall reaction: HCOOHl + 12 O2 −−−−→ CO2 + H2 Og       0.5 mol gas

2.0 mol gas

In this case, S is positive, since the moles of gas-phase species of the products are greater than the reactants. We can qualitatively predict that the maximum thermodynamic efficiency will actually increase with temperature, which would correspond to the rising line in Figure 3.13. At a high enough temperature, we expect the maximum thermodynamic efficiency to be greater than 100%! How can this possibly be true? When the theoretical maximum thermodynamic efficiency is greater than 100%, it means that, thermal energy is taken from the environment surrounding the fuel cell and converted into electrical potential. Although use of ambient heat to generate power with an efficiency greater than 100% seems like an amazing possibility, it is of course not realistic in practice. Removal of heat from the environment at a lower temperature than the fuel cell and transforming this heat into electrical energy would be a violation of the second law by pumping heat from a lowtemperature to a high-temperature reservoir without doing work. This process can work if the ambient temperature is higher than the fuel cell, but then the actual efficiency must then include the energy required to increase the ambient temperature above that of the fuel cell. Le Chatelier’s Principle: Open-Circuit Voltage Dependence on Temperature and Pressure Le Chatelier’s principle can be stated a follows: “Any change in one of the variables that determines the state of a system in equilibrium causes a shift in the position of equilibrium in a direction that tends to counteract the change in the variable under consideration” [7]. There is a deep meaning beyond the field of fuel cells to this statement, and it can be considered an incarnation of nature’s balance. In the context of the fuel cell, Le Chatelier’s principle can be applied to understand and predict the effect of a change in temperature or pressure on voltage. Nature tries to balance out new stresses to the system to a change in equilibrium. If the temperature or pressure is increased, the new equilibrium will be shifted to counteract the effect of the temperature or pressure change. Consider the hydrogen fuel cell global reaction: H2 + 1 O2 −−−−→ H2 Og     2  1.5 mol gas

1 mol gas phase

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1. If pressure of the reactants increases, nature will work to relieve the new stress, favoring the forward reaction toward hydrogen oxidation, because this will reduce the number of gas-phase moles to counteract the increase in pressure. The effect on voltage would be to shift the reaction toward the products, which would increase the voltage (i.e., potential for reaction) at a given condition. 2. If the pressure of the reactants decreases, nature will work to relieve the new stress, favoring the reverse reaction toward reactants, to counteract the decrease in pressure. The effect on voltage would be to shift the reaction toward the reactants, which would decrease the voltage at a given condition. Later in this chapter we will see the mathematical reasoning for this and develop the Nernst equation to predict the expected OCV as a function of temperature and pressure. Using this principle, however, we can already qualitatively predict the functional dependence of temperature and pressure on the OCV. Heating Value For reactions involving water as a product, there is a choice in the calculation of thermodynamic voltages between a high heating value (HHV) and a low heating value (LHV), defined as follows for a given reaction: High Heating Value: It is assumed all the product water is in the liquid phase. Low Heating Value: It is assumed all the product water is in the gas phase. Note that calculation based on HHV or LHV is an arbitrary decision and does not necessarily correspond to the actual physical state of the product water at the fuel cell electrode. The terms HHV and LHV are used in combustion calculations as well, where the product water is nearly always in the gas phase. The difference between the two values is proportional to the latent heat of vaporization of the liquid. Use of the LHV (gas-phase vapor product) will result in a lower calculated thermal voltage, since some energy is used for the latent heat of vaporization of the liquid. In practice, the LHV is completely appropriate for hightemperature fuel cells, but the HHV is also commonly used. An important point regarding low-temperature fuel cells that is often confusing is that the choice of HHV or LHV is arbitrary and 100◦ C is not a point of demarcation between the two. Often 100◦ C is thought of as a natural boundary between the HHV and LHV because it is the phase change temperature of water at 1 atm pressure. The delineation between liquid and gas, however, is more complex and is related to the local vapor pressure and total pressure, as discussed in Section 3.5. Example 3.9 Calculation of Efficiencies and Trends in OCV (a) Use Le Chatelier’s principle to predict if the maximum possible voltage of a direct liquid methanol fuel cell, E◦ , will increase or decrease with temperature. Assume a gas-phase product water product. (b) Calculate the maximum HHV and LHV cell voltage E◦ for a methanol–air fuel cell. Assume a gas-phase water product and all constituents are at 1 atm, 298 K. (c) Predict if the maximum possible thermodynamic efficiency ηth of a hydrogen fuel cell will increase or decrease with temperature.

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(d) Prove your result in part (c) by calculating the maximum thermodynamic efficiency of a hydrogen fuel cell at 298 and 1000 K. Assume LHV and all constituents are at 1 atm. (e) What do you notice about the voltages calculated for a hydrogen cell compared to the methanol fuel cell? SOLUTION

(a) Consider the direct methanol fuel cell overall reaction: CH3 OHl + 32 O2 → 2H2 Og + CO2

Since there is 3 mol of gas in the products, compared to 1.5 mol in the reactants, the entropy increases with the forward reaction. Even at 500 K, where the methanol is in vapor form, there are still more moles of gas phase in the products than in the reactants. If temperature is increased, we expect the reverse reaction to be more favored, reducing OCV. (b) n m   n i g¯ P,i − n j g¯ R, j G = products − reactants = H = products − reactants =

i=1

j=1

n 

m 

n i h¯ P,i −

i=1

n j h¯ R, j

j=1

For the HHV G = products − reactants =

n 

n g¯ P,i −

m 

i

i=1

n j g¯ R, j

j=1

Since we are at 1 atm for all constituents, 298 K, only the Gibbs function of formation remains, which we can get from Table 3.3: G = products − reactants = (2 mol)(−237,180 J/mol) + (1 mol)(−394,380 J/mol)   − (1 mol)(−166,290 J/mol) − 32 mol (0 J/mol) = −702,450 J Maximum OCV = E◦ (298): E ◦ (298) = −

−702,450 G = = 1.21 V nF 6 × 96,485

For the LHV (gas-phase water product) G = products − reactants = (2 mol)(−228,500 J/mol) + (1 mol)(−394,380 J/mol)   − (1 mol)(−166,290 J/mol) − 32 mol (0 J/mol) = −685,090 J Maximum OCV = E◦ (298): E◦ = −

−685,090 G = = 1.18 V nF 6 × 96,485

So 0.03 V of potential is used to vaporize the water in the product at these conditions.

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(c)

H2 + 12 O2 −−−−→ H2 Og       1.5 mol gas

1 mol gas phase

The maximum possible thermodynamic efficiency ηth of a hydrogen fuel cell will decrease with temperature, because the entropy change is negative (for both HHV and LHV assumptions), and ηt (T ) ∝ S (d) Prove your result in part (c) by calculating the maximum thermodynamic efficiency of a hydrogen fuel cell at 298 and 1000 K. Assume LHV and all constituents are at 1 atm. What do you notice about the voltage calculated compared to the methanol fuel cell? The hydrogen fuel cell overall reaction is H2 +

O2 → H2 O n m   G = products − reactants = n i g¯ P,i − n j g¯ R, j 1 2

i=1

H = products − reactants =

n  i=1

j=1

n i h¯ P,i −

m 

n j h¯ R, j

j=1

For the gas-phase water product, assuming 1 mol of hydrogen reacts, at 298 K G = products − reactants = (1 mol)(−228,590 J/mol)   − 12 mol (0 J/mol) − (1 mol)(0 J/mol) H = products − reactants = (1 mol)(−241,820 J/mol)   − 12 mol (0 J/mol) − (1 mol)(0 J/mol) Maximum OCV = E◦ : E ◦ (298) = −

−228,590 G = = 1.18 V nF 2 × 96,485

Thermal voltage E◦◦ : E ◦◦ (298) = −

−241,820 H = = 1.25 V nF 2 × 96,485

Maximum thermodynamic efficiency ηth : ηth,max (298) =

1.18 V −G/n F = = 0.94 −H/n F 1.25 V

At 1000 K G = 1[g¯ ◦f + h¯ s − T (¯s1000 − s¯298 )]H2 O − 12 [g¯ ◦f + h¯ s − T (¯s1000 − s¯298 )]O2 − 1[g¯ ◦f + h¯ s − T (¯s1000 − s¯298 )]H2

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

 1000  1000   ¯ p,H2 O c c¯ p,H2 O dT − T  = 1 −237,180 + dT T 298

298

H2 O

  1000 1000   ¯ p,O2 c 1 dT c¯ p,O2 dT − T  − 0+ 2 T 

298

 − 1 0 +

298

  1000  c¯ p,H2  dT c¯ p,H2 dT − T  T

O2

1000 

298

298

H2

Using the polynomial expressions for the specific heat and an analytical solver on a computer, the above expression can be solved: G = −223,766 kJ Similarly, the total enthalpy change can be found:   1000  H = 1 −285,830 + c¯ p,H2 O dT 298





1000 

− 1 0 +

c¯ p,H2 dT

298

  1000  1 c¯ p,O2 dT − 0+ 2

H2 O

298

O2

= −247,876 kJ

H2

Maximum OCV = E◦ (1000): E ◦ (1000) = −

−228,590 G = = 1.16 V nF 2 × 96,485

Thermal voltage E◦◦ (1000): E ◦◦ (1000) = −

−220,876 H = = 1.28 V nF 2 × 96,485

Maximum thermodynamic efficiency ηth : ηth,max (1000) =

1.16 V −G/n F = = 0.90 −H/n F 1.28 V

So the maximum thermodynamic efficiency does decrease with temperature, as predicted in part (c). (e) The voltages calculated for the methanol- and hydrogen-based fuel cells were similar, around 1.2 V. This trend is continues despite the choice of fuel. The higher heat of formation is also accompanied by a greater number of electrons per mole of fuel, n. The result is that most fuels have a similar range of predicted OCV. COMMENTS: Note that the actual OCV is also a function of the mole fractions of the constituents and several other factors, so that the calculated value is only the maximum

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potential value for unit activity (i.e., 1 atm of all constituents). Pressure variation also results in a voltage change, as described in the following section.

3.7

MAXIMUM EXPECTED OPEN-CIRCUIT VOLTAGE: NERNST VOLTAGE While the thermal (E◦◦ ) voltage is a function of only temperature, the reversible voltage (E◦ ) is actually a function of temperature and pressure of the reactants and products. The Nernst equation is an expression of the maximum possible open-circuit (zero-cell-current) voltage as a function of temperature and pressure and is an expression of an established thermodynamic equilibrium. Consider a global redox reaction in a fuel cell: ν A A + ν B B ↔ νC C + ν D D

(3.107)

where the v’s are the stoichiometric coefficients of the balanced electrochemical reaction. From thermodynamics of systems in equilibrium [1] $

aν A aνB G = G (T ) − Ru T ln νA νB aC C a D D

%

◦

(3.108)

where the a’s are the thermodynamic activity coefficients for the reacting species. To convert to voltage, we can divide by nF: $ % a νA A a Bν B −G ◦ (T ) Ru T ln ν ν + E(T, P) = nF aC C a D D  nF     I

(3.109)

II

where I is the temperature dependence on the voltage evaluated at 1 atm pressure for all components and II accounts for the thermodynamic activity dependence on the Nernst voltage. The thermodynamic activity can be calculated or approximated in several ways: 1. For a concentrated solution, the activity coefficient of the species is taken to be unity. 2. For an ideal gas, a = Pi /P◦ , where Pi is the partial pressure of the species of interest and P◦ is the reference pressure, 1 atm (101,325 Pa). 3. For water vapor, the partial pressure of the vapor cannot exceed the saturation pressure, Psat , which is a function of temperature. Thus, the reference pressure is set to Psat , and a = Pv /Psat , which is the relative humidity, RH. This can normally be considered to be 1.0 in the immediate molecular region of the water-generating electrode. This is a reasonable assumption because water generation is always at the catalyst surface, and the activity of water here is 1. Also, the reaction itself is not limited by the product water concentration at this surface. 4. For a dilute solution, a more complex theory is beyond the scope of this text. This is treated in advanced electrochemistry texts such as [8].

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For an ideal gas reaction mixture, we can substitute the partial pressures for the activities in Eq. (3.109): ' & (PA /P ◦ )ν A (PB /P ◦ )ν B −G ◦ (T ) Ru T (3.110) E(T, P) = + ln (PC /P ◦ )νC (PD /P ◦ )ν D nF nF where the partial pressures are evaluated at the particular electrode where the reaction involving the species occurs. Using this expression, we can solve for the expected maximum (Nernst) voltage for a given fuel cell reaction. Two important points are as follows: 1. The Nernst equation is a result of the equilibrium established at the electrode surfaces. A significant gradient can exist between the concentration of a species in the channel of a fuel cell and the electrode, especially under high-current-density conditions, which cannot be considered a true thermodynamic equilibrium situation anyway. 2. Only species directly involved in the electrochemical reaction of Eq. (3.107) are represented directly in the activity terms of Eq. (3.109). Species not participating in the electrochemical charge transfer reaction only indirectly alter the voltage through the species mole fractions of the participating species. To solve problems using the Nernst equation, the following steps should be taken: Step 1: Write down the Nernst equation (3.109) in symbols. Step 2: Determine the number of electrons released per mole of fuel oxidized (n); then determine the stoichiometric coefficients (ν’s) of the balanced overall cell redox reaction equation. Step 3: Determine the activities of all reactants/products and insert into Eq. (3.109). Step 4: Reduce as needed for convenience to solve. Example 3.10 Nernst Equation for Hydrogen Air Fuel Cell Given a hydrogen air fuel cell operating at 353 K. Solve for the expected LHV open-circuit voltage if the hydrogen and water vapor mole fractions in the anode are 0.8 and 0.2, respectively, and the oxygen, nitrogen, and water vapor mole fractions in the cathode are 0.15, 0.75, and 0.1, respectively. The cathode and anode pressures are 3 and 2 atm, respectively. SOLUTION

For an H2 + 12 O2 → H2 O cell, the Nernst equation can be written as ' & Ru T aH2 (aO2 )1/2 −G ◦ (T ) + ln E(T, P) = nF nF aH2 O

Substituting in the proper activity coefficients for the ideal gases, we can reduce this to
 (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 Ru T ln E(T, P) = E ◦ (T ) + 2F yH2 O Pcathode /Psat (T ) The first term on the right, the standard voltage E◦ (T), can be determined as E ◦ (T ) =

H (T ) − T S(T ) −G ◦ (T ) =− nF nF

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Recall H P–R =

 n 

  m  − n j h¯ j 

 n i h¯ i

i=1

j=1

P

R

For the reacting mixture, we can write 

T=353

H P–R = h¯ ◦f,H2 O +

 c¯ P,H2 O (T ) dT

Tref =298

 − h¯ ◦f,H2 +



T=353

Tref =298

−

1  ¯◦ h f,O2 + 2

H2 O

T=353

 c¯ p,o2 (T ) dT

Tref =298

O2

 c¯ p,H2 (T ) dT H2

We can either directly integrate the specific heat functions or assume constant specific heat. Since the operating temperature is only about 50 K above the standard temperature, there is not much error associated with assuming a constant specific heat at an average temperature of 325 K: " " # # H = h¯ ◦f,H2 O + c¯ p,H2 O,ave (353 − 298) H2 O − 12 h¯ ◦f,O2 + c¯ p,O2 ,ave (353 − 298) O2 " # − h¯ ◦f,H2 + c¯ p,H2 ,ave (353 − 298) H2

The heats of formation are available in thermodynamics reference books, and online, Tables 3.2 and 3.3. The average specific heats can be found by using an average temperature of 325 K in Eqs. (3.24), (3.25), and (3.28): c¯ p (325)H2 ,ave = [3.057 + 2.677 × 10−3 (325) − 5.810 × 10−6 (325)2 + 5.521 × 10−9 (325)3 − 1.812 × 10−12 (325)4 ]Ru = 28.9 kJ/kmol · K c¯ p (325)O2 ,ave = [3.626 − 1.878 × 10−3 (325) + 7.055 × 10−6 (325)2 − 6.764 × 10−9 (325)3 + 2.156 × 10−12 (325)4 ]Ru = 29.5 kJ/kmol · K c¯ p (325)H2 O,ave = [4.070 − 1.108 × 10−3 (325) + 4.152 × 10−6 (325)2 − 2.964 × 10−9 (325)3 + 0.807 × 10−12 (325)4 ]Ru = 33.7 kJ/kmol · K Plugging in all the numbers, we can solve for the change in enthalpy for the reaction for a LHV solution: H = [−241,820 + 33.7 (353 − 298)]H2 O − 12 [29.5 (353 − 298)]O2 − [28.9 (353 − 298)]H2 = −242,370 kJ

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The change in entropy with respect to temperature can be found: 

T=353

S = s¯ ◦f,H2 O +

Tref =298



− s¯ ◦f,H2 +

 c¯ p,H2 O (T ) dT  T

T=353

Tref =298

 1 ◦ s¯ f,O2 + − 2 H2 O



T=353

Tref =298

 c¯ p,o2 (T ) dT  T O2

c¯ p,H2 (T ) dT  T H2

Again, the specific heat terms can be easily integrated, but the error is quite small in assuming constant specific heats at an average temperature. The entropy of formation at 1 atm pressure is available in thermodynamics reference books and the Appendix. Plugging in the numbers we find that 

353 1 353 205.0 + c¯ p,O2 ,ave ln − S = 188.7 + c¯ p,H2 O,ave ln 298 H2 O 2 298 O2 
353 − 130.57 + c¯ p,H2 ,ave ln = −43.61 kJ/K 298 H2 Now we can solve for the reversible voltage E◦ : E ◦ (T ) =

H (T ) − T S(T ) −242,370 + 353 × 43.61 −G(T ) =− = = 1.176 V nF nF 2 × 96,485

The pressure effect is more directly calculated:
 Ru T (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 ln 2F yH2 O Pcathode /Psat (T )
 (0.8 × 2 atm/1 atm)(0.15 × 3 atm/1 atm)1/2 [8.314 J/(mol · K)](353 K) ln = (2 eq/mol)(96,485 C/eq) 1 = 7.92 mV where we have assumed the relative humidity at the cathode electrode surface is 1.0 since water is generated at this location and the reaction is limited not by the amount of water but by the amount of reactants. Finally, the maximum expected voltage can be determined: ' & aH2 O (aO2 )1/2 Ru T = 1.176 + 0.00792 ln E(T, P) = E (T ) +   = 1.184 V nF aH2 O ◦

3 Partial pressure effect

COMMENTS: The species chosen in the Nernst equation pressure term are only the species which participate in the overall electrochemical reaction. For example, the nitrogen in the cathode is not represented directly since it does not participate in the electrochemical

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reaction. Inert species do have an effect on the Nernst voltage, though, through reduction of the mole fraction of the active species. Also note that the activity values use the pressure of the electrode where the reacting species is located. That is, even though there is water at the anode, it is inert in terms of the hydrogen oxidation reaction and only a participant in the electrochemical reaction at the cathode. While the Nernst voltage is easily calculated using a computer program, hand calculations can be very tedious, especially considering the fuel cell temperature is usually confined to a narrow range for a particular fuel cell type and the thermodynamic pressure effect is small. Thus, constant specific heat assumptions are usually appropriate. The Nernst equation can be used to determine the expected thermodynamic effect of changes in species concentration. Looking at Example 3.10, however, the pressuredependent part of the equation is a relatively small component of the equilibrium voltage. Essentially, this term corrects for the fact that the constituents are not all at unit activity. As long as the ratio of reactant activity terms to product activity terms in Eq. (3.109) are greater than unity, the net effect will be to increase the voltage. This is also consistent with the results from application of Le Chatelier’s principle. That is, changes which increase the ratio of reactant to products tend to shift the reaction to a higher voltage. So we expect that any action to increase the partial pressure of hydrogen at the anode or oxygen at the cathode in a hydrogen air fuel cell would increase the thermodynamic expected OCV. Keep in mind that, under generation of current, reactions at each electrode take the system away from a true thermodynamic equilibrium and kinetic effects will also impact the voltage, but the qualitative effect of a gas concentration shift will remain the same. Example 3.11 Thermodynamic Effect of Oxygen Enhancement Given an H2 –air fuel cell operating at 100◦ C with vapor phase water as the product. Determine the approximate expected change in voltage if air is replaced with oxygen, with all else remaining the same. SOLUTION The only difference between air and oxygen is the mole fraction of oxygen in the cathode gas:
 (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 Ru T ln E(T, P)air − E(T, P)O2 = E ◦ (T ) + 2F yH2 O Pcathode /Psat (T )
' & (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 Ru T ln − E ◦ (T ) + 2F yH2 O Pcathode /Psat (T )   (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 ln yH2 O Pcathode /Psat (T ) Ru T   E(T, P)O2 − E(T, P)air = 2F ln (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 yH2 O Pcathode /Psat (T )

=


1 Ru T 8.314 × 353 (1)1/2 = = +11.87 mV ln ln 2F (0.21)1/2 2 × 96,485 0.210.5

COMMENTS: Based on thermodynamics alone, we expect about a 12-mV increase in voltage going from an air to a pure oxygen oxidizer. Since air is essentially free, this seems small. However, the actual increase in performance one gets from using pure oxygen is much greater than this because of kinetic effects, which are discussed in Chapter 4. Despite

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the increase in performance, however, use of pure oxygen is rarely justified in terrestrial fuel cell applications due to increased cost, oxidizer storage requirements, and safety concerns. Space applications, where pure oxygen is already available for liquid rocket propulsion, do use pure oxygen, however. Example 3.12 Thermodynamic Effect of a Pressure Increase Given an H2 –air fuel cell operating at 60◦ C with vapor-phase water as the product. Determine the approximate expected change in thermodynamic maximum OCV if the cathode pressure is doubled and all else stays the same. SOLUTION E(T, P) p2 − E(T, P) p1


 (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 Ru T ln = E (T ) + 2F yH2 O Pcathode /Psat (T ) &
' (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 Ru T − E ◦ (T ) + ln 2F yH2 O Pcathode /Psat (T )   (yH2 Panode /P ◦ )(yO2 Pcathode /P ◦ )1/2 yH2 O Pcathode /Psat (T ) Ru T ln (Pcathode,2 )1/2 Ru T =  = ln ◦ )(y ◦ )1/2 (y P /P P /P O2 cathode 2F ln H2 anode 2F (Pcathode,1 )1/2 ◦

yH2 O Pcathode Psat (T )

=

8.314 × 353 ln(20.5 ) = +5.27 mV 2 × 96,485

COMMENTS: The actual increase in performance expected from the thermodynamics is smaller than what is typically observed in practice. There is also a strong kinetic effect, which is discussed in Chapter 4. Also, we have assumed that at the catalyst surface, the cathode is fully humidified, so that the activity of the cathode water vapor is unity for both the high- and low-pressure cases at the cathode surface. Example 3.13 Expected OCV

Given a H2 –O2 PEFC with the following properties: H2 + 12 O2 → H2 O

Anode: yH2 = 40%, yH2 O = 20%, yO2 = 5%, yN2 = 35%, pressure = 4 atm, and λa = 1.5. Cathode: yO2 = 20%, yH2 O = 10%, yN2 = 70%, pressure = 6 atm,and λc = 2.5. Find: (a) Maximum expected OCV at 90◦ C (b) Change in voltage if we take our cathode down to 3 atm, all else the same (c) Ratio of initial to final voltage expected if we boost oxygen mole fraction to 40% and reduce nitrogen fraction to 50% in the cathode SOLUTION

(a) First we find the reversible voltage at 90◦ C, E◦ (363):

H = [−241,820 + 33.5(363 − 298)]H2 O − 12 [0 + 29(363 − 298)]O2 − [0 + 26.5(363 − 298)]H2 = −249,907 J

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where the specific heats are assumed to be constant and evaluated at appropriate mean temperatures. Assuming constant specific heats and looking up the values for the reactants, we can solve for the entropy change: ' &
' &
363 363 1 205.03 + 29 ln S = 188.72 + 33.5 ln − 298 H2 O 2 298 O2 ' &
363 − 130.57 + 26.5 ln = −45.84 J/K 298 H2 The Gibbs energy change is G ◦ (T ) = H (T ) − T S(T ) = −249,907 J − (363 K)(−45.84 J/K) = −233,265 J Now we can solve for the maximum reversible voltage at 90◦ C, including only temperature effects: 
−G ◦ (T ) −233,265 J ◦ = E(T ) = − = 1.21 J/C = 1.21 V nF (2 e− eq/mol)(96,485 C/eq) The partial pressures of the reacting species are accounted for by the Nernst equation: $ % a νA A a Bν B Ru T −G ◦ (T ) + ln ν ν E(T, P) = nF nF aC C a D D Assuming ideal gas activities, we can plug in the numbers for the activity terms: $ % & ' a νA A a Bν B (yH2 Pa /P ◦ )(yO2 PC /P ◦ )1/2 Ru T (8.314 J/mol · K)(363 K) ln ν ν ln = nF aC C a D D (2 e− eq/mol)(96,485 C/eq) yH2 O Pc /Psat (T ) & ' (yH2 Pa /P ◦ )(yO2 PC /P ◦ )1/2 (8.314 J/mol · K)(363 K) ln (2 e− eq/mol)(96,485 C/eq) yH2 O Pc /Psat (T ) $

 % 0.4 × 4 0.2 × 6 1/2 = (0.01564 J/C) ln = 0.0088 V 1 1 =

So the various pressures and concentrations have the effect to boost the excepted OCV by 8.8 mV. Adding the temperature and activity contributions together, we have our Nernst voltage: $ % a νA A a Bν B Ru T −G ◦ (T ) + ln ν ν E(T, P) = = 1.21 + 0.0088 = 1.22 V nF nF aC C a D D

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(b) The change in voltage if we take our cathode down to 3 atm and all else stays the same is calculated as follows: & ν A νB ' −G ◦ (T ) RT aA aB E(T, P) = + ln νC nF nF aC a νDD & ν A ν B '
Ru T aA aB −G ◦ (T ) + ln νC E 2 (T, P2 ) − E 1 (T, P1 ) = nF nF aC a νDD 2 & ν A ν B '
Ru T aA aB −G ◦ (T ) + ln νC − nF nF aC a νDD 1

& ν A ν B ' & ν A ν B ' Ru T Ru T aA aB aA aB = − ln νC ln ν D nF nF aC a D aCνC a νDD 1 2 Recall ln(a) − ln(b) = ln(a/b):

$" ν ν # % a AA a BB /aCνC a νDD 2 Ru T = ln " ν A ν B νC ν D # nF a A a B /aC a D 1   
( yH2 Pa /P ◦ )( yO2 PC /P ◦ )1/2 yH2 O Pc /Psat (T )  Ru T 
2  ln  E 2 (T, P2 ) − E 1 (T, P1 ) = 1/2   ◦ ◦ nF ( yH Pa /P )( yO PC /P ) 2

2

yH2 O Pc /Psat (T )

1

  (0.4×4/1)(0.2×3/1)1/2  

=

1 8.314 × 363  2  ln  (0.4×4/1)(0.2×6/1)1/2 2 × 96,485 1


= 0.01564 ln

((1.5)1/2 /1)2 ((3)1/2 /1)1

1




= 0.01564 ln

1.51/2 31/2



= −0.0827 V (c) The ratio of initial to final equilibrium OCV expected if we boost oxygen mole fraction to 40%, and reduce nitrogen fraction to 50% in the cathode is calculated as: 
( yH2 Pa /P ◦ )( yO2 PC /P ◦ )1/2 E ◦ (T ) + RnuFT ln yH2 O Pc /Psat (T ) E 1 (T, P2 ) 1
= ◦ ◦ 1/2 E 2 (T, P2 ) y P /P y P /P )( ) ( H a O C R T 2 2 E ◦ (T ) + nuF ln yH O Pc /Psat (T ) 2

=

=

1.21 + 0.01564 ln 1.21 + 0.01564 ln

 

(0.4×4/1)(0.2×6/1) 0.1×6/0.75

1/2

(0.4×4/1)(0.4×6/1)1/2 0.1×6/0.75

2

 1 2

1.21 + 0.01564 ln(0.21/2 )1 = 0.995 or 99.5 % 1.21 + 0.01564 ln(0.41/2 )2

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COMMENTS: Note the appropriate pressure and mole fractions are chosen based on the global oxidation or reduction equation and from which electrode the products/reactants are formed/consumed. If the species is not a reactant in the primary electrode reaction (e.g., the oxygen at the anode in the example), it does not appear directly in the Nernst equation and only indirectly affects the voltage by changing the mole fractions for the active species. Also, it is important to emphasize again that the Nernst equation accounts only for the thermodynamic equilibrium effect of concentration change, and in practice, a change in the mole fraction has a greater effect than predicted above due to kinetic effects not yet accounted for. In Chapter 4, the voltage loss from nonequilibrium reaction kinetic losses will be accounted for.

3.8

SUMMARY The purpose of this chapter was to introduce the reader to the thermodynamics of electrochemical reactions and provide a linkage between macroscopic thermodynamic measurable variables such as temperature and pressure and the expected voltage in electrochemical reactions. The ideal gas equation of state was examined, and several alternative methods with improved accuracy were discussed. In some situations involving fuel cells, especially in high-pressure gas storage, significant error can result if the ideal gas law is used without some form of correction. The generalized compressibility chart can be used to determine the compressibility factor Z for most gases, but unfortunately it is not well suited for hydrogen without correction or use of a hydrogen-specific compressibility chart: Pv =Z n Ru T The physical meanings of many thermodynamic parameters such as specific heat, enthalpy, entropy, and the Gibbs function were discussed, and several methods for determining their values for nonreacting and reacting liquid- and gas-phase mixtures were discussed. The heat of formation, sensible enthalpy, and latent heat of phase change make up the total enthalpy of a substance at a given temperature: h 2 = h ◦f + h s + LH The partial pressure of a species i is shown as Pi = yi P where P is the total mixture pressure and yi is the mole fraction of species i, defined as yi =

ni n˙ i = n˙ total n total

where ni is the number of moles of species i and ntotal is the total number of moles in the mixture. The n˙ i and n˙ total terms represent the molar flow rates of species i and the mixture, respectively. The sum of the partial pressures equals the total mixture pressure and the sum of the mole fractions equals 1:   and yi = 1 Pi = P

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Summary

115

Nonreacting relationships used to calculate various molar specific mixture properties were discussed, in particular x¯mix =

n 

yi x¯i

1=1

The fundamental relationships of psychrometrics, the science of moist mixtures, were presented, including discussion of the saturation pressure and relative humidity. The relative humidity is defined as the ratio of actual water vapor pressure, Pv , and saturation water vapor pressure, Psat : RH =

Pv Psat (T )

where the saturation pressure is solely a function of temperature and has been curve fit to the form for 15–100◦ C Psat (T )(Pa) = −2846.4 + 411.24T (◦ C) − 10.554T (◦ C)2 + 0.16636T (◦ C)3 The maximum possible reversible voltage of an electrochemical cell is −G = E◦ nF The thermal voltage, derived assuming all the potential chemical energy for the reaction went into electrical work, is −H = E th = E ◦◦ nF The ratio of maximum expected voltage (E◦ ) and thermal voltage (E◦◦ ) represents the maximum thermodynamic efficiency possible: ηt,max =

E◦ maximum electrical work T S = ◦◦ = 1 − maximum available work E H

For reactions involving water as a product, there is a choice in the calculation of thermodynamic voltages between a HHV, where all water is assumed in the liquid phase, and a LHV, where, from an energy perspective, all water is assumed to exist in the gas phase. The Nernst equation was derived to show the reversible cell voltage as a function of temperature and pressure. For an ideal gas mixture: ' & Ru T (PA /P ◦ )ν A (PB /P ◦ )ν B −G ◦ (T ) + ln E(T, P) = nF nF (PC /P ◦ )νC (PD /P ◦ )ν D It should be emphasized that the thermodynamic foundation established in this chapter is valid only for true or quasi-equilibrium states. During fuel cell operation, true equilibrium is only close to being achieved under zero-power conditions, and kinetic effects are also prevalent in addition to thermodynamic effects. These are discussed in the following chapter.

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Thermodynamics of Fuel Cell Systems

APPLICATION STUDY: FINDING APPROPRIATE INTERNET RESOURCES Obviously, not all Internet resources contain accurate information. From the first two application studies in Chapters 1 and 2, you may have found a variety of information that is sometimes conflicting. The Internet is an evolving source of technical information available to engineers, and when reliable resources are used, the Internet greatly increases the speed and portability of engineering analysis. Some questions should be asked when consulting an Internet resource: (1) What is the motivation of the web page? (2) Is the web page technically reviewed for accuracy? Recalling the application study in Chapter 1, it is relatively easy to find resources that support the availability of platinum for fuel cell use. Some of these resources, however, are based on studies supported by groups that benefit from the sale of platinum and are not purely scientific in nature. Others, however, are scientifically based and peer reviewed. It is often left to the engineer to discern the difference when using Internet resources in analysis. In this assignment, you are asked to find five reliable resources that contain technical information on fuel cells and five reliable sources that contain thermodynamic data that can be used for analysis of fuel cells. A great place to start for thermodynamic data is http://webbook.nist.gov/chemistry/fluid/. This site contains accurate thermodynamic data for many species from the U.S. National Institute of Standards and Technology. This site can supplant most thermodynamic tables in textbooks and is therefore useful when a textbook is unavailable. There are many sites like this, of varying utility. List each and summarize the content available on the fuel cell information and thermodynamic data sites you choose and discuss how each site is motivated (why is it even on the Web?) and how or if the veracity of the information presented is checked.

PROBLEMS Calculation/Short Answer Problems 3.1 Consider a pure oxygen tank storage system for a fuel cell used in a space application. What mass of oxygen can be stored in a 2-m3 tank at 34 MPa, 20◦ C. Compare the results you get with the ideal gas law, the van der Waals EOS, and the generalized compressibility chart. Using the generalized compressibility chart, determine at what storage pressure the correction on the ideal gas law is 5%? 3.2 Using the generalized compressibility chart for hydrogen (with H2 correction) and oxygen, in what temperature and pressure range would you consider the ideal gas law to be <95% accurate? 3.3 Complete a first-law analysis of a fuel cell system in symbols only. Include flux of gas in and out as well as heat and electricity generated. Consider the control volume to be the fuel cell itself. 3.4 Plot the relationships for molar specific heat of hydrogen, air, and water vapor given in Eqs. (3.24), (3.27), and (3.28), respectively. Over what temperature would you estimate that you can consider the specific heats constant?

3.5 Do you expect gas-phase dimethyl ether (CH3 OCH3 ) to have a greater or lower constant-pressure specific heat than hydrogen? Why? 3.6 Determine the mass fractions of a gas-phase mixture with mole fractions of hydrogen, carbon dioxide, and water vapor of 30, 30, and 40%, respectively. 3.7 For a mixture of 20% H2 , 30% H2 Ov , and 50% CO2 by volume, determine the mixture molecular weight and enthalpy at 350 K. 3.8 Determine the change in enthalpy and entropy for a stoichiometric (balanced) hydrogen–air redox reaction, H2 + 1 O2 → H2 O, with the hydrogen and oxygen reactants and 2 products at 1000◦ C. 3.9 Given a flow inlet to a fuel cell cathode at 2 atm, 75% RH, 90◦ C, and at a cathode stoichiometry of 2.0, determine the maximum possible molar rate of water uptake into the cathode flow if a 100-cm2 active area fuel cell is operating at 1.2 A/cm2 . You can assume the flow rate, pressure, and temperature are constant in the fuel cell.

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Problems

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3.10 Given a PEFC fuel cell stack with each cell generating 100 A, if the air flow in the cathode is at a stoichiometry of 2.5, a back pressure of 2 atm, and an inlet RH of 0%, what must the outlet RH be at 90◦ C to remove exactly the amount of water generated by reaction in vapor form? You can assume the flow rate, pressure, and temperature are constant in the fuel cell and the exit RH is 100%.

reformation schemes. Consider the fuel cell to be operating at 1.5 atm pressure on the anode, 3 atm pressure on the cathode, a hydrogen stoichiometry (λa ) of 1.5, and a cathode stoichiometry (λc ) of 3.0.

3.11 Given a fuel cell stack with each cell generating 1 A/cm2 and a geometric area of 150 cm2 per plate, if the air flow in the cathode inlet RH is 25% at 80◦ C and 1.5 atm, what must the cathode stoichiometry be to remove exactly the amount of water generated by reaction as water vapor at 80◦ C? You can assume the flow rate, pressure, and temperature are constant in the fuel cell and the exit RH is 100%.

Species

SR

ATR

H2 O H2 CO2 N2

0.32 0.55 0.13 0.00

0.31 0.28 0.12 0.29

3.12 Given a fuel cell stack with each cell generating 100 A, if the air flow in the cathode inlet RH is 20% at 80◦ C and 1.5 atm at a stoichiometry of 2.0, what must the exit temperature be to remove exactly the amount of water generated by reaction as water vapor? You can assume the flow rate and pressure are constant in the fuel cell and the exit RH is 100%. 3.13 Determine the maximum thermodynamic efficiency for a methane fuel cell at 298◦ C based on LHV and HHV. Does the efficiency increase or decrease with temperature? With pressure? 3.14 Determine the maximum thermodynamic efficiency for a methanol fuel cell at 100◦ C based on LHV and HHV. Does the efficiency increase or decrease with temperature? With pressure? 3.15 Determine the maximum thermodynamic efficiency for an ethanol fuel cell at 1000◦ C based on LHV and HHV. Does the efficiency increase or decrease with temperature? With pressure? 3.16 Which has a higher maximum allowable thermodynamic voltage, one calculated with a HHV or a LHV? 3.17 Consider a stationary hydrogen–air PEFC. Since hydrogen is not directly available, the fuel cell at 353 K is to be fed by reformed natural gas. That is, natural gas will be chemically converted into a mixture of hydrogen and other nonreactive components. This gas mixture will be fed into the anode side of the fuel cell, which will use the hydrogen in the mixture as fuel. The cathode is to be run on humidified air of average composition (75% N2 , 15% O2 , 10% H2 Ov ). Two types of reforming systems are offered, steam-based reformation (SR) and autothermal reformation (ATR). The mole fractions of all species to be input to the anode are shown in the table below for the two different

Anode Mole Fractions of Species for Two Reformation Options

c¯ p,H2 = 29 J/mol · K

c¯ p,O2 = 30 J/mol · K

c¯ p,H2 O = 34 J/mol · K h¯ ◦f,H2 O,v = −241,000 J/mol Ru ◦ s¯H2 O,v

= 8.314 J/mol · K = 188.83 J/mol · K

h¯ ◦f,H2 O,l = −285,000 J/mol F = 96,485 C/eq s¯H◦ 2 O,l = 70.05 J/mol · K

(a) Determine the thermodynamically expected reversible Nernst OCV of the ATR case at 353 K? Assume LHV. (b) What is the change in expected voltage to switch from ATR to SMR reformation for the anode gas (assume all else stays the same besides anode feed gas)? (c) What is the maximum expected thermodynamic efficiency at OCV for the ATR case (Assume LHV)? 3.18 Consider the generic fuel cell complete redox reaction: Case (a): 3A + 2B → 2C + 1D Case (b): 2A + 2B → 2C + 3D Case (c): 3A + 2B → 2C + 3D

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Where A, B, C, and D are different gas-phase species. Draw a qualitative plot showing the expected maximum thermodynamic efficiency with respect to temperature. 3.19 One way to get hydrogen to operate a fuel cell is by reforming gasoline into hydrogen. This is not totally efficient, and CO2 and N2 end up in the flow. You desire to compare this technique to using pure hydrogen. What is the expected change in voltage for a hydrogen fuel cell if the anode is switched from pure hydrogen to 30% hydrogen and the remainder is water vapor and CO2 ? Assume T cell =100◦ C. 3.20 In a SOFC, water vapor is created at the anode as a product, just like it is created in a PEM fuel cell at the cathode. What would the effect of the water content at the anode be on fuel cell voltage (no numbers, just qualitative response). Would voltage go up, down, or stay the same? Is this similar to the effect of water vapor at the cathode of a PEFC? 3.21 Le Chatelier’s principle is very powerful. It states that any system initially at equilibrium, when subjected to a change in temperature or pressure, will react in such a way as to reduce stress. Discuss this principle for equilibrium in relation to the expected shifts in voltage for changes in reactant and product concentrations seen from the pressuredependent component of the Nernst equation. Can you tell "just by looking" if the voltage will go up or down for a given shift in concentration of reactants or products? 3.22 Given a hydrogen–air PEFC operating at 130◦ C, a cathode oxygen Faradic efficiency of 0.6, and an anode fuel utilization fraction of 0.8. The average anode flow is 60% hydrogen and 40% water vapor, and the average cathode flow is 15% oxygen and 75% nitrogen and 10% water vapor. Initially, the anode is at 5 atm pressure and the cathode is at 3 atm total pressure. Take the following specific heats to be constant: c¯ p,H2 = 29 J/mol · K

c¯ p,O2 = 30 J/mol · K

c¯ p,H2 O = 34 J/mol · K h¯ ◦f,H2 O,v = −241,000 J/mol · K h¯ ◦f,H2 O,l = −285,000 J/mol · K Ru = 8.314 J/mol · K

F = 96,485 C/eq

(a) Using the Nernst equation, determine the expected voltage at the given pressures and mole fractions. Be careful how and where you put the water components and what pressures you use. One of the water vapors is "inert" and one is "active."

(b) How does the inert H2 O affect the results? A qualitative answer is sufficient. (c) From the Faradic efficiencies, you can see that the reactants enter and deplete along the reaction path. If you were to look at the calculated "Nernst voltage” as you go along the channel from inlet to outlet (as a function of x), what would happen to the calculated value from inlet to exit (up or down or stay the same)? A qualitative answer is sufficient. 3.23 It is proposed to develop a fuel cell that runs directly on propane (C3 H8,g ) at a propane stoichiometry (λC3 H8 ) of 2.5 and a cathode oxygen stoichiometry (λc ) of 2 (note the cathode is running on air, 79% N2 , 21% O2 by volume). In the laboratory, the cell operates at 0.3 V at a current density of 0.1 A/cm2 . The superficial active area of the cell is 25 cm2 . The anode electrochemical reaction is (C3 H8 )g + 6 (H2 O)g → 20H+ + 20e− + 3CO2 The basic cathode electrochemical reactions are O2 + 4e− + 4H+ → 2H2 O (C3 H8 )g + 5O2 → 4H2 O + 3CO2 where the molecular weights are as follows: C3 H8 = 44 g/mol H2 O 18 g/mol O2 32 g/mol Air 28.85 g/mol CO2 28 g/mol Other values needed can be found in the Appendix or the text. (a) Determine the balanced overall electrochemical redox reaction. (b) Find E◦ , E◦◦ , and ηth at 298 K, 1 atm based on HHV. (c) Would the LHV result in a higher or lower ηth ? (d) What is the voltaic efficiency of the fuel cell in operation (εv )? (e) What is the overall fuel cell efficiency (εcell )? (f) Is the overall cell producing or consuming water? At what rate in moles per second? (g) What is the actual supply rate of air at the cathode in grams per hour?

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References (h) Qualitatively sketch a plot of the expected maximum thermodynamic efficiency versus temperature for this type of fuel cell. 3.24 For a hydrogen PEFC based on the concepts in this chapter, do you expect the open-circuit voltage to (circle one): (a) Increase/decrease/stay the same if the cathode oxygen mole fraction increases (b) Increase/decrease/stay the same if the cathode total pressure increases (c) Increase/decrease/stay the same if the anode humidity is increased (d) Increase/decrease/stay the same if the operating temperature increases (e) Increase/decrease/stay the same if the cathode humidity is increased (f) Increase/decrease/stay the same if helium is mixed with the air before entry into the cathode 3.25 Using constant specific heats, develop a simplified expression for the variation of E◦ with temperature for a hydrogen–air PEFC in the range 300–400◦ C. Would a similar expression be valid for a hydrogen–air SOFC in the range 900–100◦ C? 3.26 Using constant specific heats, develop a simplified expression for the variation of E◦◦ with temperature for a hydrogen–air PEFC in the range 300–400◦ C. Would a similar expression be valid for a hydrogen–air SOFC in the range 900–100◦ C.

Computer Program Problems 3.27 Develop a computer program to calculate the E◦ , E◦◦ , and ηth for a hydrogen–air fuel cell as a function of temperature.

119

(a) Plot the LHV ηth as a function of T between 300 and 1000◦ C at 100◦ C increments. (b) On the same figure, plot the HHV ηth as a function of T between 300 and 1000◦ C at 100◦ C increments. (c) Check the validity of your model versus a hand calculation at 500◦ C. This is called model verification and is a critical step to assure your computer is giving good results. (d) Compare the accuracy of your exact answers [done by integrating the cp (T) equations] with those done if you assume constant cp (easily done on a spreadsheet by entering a constant value for cp ). Is there a lot of error associated with assuming cp = const? 3.28 Develop a computer program to calculate the E◦ , E◦◦ , and ηth for a methanol–air fuel cell as a function of temperature. (a) Plot the LHV ηth as a function of T between 300 and 1000◦ C at 100◦ C increments. (b) On the same figure, plot the HHV ηth as a function of T between 300 and 1000◦ C at 100◦ C increments. (c) Check the validity of your model versus a hand calculation at 500◦ C. This is called model verification and is a critical step to assure your computer is giving good results.

Open-Ended Problem 3.29 Go beyond the text and learn a little more about condensation and evaporation. Specifically, how are the processes modeled? Do condensation and evaporation occur at thermodynamic saturation points? Inside a PEFC at uniform temperature that is cooling, where would you expect the water to condense first during steady operation?

REFERENCES 1. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 3rd ed., Wiley, New York, 1995. 2. Y. A. C ¸ engel and M. A. Boles, Thermodynamics, an Engineering Approach, 4th ed., McGrawHill, New York, 2002. 3. F. D. Maslan and T. M. Littman, “Compressibility Chart for Hydrogen and Inert Gases,” Ind. Eng. Chem., Vol. 45, No. 7, pp. 1566–1568, 1953. 4. ANR-1057B, New October 2000, Arlie A. Powell, Extension Horticulturist, Professor, and David G. Himelrick, Extension Horticulturist, Professor, both in Horticulture at Auburn University.

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Thermodynamics of Fuel Cell Systems 5. N. Laurendeau, Statistical Thermodynamics: Fundamentals and Applications, Cambridge University Press, New York, NY, 2005. 6. T. E. Springer, T. A. Zawodzinski, and S. Gottesfeld, J. Electrochem. Soc., Vol. 138, No. 8, pp. 2334–2341, 1991. 7. S. Turns, An Introduction to Combustion: Concepts and Applications, 2nd ed., McGraw-Hill, New York, 2000. 8. J. Newman, Electrochemical Systems, 2nd ed., Prentice-Hall, Englewood Cliffs, N. J., 1991.

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Fuel Cell Engines Matthew M. Mench

4

Copyright © 2008 by John Wiley & Sons, Inc.

Performance Characterization of Fuel Cell Systems Q: When will we see the first production fuel-cell vehicle from Toyota? A: A realistic date is 2010. There are still a few technical and infrastructural difficulties to overcome. Problems include space and the safe storage of hydrogen on board the vehicle. In terms of the fuel cell stack itself, however, we have found most of the answers. —Katsuaki Watanabe, President of Toyota Motor Company, in a March 2006 interview in Automobile Magazine

4.1 POLARIZATION CURVE Figure 4.1 is an illustration of a typical polarization curve for a fuel cell with negative entropy of reaction, such as the hydrogen–air fuel cell, showing five regions of interest labeled I–V. The polarization curve, which represents the cell voltage–current relationship, is the standard figure of merit for evaluation of fuel cell performance. Voltage versus current density, scaled by geometric electrode area, is typically shown, so that the results are scalable between differently sized cells. Returning to the five regions labeled on the polarization curve of Figure 4.1: Ĺ The losses in region I are dominated by the activation (kinetic) overpotential at the electrodes. Ĺ The losses in region II are dominated by the ohmic polarization of the fuel cell. This includes all electrical and ionic conduction losses through the electrolyte, catalyst layers, cell interconnects, and contacts. Ĺ The losses in region III are dominated by the concentration polarization of the fuel cell, caused by mass transport limitations of the reactants to the electrodes. Ĺ The losses in region IV represent the departure from the Nernst thermodynamic equilibrium potential. This loss can be very significant and can be due to undesired species crossover through the electrolyte, internal currents from electron leakage through the electrolyte, or other contamination or impurity. Ĺ The losses in region V represent the departure from the maximum thermal voltage, a result of entropy change which cannot be engineered. Figure 4.1 is shown for a fuel cell with negative
S. If the entropy change is positive, the Nernst voltage is actually greater than the thermal voltage, and the heat generation by entropy change is negative, as discussed in Chapter 3. 121

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Figure 4.1 Typical polarization curve for fuel cell with significant kinetic, ohmic, concentration, and crossover potential losses.

It is important to note that regions I–III in Figure 4.1 of dominant kinetic, ohmic, or mass transfer polarizations are not discrete. That is, all modes of loss contribute throughout the entire current range. For example, ohmic losses occur whenever there is current but only dominate losses in region II. As another example, although the activation overpotential dominates in the low-current region I, it still contributes to the cell losses at higher current densities where ohmic or concentration polarization dominate. Thus, each region shown in Figure 4.1 is not unique and separate, and all losses contribute throughout the operating current regime. Also shown in Figure 4.1 are the regions of electrical and heat generation. The actual electrical and heat generation rates are shown on Figure 4.2. The electrical power generated is the cell current multiplied by the fuel cell voltage, where the heat generation rate is the cell current multiplied by a different voltage, the voltage departure from the thermal voltage. Since the thermodynamically available energy not converted to electrical energy is converted to heat, the thermodynamic efficiency can be qualitatively observed by comparing the relative magnitude of the voltage potential converted to waste heat and to electrical power. It should be noted that voltage loss, polarization, and overpotential are all interchangeable terms and refer to a voltage loss. In general, the operating voltage of a fuel cell can be represented as the departure from ideal voltage caused by the various polarizations: E cell = E ◦ (T, P) − ηa,a − |ηa,c | − ηr − ηm,a − |ηm,c | − ηx

(4.1)

where E◦ (T,P) is the theoretical equilibrium open-circuit potential of the cell, calculated from the Nernst equation. The activation overpotentials at the anode and cathode are

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4.1 Polarization Curve

r

˝

123

d th

cell

c d

c04

d

d

˝

cell

,i

Figure 4.2 Illustration of polarization curve, waste heat generation, and useful electrical power generation rate density.

represented by ηa,a and ηa,c , respectively. The polarization in region IV results from crossover of fuel and oxidizer through the electrolyte or internal short circuits in the cell. This departure from the Nernst equilibrium voltage (ηx ) can be modeled as a result of crossover current. The ohmic (resistive) polarization is shown as ηr . The concentration (mass transfer) polarization at the anode and cathode are represented as ηm,a and ηm,c , respectively. Throughout the remainder of the chapter, we will discuss each of these losses in detail. We return to the waterfall analogy of Chapter 2, shown in Figure 4.3. In Chapter 2, we did not yet know how to calculate the expected cell voltages, and the waterfall analogy was Flow rate over falls ∝ current Ecathode

Ecell = Ecathode - Eanode

Eanode

Standard reference: standard hydrogen electrode (SHE = 0.0 V)

Figure 4.3 Waterfall analogy illustrating voltage potential at each electrode and for the fuel cell.

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Eanode

- Ecell +

Ecathode Air in

H2 in

Cathode

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Anode

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Standard reference electrode (SRE)

Pt

H2 bubbles

Air out

H2 out Electrolyte

Figure 4.4 Illustration of measurement of cell and individual electrode voltage in a fuel cell.

used to illustrate the concepts of the current and potential for reaction. Now that we know how to calculate the maximum expected equilibrium cell potential (the Nernst voltage), we can use this as the starting point for the operating fuel cell voltage. Recall that the Nernst potential is calculated for a condition of pure thermodynamic equilibrium, which is only approached at open-circuit conditions. With any current drawn, there will be ohmic, activation, and mass transfer losses. Figure 4.4 is shown to illustrate the connection between the waterfall and the fuel cell. The cell voltage Ecell is the measured potential difference between the anode and cathode and is a measure of the potential to do electrical work. From experience, we know that if a fuel and oxidizer are mixed and combusted, some heat will be released that is the reaction enthalpy: 1 O 2 2

+ H2 −−−−−→ H2 O +
H

(4.2)

From the thermal voltage from Chapter 3, E th = −
H/n F, we see that this thermal voltage potential is indeed what would occur if all of the thermal energy released in the combustion reaction were instead converted into voltage potential instead. As discussed in Chapter 3, for comparison purposes, some baseline voltage must be defined. The condition of zero-volt potential has been assigned to a platinum electrode with pure hydrogen flow at STP conditions. This reference potential is called the standard hydrogen electrode (SHE), and all other voltage potentials are relative to this baseline. This is similar to defining an arbitrary “zero” reference point in potential-energy-related problems. Returning to Figure 4.4, if we measured the voltage potential between a standard hydrogen reference electrode and the cathode, the resulting voltage could be positive or negative relative to the SHE. For the cathode in a galvanic cell, the potential must only be greater than the anode. Strictly speaking, neither the anode or cathode must be positive relative to the SHE. We can solve for the theoretical OCV or the “initial height of the waterfall” from the tools of thermodynamics discussed in Chapter 3. The next step is to understand what happens when we move the fuel cell out of equilibrium. When we leave equilibrium and begin to draw current, the system suffers various polarization losses as shown in Eq. 4.1, and the cell voltage decreases.

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4.1 Polarization Curve

Ecathode

125

η cathode will be negative, as the electrode potential decreases, the potential for reduction reaction increases. For an H2 /air system, η cathode is greater than η anode .

V Ecell η anode

Eanode i

Figure 4.5 Representation of individual electrode potentials as function of current density. Note that the polarization behavior at each electrode will likely not be linear with current density, as shown for simplicity.

At the anode at equilibrium, the oxidation reaction is balanced with the reduction reaction: Ox + ne− ↔ Re

(4.3)

As illustrated in Figure 4.5, when we move the fuel cell out of equilibrium and produce a net oxidation at the anode and a net reduction at the cathode, polarization moves the anode toward a greater oxidation potential, or higher voltage relative to the SHE. That is, as current increases, the anode becomes more positive to promote oxidation of the fuel. This makes sense, considering a more positive electrode will develop a greater attractive force to separate electrons from the reactive species (oxidation process). On the other hand, the cathode voltage is reduced as current increases to promote the oxidizer reduction reaction. There is a cost associated with this promotion of reaction rate (current): As the anode potential is increased to promote fuel oxidation and the cathode potential is decreased to promote oxidizer reduction, the resulting overall fuel cell voltage (Ecell ) is decreased. Relating to the waterfall analogy, the effect of drawing current is to raise the bottom of the waterfall and lower the top of the waterfall, so that the distance between the two is decreased and the potential voltage of the cell is reduced. Eventually, as the losses increase with increasing current, the potential difference between the electrodes will reach zero, and no additional current can be drawn. This is the limiting current, ilimiting shown in Figure 4.1. The limiting current is a result of the combined effect of all polarizations in the system, which include be ohmic, kinetic, mass transfer, and crossover or shorting. Modeling the Fuel Cell Performance Curve: Zero-Dimensional Steady-State Model We seek to develop a basic fuel cell model that can predict the polarization curve as a function of engineering parameters. That is, we seek expressions for the terms in Eq. (4.1): E cell = E ◦ (T, P) − ηa,a − |ηa,c | − ηr − ηm,a − |ηm,c | − ηx

(4.4)

In this chapter, a single-phase zero-dimensional steady-state model will be developed that describes the individual regions of the polarization curve. Obviously, this is a starting point and should be considered as a general learning tool. Much more complex models

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Performance Characterization of Fuel Cell Systems

are developed in the literature, including multidimensional, multiphase effects with various length and time scales. In the following sections, we will develop fundamental, analytical and emperical models to describe each of the losses in Eq. (4.4). By the end of the chapter, the student will be able to model fuel cell performance and generate an entire polarization curve for any fuel cell system.

4.2

REGION I: ACTIVATION POLARIZATION Activation polarization, which dominates losses at low current density, is the voltage overpotential required to overcome the activation energy of the electrochemical reaction on the catalytic surface. From Eq. (4.1) E cell = E ◦ (T, P) − ηa,a − |ηa,c | −ηr − ηm,a − |ηm,c | − ηx
 

(4.5)

Activation polarization

The activation polarization at the anode and cathode are shown as ηa,a and ηa,c , respectively. Physically, the activation polarization represents the voltage loss required to initiate the reaction. In a somewhat similar fashion, consider a purely chemical reaction between gasoline vapor and air in a combustion chamber. There needs to be some ignition energy input to the system to enable the spontaneous reaction to proceed. In an electrochemical system, this manifests as voltage losses, which decrease the original maximum potential energy represented by the theoretical open-circuit potential of the fuel cell. Electrical Double Layer In addition to an analytical expression for the activation polarization at an electrode which we will develop in this chapter, an understanding of the microscopic process occurring at the electrode during charge transfer is also important. A very natural question often arises when discussion of the activation overvoltage is first introduced: What is the physical nature of the activation polarization and how exactly does the charge transfer reaction proceed? Between an electrode and the electrolyte, there exists a complex structure known as the electrical double layer. At the electrode surface and in the adjacent electrolyte, a buildup of charge occurs, as illustrated in Figure 4.6. The sign of the charge along the electrode surface depends on the electrode. At the anode, the potential is lower than the surrounding electrolyte, so the there is a buildup of negative charge along the surface of the catalyst and a positive charge in the surrounding electrolyte forming the double-layer structure. The double layer consists of a complex structure including an inner Helmholtz plane (IHP) that exists along the electrical centers of specifically adsorbed reactant ions (e.g., adsorbed hydrogen at the anode of a hydrogen fuel cell). In general, the sum of charges on the solution sides must be equal to that on the electrode side, regardless of the sign of the ionic charge in the IHP. Beyond the IHP, an outer Helmholtz plane (OHP) is formed along the locus of the centers of the nearest layer of solvated (hydrated) ions in the electrolyte. Beyond the OHP, other solvated ions in the electrolyte can also interact with the catalyst surface through long-range electrostatic interaction in the diffuse layer. All three layers form the double layer which is typically less than 10 nm deep into the electrolyte.

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4.2

Region I: Activation Polarization

127

Helmholtz layer +

Ionic excess

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

Diffuse double layer

Helmholtz surface

+ + + + +

Adsorbed ions

Figure 4.6 Schematic of electrical double layer. (Reproduced from [1].)

At the electrolyte–electrode interface, the buildup of charge occurs across the double layer. The ionic species charge transfer reaction is driven by this potential difference. The voltage difference required to drive a given electrochemical reaction rate (current) across the catalyst–electrolyte interface is the source of the activation overpotential. That is, for a given current, a certain potential buildup across the double layer is required to force the charge transfer. The role of the catalyst is to enable reaction to occur with a low buildup of charge. To illustrate the high driving force for reaction generated, consider a typical oxidation activation overvoltage of ∼0.2 V at an electrode over an estimated double-layer distance of 10 nm. The electric field strength is an amazing 2.0 × 108 V/cm, which would be equivalent to 20,000 MV across 1 m distance! No wonder the reaction takes place. The discontinuity of charge physically behaves like a capacitor, as illustrated in Figure 4.7. Typical capacitances are on the order of 5–20 mF/cm2 [2]. The fuel cell (and other electrochemical systems) can therefore be modeled as a resistance–capacitance RC circuit (R being the ohmic drop and charge transfer resistance in the circuit). Actually, the whole fuel cell can be modeled as a multiple resistance and capacitor network. The science of the use of an equivalent electrical circuit analogy to describe electrode charge transfer processes is an active area of research [3] and is considerably more complicated than shown here. The concepts, however, can be used to glean information about the electrode dynamics, charge transfer resistance, and other quantities, as discussed in Chapter 8.

Activation Polarization Activation polarization losses are highly nonlinear with current and manifest as a sharp initial drop in cell voltage from open-circuit conditions followed by diminishing additional losses as the current is increased through ohmic and concentration polarization dominated regions, as shown in region I of Figure 4.1.

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Performance Characterization of Fuel Cell Systems Helmholtz layer +

Ionic excess

+ + + + + + + + + +

Diffuse double layer

Helmholtz surface

+ + + + + +

C

+

R Figure 4.7

Schematic of electrical double layer with electrical circuit analogy. (Adapted from [1].)

Different activation losses occur at each electrode. In fact, the reactions at each electrode are only linked through conservation of charge. That is, the current passed through the anode must equal the current through the cathode: |i cell | = |i a | = |i c |

(4.6)

where we have used absolute values to avoid conflicts with sign conventions for the direction of current. Although the net current is identical at each electrode, the polarization losses required to achieve this level of current on each electrode are independent. One can imagine the resistance to reaction at an electrode as a reaction friction, that may be different at the anode and cathode. The activation polarization losses are influenced by the following: 1. Reaction Mechanism In general, the more complex a reaction mechanism, the greater the overpotential required to break the chemical bonds and generate current. For example, the HOR is less complex and involves fewer intermediate steps than the methanol electrooxidation, so that for the same current the overpotential for methanol oxidation is greater than for hydrogen oxidation. There are steric (geometric) and other factors involved as well. 2. Catalyst Type A poor choice of catalyst will require a greater polarization to enable the electrochemical reaction at that electrode to proceed. Each electrochemical reaction has different preferred catalysts, so that there is no single perfect catalyst.

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3.

4.

5.

6.

7.

8.

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129

Generally, for low-temperature reactions, noble metal catalysts such as platinum work well, and for higher temperature fuel cells, less expensive metals such as nickel and other alloys can be used. Catalyst Layer Morphology The microstructure of the catalyst has a strong effect on the overall effectiveness of the catalyst. From the generic fuel cell description of Chapter 2, the catalyst structure is highly three dimensional, and the potential reaction locations are limited to those with immediate access to ionic and electronic conductors, catalyst, and reactant gas. Maximization of this triple phase boundary area will reduce the activation polarization losses for a given current density. A catalyst layer with very low triple-phase boundary area density will have reduced number of available reaction sites and reduced performance. Operating Parameters Electrochemical reactions are catalyzed by increased temperature, just like chemical reactions (think about the chemical reaction analog: a heated mixture of gasoline vapor and air will react more readily than a cold mixture). Since the molecules participating in the reaction have a higher kinetic energy with increased temperature, the probability of collisions, as well as the fraction of collisions resulting in reaction, is strongly related to temperature. Other thermodynamic operating parameters such as pressure can have an effect as well, although temperature generally has the strongest impact. Impurities and Poisons The presence of any impurities or catalyst poisons in the reacting flow can have a highly deleterious effect on performance. Some impurities such as carbon monoxide and sulfur dioxide can reduce performance dramatically for certain fuel cells, even in levels as low as parts per million (ppm) or parts per billion (ppb). Each catalyst and fuel cell has different poisons. For instance, carbon monoxide is a serious poison for low-temperature PEFCs but can be oxidized as a fuel in high-temperature MCFCs and SOFCs. Species Concentrations The species dependence on the expected Nernst voltage is a result of the equilibrium thermodynamic effect. During the highly nonequilibrium electrochemical reaction process, there is also a concentration effect on the activation polarization. As the reacting species become more sparse, the double-layer polarization required to attract sufficient reactants increases. In the extreme case, no reaction can take place across the double layer if there is no reactant available. Age The catalyst performance of a given fuel cell can change significantly over the operating lifetime of the fuel cell. This is generally a result of physical morphological or chemical changes in the catalyst. The catalyst with the highest initial reactivity may not be the best choice for a given application if the performance over time is not stable. Service History The service history of the fuel cell, including environment, load cycling, and voltage history, has an effect on the performance of a fuel cell. Dynamic load cycles can accelerate degradation, as discussed in Chapter 7.

The positive side of all of these activation loss dependencies is that most of them can be engineered to some degree to reduce losses and increase efficiency. To move from an equilibrium state and draw useful current, a net reaction must occur. Figure 4.8 is a schematic of the reaction coordinate for a galvanic (exothermic) electrochemical (or chemical) reaction, as described by transition state theory [4]. At

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Performance Characterization of Fuel Cell Systems Metastable State I

“Activated complex”

ηa

Metastable State II Total exothermic release available for work (electrical or chemical)

Initial “Push” Extent of reaction

Figure 4.8 Schematic of reaction coordinate pathway for given reaction.

the initial state which corresponds to nonreacted fuel and oxidizer, the reactants are at a metastable equilibrium with a higher energy than the product state. Under the driving force of a voltage over potential at the electrode (v/a), the reactant is moved along the reaction coordinate toward an activated complex state, where the reactant is partially converted to product. This state corresponds to the elementary charge transfer reaction step discussed in Chapter 2. The intermediate species at this state is highly reactive and cannot remain in a stable condition. This transition-state-activated complex separates the reactant from the product states along the reaction coordinate. As the reaction moves to completion, the activated complex moves to a product state, and a net chemical energy conversion occurs as the products reach a final metastable equilibrium. The difference between the initial reactant and final product chemical energy is the enthalpy of reaction, which is converted to electrical work and heat in an electrochemical reaction. Now, consider an individual electrode, initially at equilibrium. For example, consider the global HOR: H2 ↔2H+ +2e−

Reduced ←−−−−−−−−→ Oxidized

(4.7)

At equilibrium (open circuit), this reaction actually proceeds in both directions across the anode double layer, with no net reaction in either direction. Some hydrogen is being oxidized, and an equivalent amount is being reduced. This is analogous to a frictionless pendulum, shown in Figure 4.9. At equilibrium, the pendulum swings back and forth with

Figure 4.9 Mechanical pendulum analogy to describe electrode reaction and equilibrium.

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Figure 4.10

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131

Schematic of pendulum analogy of small net anodic current.

no net motion in either direction. The energy in the system is conserved and oscillates between potential energy and kinetic energy, just as the species at the electrode will oscillate between oxidized and reduced hydrogen, with no net change in the reactants. This equilibrium current exchange is termed the exchange current density io , and is an important parameter discussed in the following sections. Next, consider moving the electrode out of equilibrium and into a condition of net hydrogen oxidation and current generation. This reaction produces a net flow of electrons which are transported to the external circuit. For a very low current, a small overpotential is required to drive the net reaction in the anodic direction. As the level of current is increased beyond some equilibrium exchange value, the overpotential required to sustain the reaction rate is greatly increased. Consider again the frictionless pendulum analogy; in order to leave equilibrium and move to a net anodic reaction, if the pendulum were reflected at the midpoint in the oscillation by a perfectly elastic barrier, as shown in Figure 4.10, the pendulum would rise back to the initial height in the anodic direction to conserve the system energy. The net result is a small anodic current. In order to push the pendulum beyond the level allowed by the initial system oscillation energy, additional external energy must be input to the pendulum, as illustrated in Figure 4.11. In this analogy, the additional work input is converted to a higher height of the pendulum in the anodic direction and a greater net reaction (i.e., more current).

Figure 4.11

Schematic of pendulum analogy of larger net anodic current and energy input.

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Figure 4.12

Schematic of activation overpotential with respect to current.

With the pendulum analogy in mind, we can now examine the typical electrode activation polarization behavior, as shown in Figure 4.12. At low current density, the activation overpotential ηactivation required to maintain a net reaction rate in a given direction is small. Beyond a threshold value in current density related to the equilibrium reaction exchange rate of the electrode, the additional polarization requiredfor increasing current is greatly increased. The exchange current density io is of preeminent importance in the activation over potential for a given electrochemical reaction rate, as it is a measure of the effectiveness of the electrode in promoting the electrochemical reaction and is the electrode reaction exchange at equilibrium. At zero net cell current density, the electrode current is the exchange current density. The higher the exchange current density at a given electrode, the lower the overall activation polarization losses for a given current. 4.2.1

Butler–Volmer Model of Kinetics1 In this section, we derive a general expression to describe activation polarization losses at a given electrode, known as the Butler–Volmer (BV) kinetic model. The BV model is not the only (or necessarily the most appropriate) model to describe a particular electrochemical reaction process. Nevertheless, it is a classical treatment of electrode kinetics that is widely applied to study and model a majority of the electrode kinetics of fuel cells. The BV model describes an electrochemical process limited by the charge transfer of electrons, which is appropriate for the ORR, and in most cases the HOR with pure hydrogen. The fundamental assumption of the BV kinetic model is that the reaction is rate limited by a single electron transfer step, which may not actually be true. Some reactions may have two or more intermediate charge transfer reactions that compete in parallel or another intermediate step such as reactant adsorption (Tafel reaction from Chapter 2) may limit the overall reaction rate. Nevertheless, the BV model of an electrochemical reaction is standard fare for a student of electrochemistry and can be used to reasonably fit most fuel cell reaction behavior.

1 Instructors

may wish to skip to Eq. (4.35) and assign the derivation of the Butler–Volmer kinetics to advanced undergraduate or graduate students.

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In a fuel cell, at each electrode, there is an equilibrium reaction that can be written as kf

AO+ + ne−
BR kb

→= Reduction (cathodic) ←= Oxidation (anodic)

(4.8)

where Ĺ The stoichiometric coefficients of the rate-limiting elementary charge transfer reaction at a given electrode are A and B. The elementary reaction should be distinguished from the global reaction occurring at a given electrode, as discussed in Chapter 2. The elementary charge transfer reaction is the intermediate reaction responsible for the charge transfer. Although the BV model assumes a single charge transfer reaction step, there can be several charge transfer steps occurring in parallel. The BV model can still accommodate this, as will be discussed. Ĺ At each electrode in the fuel cell at open circuit condition, an equilibrium as in Eq. (4.8) is occurring with no net current through the circuit (recall the equilibrium pendulum of Figure 4.9). That is, both the anode and the cathode have completely separate equilibrium reactions occurring, linked only by the net charge transfer through the circuit. At open circuit, there is no net current flowing through the electrodes, and the anode and cathode reactions are independent. For a given purely chemical reaction, we can change the temperature and pressure to affect the reaction rate. For an electrochemical reaction, there is an additional factor: the electrode overpotential across the double layer. The overpotential at the electrode surface controls the direction and rate of the net reaction. When net current is drawn, an overpotential at each electrode forces the electrode reactions out of the equilibrium condition and toward the desired direction. At the anode, the electrode potential becomes higher than its equilibrium potential (see Figure 4.5), resulting in a net oxidation reaction. At the cathode, the electrode potential becomes lower than its equilibrium potential, resulting in a net reduction reaction. Figure 4.13 shows this on a reaction coordinate. At the initial surface electrode potential φ 1 , the forward reaction is not favored. At φ 3 , the reaction is now favored because the final energy state is below the initial energy state. For electrochemical reaction circuits, spontaneous galvanic (exothermic) reactions can be reversed simply by applying an external potential to change the polarity of the electrodes. This is the principle of the reversible fuel cell discussed in Chapter 1. Consider an electrode at state φ 1 in Figure 4.14. To induce this electrode to have a net spontaneous reduction reaction, we must go from φ 1 to φ 3 . Although the potential energy of the electrode is increased to promote this reaction and support charge transfer across the double layer of the electrode, the actual surface overpotential relative to the SHE will decrease (see Figure 4.5), since we are moving toward a cathodic reduction reaction product in this example. Symmetry Factor We have added nF(φ 3 – φ 1 ) in electrical potential to the system. Only a fraction of this energy will go toward reducing the activation energy of the cathodic (reduction) reaction at the electrode. In a general case, the fraction of the additional energy

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Performance Characterization of Fuel Cell Systems φ1 is endothermic for the forward reaction φ3 is exothermic for the forward reaction φ is the surface potential (V) of the electrode φ3 φ2 φ1

Reactants

Products

Extent of Reaction

Figure 4.13

Schematic of activation overpotential with current at given electrode.

imparted to the electrode that promotes the reduction reaction is called β, the symmetry factor: 0<β<1

(4.9)

If β = 1 (see Figure 4.15), the additional overpotential at the electrode goes completely toward promoting the reduction reaction. If β = 0 (see Figure 4.16), all of the additional potential is applied toward promotion of the anodic oxidation reaction. In the particular case shown in Figure 4.15, all of the additional voltage potential increases the oxidized state energy, and none is applied to lower the reduced state energy. In practice, β varies for a given electrode and reaction and lies between 0 and 1 but is not necessarily 0.5, since certain catalysts promote oxidation of a given species more readily than others. The activation energy (polarization) required to promote charge transfer across the double layer for the reduction reaction at an electrode can be shown as E a2,c = E a1,c + βn F(φ2 − φ1 )

(4.10)

For a reduction reaction, the sign of φ 2 is more negative than φ 1 (Figure 4.5), so φ 2 − φ 1 is negative. For the oxidation reaction on the electrode, 1 − β is the anodic symmetry factor, the fraction of the polarization energy which promotes the oxidation reaction at the electrode, and the activation energy (polarization) required to promote charge transfer across the

Transition state Energy

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Ea3 φ3 φ2 φ1

Oxidized state

Reduced state

Extent of reaction Figure 4.14 Activation overpotential increase to initiate reaction at given electrode.

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nF (φ 2 − φ1)

Region I: Activation Polarization

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Ea1, c + nF (φ 2 − φ1) = Ea 2, c

Energy

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φ2 φ1 Oxidized State

Reduced State

Extent of Reaction

Figure 4.15

Symmetry factor β = 1.

double layer for the oxidation reaction at an anode can be shown as E a2,a = E a1,a − (1 − β)n F(φ2 − φ1 )

(4.11)

So when we decrease the electrode potential, the activation energy for reduction goes down by βnc F(φ 2 −φ 1 ), and the oxidation activation energy is increased by (1 − β)n F(φ2 − φ1 )

(4.12)

Returning to the elementary charge transfer reaction, kf

AO+ + ne−
BR

(4.13)

kb

For each reaction, kf and kb , a commonly used model for the rate equation is an Arrhenius expression:  k = kref exp

−E a Ru T

 (4.14)

where the reference reaction rate (kref ) and the reaction activation energy (Ea ) are different for kf and kb , the forward and reverse reactions at the electrode, respectively.

Ea Energy

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nF (φ 2 − φ1)

1, c

= Ea 2, c

No help in promoting reduction reaction

φ2 φ1 Oxidized State

Reduced State

Extent of Reaction Figure 4.16

Symmetry factor β = 0.

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A rate equation for the electrochemical reaction can be written considering Faraday’s law and the reaction rate constant:   dC n i −E a mol  γ = k = = [C] exp |r | = s · cm2 nF Ru T dt

(4.15)

where γ is the reaction order of the elementary electron transfer step, r is the rate of consumption/formation of species, and C is the concentration of species in reaction of interest in units of moles per cubic centimeter. For an ideal gas, C=

P Ru T

(4.16)

Taking the anodic (oxidation) reaction branch of Eq. (4.13), kb

BR −−−−−−−→ AO+ + ne−

(4.17)

Then the oxidation rate of the elementary charge transfer reaction can be written as |ra | =

  (1 − β) n F (φ − φref ) mol ia  Pa = k = [C ] exp −E − R a,a a s · cm2 na F Ru T

(4.18)

Let the reference potential for the anode and cathode electrodes (øref ) be 0 V (SHE potential)   (1 − β) n F(φ) ia Pa = ka [C R ] exp |ra | = na F Ru T

(4.19)

where we have absorbed Ea,a , the oxidation reaction reference activation energy, into the ka term to become ka , the anode reaction rate constant. For the reduction reaction rate at the cathode |rc | =

  ic −βn F(φ) = kc [C O ] Pc exp nc F Ru T

(4.20)

Some derivations also absorb the electron transfer number n into β as nβ = αc

(4.21)

where α c is known as the cathodic charge transfer coefficient, and n(1 − β) = αa

(4.22)

where α a is known as the anodic charge transfer coefficient. It is important to note that n is the number of electrons transferred in the elementary charge transfer step. This is very different from the global reaction n we defined for

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Faraday’s law and in the Nernst equation. Typically, n here is less than 2. Based on the single charge transfer reaction step used in Eq. (4.8), the value of n should be an integer. However, experimentally this value is often determined to be a noninteger, which can be true if more than one reaction is acting as a limiting charge transfer step in parallel. In this case, the BV model can still be applied to model an electrode’s reaction kinetics, but the value of n determined experimentally will be a noninteger value, a result of the cumulative effect of the multiple charge transfer reaction steps. Charge Transfer Coefficient From the definition of the cathode charge transfer coefficient α c , it physically represents the fraction of additional energy that goes toward the cathodic reduction reaction at an electrode. It can also be thought of as a symmetry coefficient of the electrode reaction. In terms of the pendulum analogy shown in Figure 4.9, the pendulum does not have to be balanced. If the pendulum is tilted sideways with respect to the ground reference, additional work input to the system will asymmetrically add potential energy to the maximum height on each swing. Many reactions tend toward symmetry, so with no information it is usually reasonable to assume a value of 0.5 = α c . The effect of the charge transfer coefficient on the electrode polarization symmetry is shown in Figure 4.17. The negative values of overpotential correspond to the cathode polarization, and the positive values of polarization correspond to the anode reaction. The vertical axis corresponds to the current density. For a charge transfer coefficient of n × 0.5, polarization affects the anodic and the cathodic reaction at a given electrode equally, and the curve is symmetric around the axis. For a cathodic charge transfer coefficient that is n × 0.75, the polarization required for the cathodic reduction reaction for a given current is much less than the polarization required for the anodic oxidation. Obviously, a cathode with α c > n × 0.5 would be preferred for the cathode. However, as an engineering design parameter, there is little we can do to alter this value in practice for a given electrode, and other parameters we can affect through engineering, such as the exchange current density io , have a much greater impact.

α c = 0.25n

α c = 0.50n

i α c = 0.75n

Positive

Negative

Positive

η

α c = 0.75n Negative

α c = 0.50n

α c = 0.25n

Figure 4.17 Effect of charge transfer coefficient on symmetry of current–overpotential curves. (Reproduced from [1].)

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Performance Characterization of Fuel Cell Systems

Note that we are still not considering the entire fuel cell yet! We are discussing a single electrode with simultaneously occurring oxidation and reduction reactions. For nonequilibrium operating conditions, we desire a net current density. For a net oxidation current density at the anode we consider the net oxidation reaction rate: rnet,anodic = ra − rc = = ka [C R ] Pa

ia ic i − = na F nc F nF     αa F(φ) −αc F(φ) − kc [C O ] Pc exp exp Ru T Ru T

(4.23)

At open circuit, the fuel cell net current density is zero, but the rates of exchange ra and rc are not zero but equal. We can solve for this resting exchange current density io :   io αa Fφ ◦ Pa = ra = rc = ka [C R ] exp nF Ru T  ◦ Fφ α c = kc [C O ] Pc exp − Ru T

(4.24)

where ø◦ is the equilibrium potential (OCV) at i = 0. If we rearrange Eq. (4.24) and take the natural log of both sides,  Pr  Cr RT RT kc − φ = ln ln nF ka nF CoPo ◦

or

 νr  Cr RT E(OCV) = E (T ) − ln nF Coνo (4.25) o

which is the Nernst equation! This makes sense, since any kinetic theory must reduce to the thermodynamic theory at equilibrium. So at inet = 0, we are at equilibrium, and the expected maximum voltage is determined from the Nernst equation, as we have already shown in Chapter 3. Now, consider the overpotential at an electrode, η, which represents a departure from this equilibrium potential: η = φ − φo

(4.26)

Plug this into Eq. (4.23), and we can show that rnet =

    i αa F(φ) −αc F(φ) − kc [C O ] Pc exp = ka [C R ] Pa exp nF Ru T Ru T

(4.27)

and the net current density in the oxidation (anodic) direction, inet , at a single electrode can be shown as    Ru T kc C Pc αa F Ru T η+ ln ln oPa + i net = n Fka C RPa exp Ru T nF ka nF CR (4.28)    Ru T αc F Ru T kc CoPc Pc η+ − n Fkc C O exp − + ln ln Pa Ru T nF ka nF CR

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Simplifying yields

i net =

(1−β)Pc β Pa n Fkc(1−β) ka(−β) C O CR

  αa F −αc F exp η − exp η Ru T Ru T

(4.29)

At open-circuit conditions, inet = 0, but each component of anode/cathode current must equal the exchange current density io . So the first term in brackets at OCV (η = 0) is the oxidation branch at the electrode, and the second term is the reduction branch. At η = 0, each branch must be at the exchange current density, so that io – io = inet = 0. So we see that the term outside the brackets in Eq. (4.29) is really the exchange current density. We can now rewrite our standard BV model of kinetics for an individual electrode: i net

  αa F −αc F = i o exp η − exp η Ru T Ru T

(4.30)

If  i o = i o,ref

C C∗

γ

 = io

C C∗

γ (4.31)

where α a and α c refer to the anodic and cathodic charge transfer coefficients at the electrode, respectively. This is to be applied at each electrode. For example, for the anode i cell = i net,anode

  αa,a F −αc,a F ηa − exp ηa = i o,a exp Ru T Ru T

(4.32)

  αa,c F −αc,c F ηc − exp ηc = i o,c exp Ru T Ru T

(4.33)

For the cathode i cell = i net,cathode

By conservation of charge, ia = ic = icell , so that

γH2   CH2 ,surface αa,a F −αc,a F exp η η i o,a − exp a a CH∗ 2 Ru T Ru T

γO2   CO2 ,surface αa,c F −αc,c F exp ηc − exp ηc = i o,c CO∗ 2 Ru T Ru T

(4.34)

In words, this means that the net current at the cathode and anode is conserved, providing the linkage between the two electrodes. The overpotential at each electrode will adjust to

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Performance Characterization of Fuel Cell Systems

match this current as long there is enough voltage potential available. If not, the limiting current is reached and the current level is not possible. In general,  γ      Cs αa F −αc F exp η − exp η (4.35) i cell = i o C∗ Ru T Ru T I

II

where Eq. (4.35) can be used for net oxidation or reduction reactions, with I representing the oxidation branch of the electrode reaction and II representing the reduction branch. This is our standard model of BV kinetics and can be used to solve for the activation and mass transfer polarization at each electrode. Some points to remember: Ĺ I in Eq. (4.35) is the oxidation reaction at the particular electrode. Ĺ II in Eq. (4.35) is the reduction reaction at the particular electrode. Ĺ icell is the fuel cell total current density (the same for both electrodes by conservation of charge). Ĺ io is the exchange current density of the electrode of interest and is a function of reaction concentration, temperature, catalyst, age, and other factors. It is different for anode and cathode reactions on an electrode: io,c = io,a . Ĺ Cs is the electrode reactant concentration at the catalyst surface. Ĺ C* is the reference concentration of the reactant at STP conditions. Ĺ α a is the anodic charge transfer coefficient, the fraction of the activation polarization energy of reaction that goes toward enhancing the oxidation branch of the reaction at a given electrode. The parameter α a,a refers to the anodic charge transfer coefficient at the anode, and α a,c refers to the cathodic charge transfer coefficient at the anode. Ĺ α c is the fraction of the additional activation polarization energy of the reaction that goes into enhancing the reduction branch of the equilibrium; α c + α a = n, where n is the number of electrons transferred in the elementary reaction step for the electron transfer. Experimentally, this value is often found to be a noninteger between 1 and 2 due to multiple charge transfer reactions. Ĺ γ is the reaction order for the elementary charge transfer step, which can vary for different electrodes and reactants and is typically determined experimentally. Ĺ η is the activation overpotential at the given electrode and is in units of volts.

Exchange Current Density Exchange current density io is a very important parameter that has a dominating influence on the kinetic losses. It appears from Eq. (4.35) that activation polarization should increase with temperature. However, io is a highly nonlinear function of the kinetic rate constant of reaction and the local reactant concentration and can be modeled with an Arrhenius form as    CR γ Ea i o (T, C R ) = i o,ref exp − (4.36) Ru T C R,ref where R refers to the reactant at that electrode and io,ref is the reference exchange current density with no concentration loss and at a reference temperature. It is important to note that the exchange current density is not an intrinsic function of a catalyst, although it is

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Figure 4.18 Typical polarization curve for low-temperature PEFC. Despite the use of an expensive platinum catalyst, there is still significant activation polarization. The fuel cell is operating at 65◦ C, with zero back pressure, 100% RH on anode and cathode, anode stoichiometry of 1.5, and cathode stoichiometry of 2.0.

most strongly related to the catalyst choice. It is also a function of electrode morphology, catalyst type, reactant, temperature, pressure, age, and other factors. Two electrodes with the same catalyst density can have different exchange current density values. Another point concerning the exchange current density is as follows: In general, the more complex the reactant molecule, the lower the exchange current density. Therefore, we expect the hydrogen oxidation exchange current density for a given electrode to be high relative to a methanol oxidation exchange current density for the same electrode. Thus, io is an exponentially increasing function of temperature and the net effect of increasing temperature is to significantly decrease activation polarization in a highly nonlinear fashion. For this reason, high-temperature fuel cells such as SOFC or MCFC typically have very low activation polarization and can use less exotic catalyst materials. Accordingly, the effect of an increase in electrode temperature is to decrease the voltage drop within the activation polarization region. Typical polarization curves from a lowtemperature PEFC and a high-temperature SOFC are shown in Figures 4.18 and 4.19, respectively. Within the various fuel cell systems, however, the operating temperature range is typically dictated by the electrolyte and material properties, so that temperature cannot be arbitrarily increased to reduce activation losses. For example, the operating temperature of a conventional PEFC is limited to <120◦ C due to electrolyte material limitations. Roughness Factor In some cases, the ratio of the actual electrochemically active catalyst surface area to the planform geometric surface area is used as a separate parameter to delineate morphology effects, called the roughness factor a: a=

actual electrochemically active area planform geometric area

(4.37)

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Figure 4.19 Typical polarization curves for high-temperature SOFC in different gas environments at 1000◦ C. The high operating temperature enables the use of low-cost catalyst materials such as nickel (anode) and strontium-doped lanthanum manganite (cathode), with very low kinetic polarization losses. (Reproduced with permission from [5].)

Roughness factors for carbon-supported platinum electrodes are typically between 600 and 2000 [6], and can decrease with age and operation due to catalyst sintering and morphological changes due to stresses in the catalyst layer. When the roughness factor is used as a separate parameter, the BV expression is then shown as      αa F −αc F η − exp η (4.38) i cell = ai o exp Ru T Ru T and thus some inclusion of catalyst morphological effects can be included in the formulation. The exchange current density is the dominant parameter in the BV equation and has a strong effect on the activation loss. Typical values for the exchange current density for various reactions with an acid electrolyte are given in Table 4.1. Exchange current densities for alkaline electrolytes are given in Table 4.2. Keep in mind that the exchange current density is a strong function of temperature, electrode active catalyst area and morphology, concentration, and other factors. Nevertheless, the relative orders of magnitude are consistent, and several trends can be noted 1. The HOR for both low- and high-temperature fuel cells in acid (cation transfer) and alkaline (anion transfer) electrolytes is much more facile than the ORR. 2. A key advantage of alkaline electrolytes is the relatively high exchange current density for the ORR compared to acid electrolytes which is in general 10 to 100 times greater than for acid-based electrolytes. Very high operating efficiencies are possible with these systems, although other limitations certainly exist. 3. Obviously, temperature has a large effect. Comparing the same reaction in a lowtemperature PEFC (80◦ C) to a high-temperature SOFC (1000◦ C), io for the HOR

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Table 4.1 Selected Typical Exchange Current Densities for Different Reactions and Smooth Electrodes in an Acid Electrolyte at 300 K, 1 atm. Electrode Reaction

Catalyst

Value* (A/cm2 )

HOR HOR HOR ORR ORR ORR ORR-PEFC ORR-PEFC ORR-PEFC ORR-PEFC

Pt Pd Ni Pt Pd Rh Pt-C PtCr-C PtNi-C PtFe-C

1 × 10−3 1 × 10−4 1 × 10−5 1 × 10−9 1 × 10−10 1 × 10−11 3 × 10−9 9 × 10−9 5 × 10−9 7 × 10−9

∗ Value

given is for smooth electrode surfaces. The roughness factors in fuel cells can range from 600 to 2000, however, increasing the effective exchange current density. Source: Data adopted from [7].

and the ORR is orders of magnitude higher for the SOFC, even using inexpensive nonnoble catalysts that would be entirely ineffective at PEFC temperatures. 4. Surface roughness also plays a key role. The more electrode area is available for reaction, the higher the effective exchange current density (aio ) can be. 4.2.2 Butler–Volmer Simplifications Considering the electrode polarization–current relationship, there are three regions, as shown in Figure 4.20: 1. A low-overpotential region where kinetics are facile and relatively low losses occur 2. A higher overpotential region, where losses become much more significant 3. A very high current region where mass transport losses dominate The BV equation is a very common model for electrode kinetics applied in most studies of fuel cells but does not provide an explicit analytical solution for the electrode overpotential η. Although we can still solve the full BV equation computationally, we would still prefer an explicit solution for η to enable more simplified calculation and decreased computational Table 4.2 Selected Typical Exchange Current Densities for Different Reactions and Smooth Electrodes in an Alkaline Electrolyte at 300 K, 1 atm. Electrode Reaction

Catalyst

HOR HOR HOR

Pt Pd Ni

∗ Value

Value* (A/cm2 ) 1 × 10−4 1 × 10−4 1 × 10−4

given is for smooth electrode surfaces. The roughness factors in fuel cells can range from 600 to 2000, however, increasing the effective exchange current density. Source: Data adopted from [7].

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ηactivation Linearized Kinetics Region

io Figure 4.20

Region 1

Region 3

Region 2

Tafel Kinetics Region

logi

Schematic of activation polarization behavior at an electrode.

complexity. Based on the mathematical form of the BV equation, there are several common simplifications that can be made to achieve this goal. Simplified Butler–Volmer Equation 1: Facile Kinetics—Linearized Butler–Volmer Model Whenever the exchange current density is very high and the current is low, a special form of the BV model can be applied. One has to be careful in its use, however, because the exchange current density is rarely large enough to justify its use for appreciable operating current densities. Nevertheless, in situations where the electrode polarization is very low (see Example 4.1), it is applicable. One example where this linearized version has been applied is for a pure hydrogen oxidation at high temperatures. The exchange current density for this reaction can reach 0.5 A/cm2 [8], which actually covers much of the normal operating range. Even the SOFC cathode exchange current density can reach 0.2 A/cm2 at this elevated temperature. From the BV equation      αa F −αc F η − exp η i cell = i o exp Ru T Ru T

(4.39)

Let x = α i Fη/Ru T. Using a power series expansion to describe ex and eliminating the higher order terms for a numerically small values of x, ∼0 for small x, x3 x2 + +... 2! 3!     αa F −αc F η+1 − η+1 = io Ru T Ru T

x = 1+x + i cell

(4.40) (4.41)

With algebra we can show the desired result, an explicit expression for the activation polarization at the electrode as a function of current density. Keep in mind that this expression is only valid in the low-loss region circled in Figure 4.21. η=

i i Ru T Ru T = i o (αa + αc ) n F io n F

(4.42)

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Slope breakoff due to mass transfer effects

ηactivation Linearized kinetics region

Tafel kinetics region

io Figure 4.21

Region I: Activation Polarization

log i

Region of applicability for linearized Butler–Volmer model.

Example 4.1 How Applicable Is the Linearized Assumption? We should always desire to understand the limitations of our approximations. In this case we would like to examine the applicability of our assumption that, for values of low polarization, we can assume that, mathematically, ex ≈ 1 + x (a) Calculate the activation polarization η where the linearized assumption is appropriate for a low-temperature PEFC at 80◦ C and a high-temperature SOFC at 1000◦ C. (b) Calculate the value of x = α i Fη/Ru T where the linearization is appropriate. SOLUTION

(a) To approximate the BV equation as linear, we assume e x ≈ 1 + x, where x=

αi Fη Ru T

Assuming α a ∼ α c ∼ 0.5 as a reasonable value with a single electron transfer (n = 1), we can show that x=

0.5 × 96,485η 8.314T



C J mol mol C J



Rearranging for η, x = 5802

η T

If we compare ex to the approximation e x ≈ 1 + x at 353 and 1000 K, we can plot the following figure:

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So for 353 K, as long as the polarization is less than around 40 mV, the linearized approximation is fairly precise. For the higher temperature SOFC case, the approximate and exact solutions diverge significantly around 0.1 V. (b) In this case, we simply plot the exact versus approximate solution for different values of x. Divergence from the exact solution indicates the imprecision in the linearization approximation.

From this plot, we can see that the linearized approximation is effective until x = α i Fη/Ru T > ∼ 0.15. At x = 0.15, the error is only a little over 1%. COMMENTS: This result shows another way to check the accuracy of the linearized BV approximation. Although the simplifications to the BV are convenient, it is important to be

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Slope breakoff dueto mass transfer effects

ηactivation

Linearized kinetics region

io Figure 4.22

Region I: Activation Polarization

Tafel kinetics region

log i

Region of applicability for Tafel kinetics model.

sure they are applied correctly. In this case, if x = α i Fη/Ru T < 0.15, the linearized BV is an acceptable approximation. Simplified Butler–Volmer Equation 2: High-Electrode-Loss Region of Butler–Volmer Model—Tafel Kinetics Whenever the exchange current density is very low or the polarization is significant, a special form of the BV model can be applied that applies to the high-loss region of the electrode polarization curve circled in Figure 4.22. In most cases, the Tafel kinetics can be applied with little error, since only the small region where the linearized kinetics are valid is ignored (this region is actually quite smaller in most cases than Figure 4.22). Examples where Tafel kinetics are applicable include almost every fuel cell reaction besides pure hydrogen oxidation at high temperature. From the BV equation, we see that for high polarization one of the branches will dominate. For an anode reaction with positive η, the anodic branch will exponentially increase, while the cathodic branch will be a diminishing function. For a cathodic reaction with negative η, the cathodic branch will exponentially increase, while the anodic branch will be a diminishing function: i cell = i o exp

αaF −αcF η −exp η RuT RuT

(4.43) One of the branches will dominated for high η Therefore, with high losses at a given electrode, one of the branches can be neglected, leaving the Tafel kinetics model. This can be rearranged to provide an explicit expression for η as a function of cell current:      ±α j F Ru T i η ⇒η=± ln i cell = i o ± exp Ru T αj F io

(4.44)

where the subscript j is used to indicate the value is related to the dominant branch of the electrode. Since the ± is awkward to include, it is omitted in the rest of the book. However, cathode polarization is negative with reference to the SHE and anode polarization is positive with reference to the SHE, as shown in Figure 4.5.

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Example 4.2 How Applicable Is the Tafel Assumption? Here we wish to evaluate the range of validity of the Tafel kinetics assumption. As in Example 4.1, we wish to evaluate a general criterion for the range where x = α i Fη/Ru T results in one of the branches of the BV becoming negligible. SOLUTION To solve, rearrange the two branch terms from the BV equation to form a ratio of the anodic to cathodic branch:  exp αRau FT η  = branch ratio cF exp −α η Ru T Assuming positive polarization (net anodic current), we can plot the following:

When x > 1.2, the branch ratio is approximately 10 : 1, and we can apply Tafel kinetics. COMMENTS: This represents a general criterion for the applicability of the Tafel kinetics assumption with low error. Before detailed calculations are made, one should always check the applicability of the assumptions and simplifications made. Example 4.3 Calculation of Expected Polarization with Tafel Kinetics Plot the activation polarization as a function of current density for an electrode ignoring all other losses for an initial OCV of 1.2 V. Use the following values for the parameters: io = 0.3 to × 10−4 A/cm2 . Assume the reaction is occurring at 353 K and α a = α c = 0.5. SOLUTION From the last example we know Tafel kinetics will be valid when x = α i Fη/Ru T > 1.2, which occurs for η > 0.07 V in this case. With the Tafel approximation, we have to evaluate   i Ru T ln η= αj F io

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The plot is shown below:

These polarization curves were deduced using Tafel kinetics at a single electrode only and no other losses. Note that the Tafel expression results in zero losses (mathematically, it will actually predict negative polarization, which is physically unrealistic) until i > io . The exact solution shown for io = 0.3 A/cm2 shows the error associated with the Tafel approximation with a higher exchange current density. COMMENTS: Notice the strong effect of the exchange current density near the open circuit. There are still activation polarization losses accumulating throughout the entire polarization curve, but the effect is most dramatic at low current density. Determination of Exchange Current Density In 1905, based on experimental observation, Tafel proposed the following relationship between electrode overpotential and current density [10]: η = a + b log i

(4.45)

Using the Tafel approximation from the BV equation (4.35), we can show that a = 2.303

Ru T log i o αj F

b = −2.303

Ru T αj F

(4.46)

where b is the Tafel slope. Experimentally, the exchange current density and charge transfer coefficient are found with a Tafel plot, which is a plot of the log of current density versus overpotential for a given reaction. From the slope of a semilog plot of voltage versus current, the charge transfer coefficient can be determined, and from the intercept the exchange current density can be found. Figure 4.23 is a Tafel plot for a hydrogen PEFC. Near zero overpotential, these curves deviate from linearity on a log scale (Not shown in

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Figure 4.23 Experimental Tafel plot of cell voltage versus current, corrected for fuel cell ohmic and other losses, so that only cathode polarization losses are remaining. The results are normalized to platinum loading. Results with open circles are with humidified oxygen, and closed circles are with humidified air. The dashed line represents the Tafel slope behavior. Note that for all loadings the Tafel slope for oxygen reduction on platinum is the same but deviates from this behavior under masslimiting behavior. Also note that the vertical axis is ohmic corrected fuel cell voltage, not electrode overpotential, so the voltage falls with increasing current density. (Reproduced with permission from [9].)

Figure 4.23), since the opposing branch of the BV equation can no longer be neglected, and the Tafel approximation is not valid. At very high current density, deviation is observed experimentally due to concentration polarization effects. An experimental Tafel slope for the ORR in a humidified H2 /O2 fuel cell is shown in Figure 4.24. The data in Figure 4.24 were extracted from the polarization curves of fully humidified PEFCs operating on pure

Figure 4.24 Tafel plot for ORR current–overpotential curve. Data for a H2 –O2 PEFC at 80◦ C with different cathode catalyst loadings. The slope of the line (Tafel slope) for all conditions is approximately 0.65 mV/decade. (Reproduced with permission from [9].)

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Slope breakoff due to mass transfer effects

ηactivation Linearized kinetics region

io Figure 4.25

151

Tafel kinetics region

log i

Region of applicability for sinh BV simplification.

oxygen and hydrogen at high stoichiometry. After correcting for measured ohmic losses, one can measure the kinetics of a fuel cell in situ; however, careful ohmic correction and pure, fully humidified reactants are needed to avoid concentration and other unaccounted losses. For an electrode ex situ, Tafel measurements can be accomplished with the use of a reference electrode and galvanostat/potentiostat to impose a desired voltage or current on the working electrode. Simplified Butler–Volmer Equation 3: Butler–Volmer Equation with Identical Charge Transfer Coefficients–sinh Simplification A very nice simplification can be made to the BV model if the anodic and cathodic charge transfer coefficients at the electrode are equivalent (i.e., α c = α a ). In this case, no approximation is needed, and a new form explicit in η and mathematically equivalent to the original BV model can be written. This model is valid over all regions of the electrode polarization, as shown in Figure 4.25. If α c = α a = α, we can rearrange the BV equation into a general form: 

i cell



   αF −α F η − exp η = i o exp Ru T Ru T

 α Fη = i o expx − exp−x where x = Ru T

(4.47)

From mathematics sinh (x) = 12 (expx − exp−x )

(4.48)

Comparing Eqs. (4.47) and (4.48), we can show that i cell

     αF 1 αF exp = 2i o η − exp − η 2 Ru T Ru T   αF η = 2i o sinh Ru T

(4.49) (4.50)

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Taking the inverse, we can show our desired expression:   i cell Ru T η= sinh−1 αF 2i o

(4.51)

Summary of Butler–Volmer Kinetics and Useful Simplifications 1. General kinetics, applicable under all current density conditions; the general BV expression for η (solve numerically):      αa F −αc F i cell = i o exp η − exp η (4.52) Ru T Ru T 2. Low polarization, facile kinetics, linearized BV approximation (explicit η expression): η=±

Ru T i i o (αa + αc ) F

3. High polarization, Tafel approximation (explicit η expression):   Ru T i η= ln αj F io 4. Both regions, α a = α c sinh simplification (explicit η expression):   Ru T i cell =η sinh−1 αF 2i o

(4.53)

(4.54)

(4.55)

Example 4.4 Selection of Proper Butler–Volmer Kinetic Model Solve for the most appropriate symbolic expression for the activation overpotential at each electrode in the given examples. SOLUTION Case 1: Solid Oxide Fuel Cell On the anode, a pure hydrogen feed at 1000◦ C is used with low losses. The cathode shows high losses but you can assume that α a,c = α c,c : At the anode: simplified model, facile kinetics, since no information on the charge transfer coefficient is given: 

 αa,a + αc,a F Ru T i cell   ηa i cell = i o,a ηa = Ru T i o,a αa,a + αc,a F At the cathode: simplified model, sinh simplification, since α a,c = α c,c :     αF Ru T i cell i cell = i o,c × 2 sinh = ηc ηc sinh−1 Ru T αF 2i o,c

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Case 2: Direct Methanol Fuel Cell At the anode and cathode, there are significant polarizations: At the anode: simplified model, Tafel kinetics:      αa,a F i cell Ru T ⇒ ηa = ηa ln i cell = i o,a exp Ru T αa,a F i o,a At the cathode: simplified model, Tafel kinetics:      αc,c F i cell Ru T ⇒ |ηc | = ηc ln i cell = i o,c − exp − Ru T αc,c F i o,c Case 3: Hydrogen PEFC At the anode the exchange current density is very high with α a,a = α a,c . At the cathode io ∼ 1 × 10−7 A/cm2 and α c,c = α a,c : At the anode: simplified model, linearized kinetics (we should check this assumption, as in Example 4.1, with more information): 

 αa,a + αc,a F Ru T i cell   i cell = i o,a ηa = ηa Ru T i o,a αa,a + αc,a F At the cathode: simplified model, sinh simplification:     Ru T i cell αF = ηc ηc sinh−1 i cell = i o,c 2 sinh Ru T αF 2i o,c COMMENTS: The sinh simplification is generally preferred to the Tafel or lineraized BV approximation if appropriate, since it is mathematically equivalent to the full BV equation. Also, we should note the concentration effect is ignored here but can significantly affect the exchange current density through Eq. (4.31). Example 4.5 Activation Polarization Loss Calculation the following:

Given the table below, solve for

(a) Using the appropriate kinetics, calculate the anodic activation overpotential (ηa,a ) at 0.5 A/cm2 . (b) Using the appropriate kinetics, calculate the cathodic activation overpotential at 0.5 A/cm2 . Parameter

Value

Temperature na (elementary charge transfer step) nc (elementary charge transfer step) β a,a β a,c E ◦ (T, P) i o,a i o,c

363 K 1 1.2 0.5 0.5 1.15 V 1.5 A/cm2 0.005 A/cm2

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SOLUTION (a) Calculate the anodic activation overpotential at 0.5 A/cm2 (ηa,a ). The linearized BV equation can be used since α i Fη/Ru T < 0.15. Also, since in this case α a,a = α a,c = βna , sinh can be used:     Ru T i cell 0.5 8.314 × 363 = 0.0104 V = ηa,a = sinh−1 sinh−1 αF 2i o,a 0.5 × 96,485 2 · 1.5 (b) Calculate the cathodic activation overpotential at 0.5 A/cm2 (ηa,c ). The Tafel BV approximation can be used since α i Fη/Ru T > 1.2:     8.314 × 363 i cell 0.5 Ru T = ln ln = 0.24 V ηc = αc,c F i o,c 0.5 × 1.2 × 96,485 0.005 COMMENTS: The number of electrons transferred in the elementary charge transfer step at the cathode, nc , can be a noninteger value if derived experimentally since there can be more than one charge transfer reaction in parallel. The kinetic polarization voltages in this example are typical relative to one another. That is, the ORR losses usually dominate activation losses when pure hydrogen is used as the fuel. Model Development Returning to our ultimate goal of this chapter to analytically model the polarization curve, we now have an expression that includes the starting equilibrium voltage from the Nernst equation (the top of the “waterfall”) and the departure from the waterfall resulting from activation overpotential on the anode and cathode:     (4.56) E cell = E ◦ (T, P) − ηa,a − ηa,c  −ηr − ηm,a − ηm,c  − ηx
  Can now solve

Next, we need to add ohmic, concentration, and other polarization losses before our model is complete. 4.2.3

Langmuir and Tekmin Model of Kinetics2 For an electrochemical reaction to take place, the reacting species must first undergo adsorption or chemisorption onto the reacting surface followed by an intermediate reaction to an activated complex, as depicted in Figure 4.26. For example, consider the following HOR mechanism intermediate reactions: H2  2 (H − M)ad (H − M)ad  H+ + e−

(4.57) (4.58)

For the charge transfer to take place at the catalyst surface, the reacting species is first adsorbed onto the catalyst, in this case dissociating in the process into separately adsorbed hydrogen atoms. Here, M indicates the adsorbing catalyst surface. After adsorption, the charge transfer reaction can take place. In BV modeled reactions, the intermediate charge transfer steps are rate limiting, and the adsorption is comparatively facile and rapid. However, this is not always the case. In 2 This

section can be skipped without loss of continuity.

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Step 1: Dissociative chemisorption of hydrogen

H2

H H

Catalyst Surface Ionomer (a) (To Bipolar plate)

e–

e– Step 2: Electro-oxidation H

H

Catalyst surface H+

Ionomer

(To cathode)

H+

(To cathode)

(b)

Figure 4.26

Schematic of electrochemical reaction and absorption.

some situations, the rate-limiting step can be the surface adsorption or chemisorption of the reacting species onto the catalyst sites. Certain situations in fuel cells can be characterized in this fashion. Specifically, this can be important where a catalyst poison interferes with the desired reaction. As an example, when hydrogen containing part-per-million levels of carbon monoxide is introduced into the anode of a low-temperature PEFC, the carbon monoxide electro-oxidative desorption from the catalyst is very slow relative to the carbon monoxide adsorbtion and the hydrogen electro-oxidation reactions. The key rate-limiting reaction is believed to be the electrochemical oxidative desorption of CO from the catalyst site [11]. H2 O + (M − CO) −−−−−→ M + CO2 + 2H+ + 2e−

(4.59)

Other similar cases exist, such as direct electro-oxidation of alcohols such as methanol and formic acid in low-temperature fuel cells. In these cases, an alternative to the BV formulation that accounts for the limiting adsorption and charge transfer steps is appropriate. Two common models for a surface adsorption limited reaction are the Langmuir and Temkin kinetics. In the simpler Langmuir model, the surface adsorption rate constant is independent of surface coverage. In the Temkin model, the adsorption rate constant is modeled as a function of the surface coverage of adsorbed species. In both models, a two-step reaction mechanism is assumed [6]: 1. A surface adsorbtion/desorbtion reaction, one or both of which are rate determining. 2. An electrochemical reaction responsible for ion exchange and current generation that is assumed to be much faster than the adsorbtion/desorbtion step. In addition, the reaction is assumed to occur so fast that the reverse reaction is assumed to be negligible.

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This two-step mechanism can be expressed as k1 f

R + M
(R − M)ad

(rate limiting)

(4.60)

k1b

k2 f

(R − M)ad −−−−−→ R +n + ne−

(relatively fast)

(4.61)

Where k1f , and k1b represent the adsorbtion and desorption reactions (which can be physical or chemical), respectively, and R represents the molar gas-phase concentration of the reacting species. The k2f reaction represents the fast-forward ion charge transfer reaction of the adsorbed species responsible for the current generation, and it is assumed the reverse reaction is negligible. It should be noted that other species or parallel reactions can also be included in the above formulation methodology. If θ represents the fraction of the available catalysis sites that the adsorbed species occupies, we can then write dθ = k1 f y R P (1 − θ ) − k1b θ − k2 f θ  


dt I

II

(4.62)

III

Term I represents the adsorption of species R onto the remaining noncovered reaction sites. If θ becomes 1, representing uniform surface coverage, the adsorption obviously stops. The partial pressure of species R (yR P) is also included in Eq. (4.62) since the adsorption from the gas phase is proportional to the concentration in the gas phase. Term II represents the desorption of the adsorbed species from the reactive surface and decreases the surface coverage. Term III is the forward electrochemical ionization reaction responsible for current flow. From inspection of Eq. (4.62), in the case of an adsorption-limited reaction, the kinetic limiting current density should be the maximum possible adsorption rate where the surface coverage θ becomes zero, or i lim ∝ k1 f y R P (1 − θ ) − k1b θ − k2 f θ ∝ k1 f y R P

(4.63)

The constant of proportionality is the electrons per mole of reactant, nF, or i lim = n Fk1 f y R P

(4.64)

so that, for an adsorption-controlled reaction, the limiting current density is linearly proportional to the gas-phase partial pressure, and adsorption rate constant k1f can be either assumed to be constant (Langmuir model) or a function of the surface coverage (Temkin model). Here, we will show solution for the Langmuir model. The reader is referred to advanced electrochemistry texts for additional details on Temkin kinetics [e.g., 12]. The overall electrochemical reaction rate can be shown as i = n Fk2 f θ

(4.65)

Using this two-step model, which can be expanded to include other intermediate steps as well, a simple formulation for the electrode overpotential current relationship at a given electrode can be developed. If we assume that the reaction rate constants involved are independent of the surface coverage of reactant R, then we can derive the Langmuir kinetics model solution. With constant rate constants in Eq. (4.62), at steady state we can

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157

show that dθ = 0 = k1 f y R P (1 − θ ) − k1b θ − k2 f θ dt

(4.66)

Then, solving for surface coverage, we can show, from algebraic manipulation, that θ=

k1 f y R P k2 f + k1b + k1 f y R P

(4.67)

Physically, this shows the surface coverage fraction is simply the ratio of the adsorption reaction to the total sum of parallel reactions. Then the current density i becomes   k1 f y R P (4.68) i = n Fk2 f θ = n Fk2 f k2 f + k1b + k1 f y R P Now we seek to relate this expression to the overpotential required to produce that current density at the electrode of interest, so that we can predict electrode overpotential as a function of current density in a similar fashion as with the BV approach for electrontransfer-limited reactions. The electrochemical reaction rate constant k2f can be written as     1 io αn F = exp η (4.69) k2 f s nF Ru T where io is the exchange current density at θ = 1. Using Eq. (4.68), we can achieve our desired result, an explicit expression for electrode overpotential as a function of current density and other measurable parameters for an absorption-limited electrochemical reaction under the Langmuir model:    i n F k1b + k1 f y R P Ru T   ln η= (4.70) αn F i o n Rk1 f y R P − i The reaction rates required for solution would be determined from existing literature or from direct experimental results.

4.3 REGION II: OHMIC POLARIZATION At moderate current densities, a primarily linear region is evident on the polarization curve in Figure 4.1. In region II, reduction in voltage is dominated by internal ohmic losses (ηr ) through the fuel cell, resulting in the nearly linear behavior, although activation and concentration polarization in this region are still present. The ohmic polarization can be represented as n

 rk ηr = i A (4.71) k=1

where each rk value is the area-specific resistance of individual cell components, including the ionic resistance of the electrolyte, and the electric resistance of bipolar plates, cell

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RA = Ω-m I

A = Cross-sectional area

I = Linear path of ion travel

Figure 4.27

Schematic of ion travel in conductor.

interconnects, and contact resistance between mating parts and any other cell components. For most fuel cell types at the beginning of operating life, ohmic polarization is dominated by ionic conductivity in the main electrolyte and in the catalyst layers. Electronic resistance is typically relatively low, unless there are aging or assembly/contact issues. Electronic and Ionic Resistance To solve ohmic resistance problems, some basic tools are required. First, Ohm’s law can be written V = IR = iAR

(4.72)

where R is the resistance, measured in units of ohms ( = Js/C2 ), and A is the electrode geometric surface area. The resistance is a function of the geometry of the conducting material. The resistivity ρ is an intrinsic property of a material related to the resistance through the cross-sectional area of ion travel, A, and the linear path length of ion travel, l, as shown in Figure 4.27. Resistance and resistivity are terms typically used to describe ohmic drop in materials that have significant resistance. For materials with very low ionic resistivity, the inversely related conductance G and conductivity σ are commonly used. By definition 1 = 1/ m = S/m ρ 1 = −1 = S G = conductance = R σ = conductivity =

(4.73) (4.74)

and Ohm’s law, Eq. (4.72), can be shown as V = iA

l il = = iρl σA σ

(4.75)

Table 4.3 shows some typical conductivity values for selected fuel cell materials. Note the dominance of the ionic conductivity of the electrolyte. The functional dependence of electrolyte conductivity for various fuel cells is covered in Chapter 5. From a basic understanding of Ohm’s law, we can identify the critical factors governing these ohmic losses in a fuel cell: 1. Material Conductivity The electrolyte and catalyst layer should have the highest possible ionic conductivity and all other components including the catalyst layer should have the highest possible electrical conductivity.

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Table 4.3 Typical Conductivity/Resistivity Values for Selected Fuel Cell Materials

Component

Typical Bulk Through-Plane Conductivity σ i or σ e

Typical Thickness

PEFC electrolyte SOFC electrolyte

σ i = 10 S/m (hydrated) 50–200 µm 10–300 µm σ i = 1–10 S/m (>800◦ C)

AFC electrolyte

σ i on order of 1–100 S/m at operating temperature

MCFC electrolyte

0.5–2.0 mm σ i on order of 1–100 S/m at operating temperature σ i on order of 1–100 0.5–2.0 mm S/m at operating temperature σ i = 5000–20,000 S/m 2–4 mm each

PAFC electrolyte

PEFC bipolar plate (graphite) PEFC gas diffusion layer (GDL) PEFC catalyst layer

0.5–2.0 mm

σ i = 10,000 S/m (much less in plane) ∼1–5 S/m

100–300 µm

Contact resistances for cell

Very low if built well; resistance ∼30 m ·cm2

Not available, use area as contact area

Total cell resistance (based on active cell area)

Total resistance < 100 m ·cm2

Not available, use cell superficial active area

5–30 µm

Functional Dependencies Temperature, water content Temperature, dopants (conductivity through oxygen vacancies) Ion concentration, temperature, charge number on ion, dielectric constant of solution, mobility, viscosity, degree of ion dissociation, other liquids See AFC electrolyte

See AFC electrolyte

Oxide film (corrosion), materials, coatings Approximately constant Morphology, Nafion and carbon loading, age Compression, pressure, temperature, age (corrosion), number of cycles, and others, current collector total landing area See above

2. Material Thickness The ohmic losses are directly proportional to the distance traveled by the current. In addition to a compact design, this is the reason the electrolyte and other components are manufactured to be as thin as other constraints will allow. Example 4.6 Estimate Total Fuel Cell Resistance Given the experimental polarization data for a SOFC at 700◦ C from [13], estimate the ionic resistance of the electrolyte. Is this a maximum or a minimum value for the actual ohmic resistance of the electrolyte? SOLUTION To estimate the ohmic resistance of the electrolyte under these conditions, we can take the slope of the main linear region of the polarization curve. In doing so, we are assuming that the activation and concentration polarization are minor. Although not

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Voltage

0 0.03 0.07 0.1 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

1.08 1.02 0.968 0.925 0.861 0.754 0.648 0.542 0.436 0.329 0.223 0.117 0.011

a Data

from [13].

completely appropriate, this behavior is approached for a high-temperature fuel cell in the low to moderate current density regimes. A solution can be found by solving for the slope of the polarization curve in the main linear region. First, plot the polarization curve and select the appropriate region. In this case, because it is a high-temperature fuel cell operating on hydrogen, the overall polarization curve is quite linear and dominated by ohmic effects.

COMMENTS: This technique should be a maximum possible value for the ohmic resistance, because we have assumed that the slope in the middle region of the polarization curve is solely a result of ionic losses. In fact, activation and concentration polarization losses also contribute to the voltage loss in this region, although for these high-temperature fuel cells the approximation is very close. There are other experimental techniques to more accurately obtain the ohmic resistance in the cell. Some of these methods are discussed in Chapter 8 on experimental methods.

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4.3 Region II: Ohmic Polarization x 0

Figure 4.28

Catalyst layer—mixed conductivity

δCL

Electrolyte—ionic conductivity only

δe

Catalyst layer—mixed conductivity

δCL

Schematic of electrodes and main electrolyte in generic fuel cell system.

For a well-built fuel cell, the dominating ohmic polarization, ηR , is from the electrolyte. This includes the ionic transport resistance in both the main electrolyte separator and the electrodes, since the electrodes will have ionic (and electronic) conduction as well. Otherwise, reactions occurring in the electrode could not conduct the ions through the electrolyte. Even though the catalyst layer in most fuel cells is only on the order of 5–30 µm, the mixed conductivity and highly porous nature can result in a significant contribution to the overall ohmic drop of the fuel cells. The reaction in the catalyst layer not only is at the surface facing the flow field but is also distributed throughout the three-dimensional porous structure. The distribution of current throughout the three-dimensional porous structure of the catalyst layer is a complex issue that is a function of ionic and electronic conductivity, reactant concentration, catalyst distribution, and other factors beyond the scope of this text. In many models, the reaction distribution of the catalyst layer is assumed to occur in a single plane due to the thinness of the catalyst layer. A simplification can be made to allow us to estimate the resistance losses in the electrode if we assume the average location of the reaction in the electrode is at the dashed line in Figure 4.28, representing the half distance through the electrode. This implies a homogeneous current distribution throughout the thickness of the electrode structure. The effective electrode ionic conductivity can be written as [14] σi,eff =

σi,eff εelectrode τ

(4.76)

where τ is the electrolyte tortuosity, which was determined to be approximately 1 [15] for PEFCs. In Eq. (4.76), εelectrolyte is the volume fraction of electrolyte in the catalyst layer, which is typically 10–30% in PEFCs. This concept is illustrated in Example 4.7. Contact Resistance Contact resistance is a result of imperfectly matched material interfaces in the fuel cells. At every location where there is a noncontinuous contact between dissimilar materials, there is an electronic or ionic contact resistance, as illustrated in Figure 4.29. The contact resistance is a function of the material surface state and roughness and the contact pressure between the materials (values of area contact resistance are given in units of · m2 or · cm2 ): Vloss ( · cm2 ) i Vloss = ( ) i Acontact

 = Rcontact

(4.77)

Rcontact

(4.78)

where Acontact is the contact area between the two surfaces. This leads to an interesting engineering trade-off in channel design, illustrated in Figure 4.30. The smaller the landing

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Figure 4.29 Schematic of single PEFC assembly, illustrating all contact surfaces. (Image courtesy of Joseph Scott [16].)

areas, the greater the area available for mass transport, and the lower the flow channel pressure drop for the same flow rate. However, the smaller the landing area, the higher the ohmic drop from contact resistance. Therefore, a balance including this and other competing factors is sought for fuel cell design. Major factors in contact resistance include the following: 1. State of Contact Surface If contacts are oxidized, as can occur over time in a oxidative environment, this factor can become significant. Special coatings on metal contacts can be used, such as gold or nitrides that resist surface oxidation. 2. Compression Pressure from Current Collector onto Electrode or Diffusion Media In larger cells, it is difficult to achieve an ideal state of uniform compression, and current collection can be biased toward locations with better contact.

L

C

L

C

L

L

C

L = 2C (a)

C

L

C

C = 2L (b)

Figure 4.30 Illustration of trade-off between contact resistance transport. Typical channel to land ratios in fuel cells range from 1 : 1 to 3 : 1. (a) Wide land, low contact resistnace. (b) Narrow land, high contact resitance.

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3. Tolerance and Flatness of Individual Fuel Cell Bipolar Plates To achieve a uniform compression on a stack that can have as many as 300 fuel cells in series, a very tight manufacturing tolerance on the flatness of individual bipolar plates must be achieved. The change in a hundred or so micrometers can have a major effect on the distributed contact resistance. Example 4.7 Cell Ohmic Loss Limiting Current Calculation Consider an ideal PEFC with only the ionic ohmic losses in the electrolyte and catalyst layers. Ignore kinetic, electronic, and other losses for this problem. The OCV is 1.0 V, and the electrolyte conductivity σ e is 8.3 S/m. The catalyst layers can be assumed to be 40% ionomer equivalent and 30 µm thick. Consider two cases: (a) The electrolyte is Nafion 112, which is 51 µm thick. (b) The electrolyte is Nafion 117, which is 178 µm thick Find the maximum current density that each electrolyte can support, ignoring other polarizations besides ohmic losses. SOLUTION

From Ohm’s law

l l = A σA  l    l =i V =I R = iA R=i A σA σ  −1 la le lc i max,112 = V  + +  σa σe σc R=ρ

I

 = (1.0 J C)

II



III

15 × 10−6 m 51 × 10−6 m 15 × 10−6 m  +   + 0.4 × 8.3 S m 8.3 S m 0.4 × 8.3 S m

−1

1 m2 = 6.58 A/cm2 10,000 cm2 where I, II, and III represent the ionic resistances in the anode catalyst layer, main electrolyte, and cathode, respectively. The ionic conductivity of the electrodes is reduced by the ionomer fraction via Eq. (4.76), and the average location of the reaction in the electrodes is assumed to occur midway through the catalyst layer. For the Nafion 117 electrolyte  le lc −1 la + + σa σe σc

−1  15 × 10−6 m 178 × 10−6 m 15 × 10−6 m  +   = (1.0 J C) + 0.4 × 8.3 S m 8.3 S m 0.4 × 8.3 S m 

i max,117 = V

1 m2 = 3.28 A/cm2 10,000 cm2

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As we expect, the thicker electrolyte supports a significantly lower maximum current density. Based on ohmic losses only, if we plotted the predicted polarization curves, they would look as follows:

COMMENTS: Although low-temperature PEFCs tend to be limited by reactant availability (concentration polarization), many high-temperature fuel cells are ultimately limited by the ionic conductivity of the electrolyte, because mass transport and kinetics are facilitated at high temperature (e.g., see polarization curve in Example 4.6). Also, note the relative importance of the electrolyte in the overall loss. Considering that some PEFC electrolytes can be as thin as 18 µm, the electrode resistance can even be larger than that of the main electrolyte. Also it should be noted that the use of ionomer percentage to adjust ionic conductivity is an approximation, as well as the approximation that reaction occurs in the middle of the catalyst layer. More complex modeling of these reactions and losses are available in literature but are beyond the scope of this text. Cell Assembly In terms of the compression pressure on the fuel cell, there are initially high benefits to increased compression and reduced contact resistance. Think of a stack loosely held together by gravity. Contact losses would obviously be high, as shown in Figure 4.31. As the compression is increased, there is a plateau region where optimal contact pressure is reached. If the compression is increased too far beyond this level, however, the components in the fuel cell will suffer plastic (permanent) deformation and cause a very sharp drop-off Plateau region Cell voltage

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Desired design point Compression pressure

Figure 4.31

Cell performance at given current as function of stack compression pressure.

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in performance that is not recoverable. In a brittle fuel cell or one with significant thermal expansion of the materials such as the SOFC, thermal and compressive stresses can result in catastrophic failure of components. Different types of fuel cells obviously have different material limits for plastic deformation, but the qualitative shape is the same as Figure 4.31. For low-temperature fuel cells, the presence of liquid water does not influence the contact resistance since pure water is nonconductive. Over time, various components may deform to relax the compression stress in the materials, loosening contacts. Some stacks are designed to be spring loaded at the endplates to provide consistent compression. Also, since each channel design is different, with different channel-to-land ratios, it is impossible to state an optimal compression pressure for a fuel cell. For PEFCs, the compression pressure of 1–2 MPa is generally appropriate, but the optimal compression pressure must be determined experimentally for a given fuel cell and components. In general, several criteria can be used to determine the best compression on a cell or stack: 1. Prescribed Torque or Spring Loading Imposed on All Compression Bolts or TieDowns This method is common in laboratories with single cells. However, this method is highly unreliable and can lead to significant variation in compression pressure and uniformity, since the compression torque is a function of the interfacial friction on the bolt threads or between the nut and washer and the back compression plate. In general, this method should only be used with caution on a well-characterized fuel cell. 2. Compression Gap Width The materials under compression will have a measurable gap width decrease under compression, and the compression force on the fuel cell is increased until a desired elastic deformation is achieved in the stack. For example, in the PEFC, many diffusion media work best when compressed by 10–20% of their original thickness. Another advantage is that the gap width can be measured at locations around the periphery to ensure uniformity of compression. 3. Compression Pressure Specification The compression pressure of the flow field on the fuel cell is prescribed. The compression pressure can be determined experimentally with a load cell inserted in the fuel cell or with pressure-sensing contact paper as shown in Figure 4.32. The proper compression pressure can then be correlated with the measured gap width or bolt torque.

Figure 4.32 Pictures of Pressurex pressure-sensing paper used to measure contact pressure distribution in 5-cm2 fuel cell with different torque on fuel cell bolts. The higher the compression, the better the electrical contact. At some point, however, the cell will become overcompressed.

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In practice, large stacks of hundreds of cells are assembled using large automated presses to ensure uniformity of assembly and proper cell sealing. Example 4.8 Equivalent Ohmic Loss Thermal Network resistance network for a single PEFC.

Draw an equivalent ionic

SOLUTION

COMMENTS: The cell and resistance network above shows all the resistances present, electronic and ionic. Note the mixed ionic and electronic conductivity required in the catalyst layer. In most cases except the catalyst layer, the electronic resistance is negligible. Of the various contact resistances, the electronic contact resistance between the land and diffusion media tends to become dominant for PEFCs [17]. Example 4.9 Resistance Calculation Consider a PEFC operating at 0.6 V, 1 A/cm2 , 2 with 500 cm active area electrodes. Nafion 112 (51-µm) electrolyte and a graphite current collector are used, with 3-mm-thick current collection plates, a 200-µm GDL on the anode, and a 300-µm GDL on the cathode. The catalyst layers are 10 µm thick on the anode and 20 µm on the cathode and can be approximated as 0.3 fraction ionomer on the anode and 0.35 fraction ionomer on the cathode. The electrolyte ionic conductivity can be assumed to be 8.3 S/m. The landing to channel area ratio is 1 : 2, and the measured total contact resistance is 30 m · cm2 (a) Estimate ηR , the voltage loss from resistance. (b) Estimate the percentage of total potential power wasted due to ohmic losses at this condition if Eth = 1.25 V.

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SOLUTION (a) We can neglect the electronic resistance in most cases relative to the ionic resistance: ηR = i A

n 

Ri = i A(Ranode + Rcathode + Relectolyte + Rcontact + Relectric ≈ 0)

j=1

Plugging in the equations and the current and active area,   n  1 1 R  1 + + + contact ηR = i A Ri = (1 A/cm2 )(500 cm2 ) σa A σe A σc A Acontact j=1 The contact area is one-third of the active area since the landing to channel ratio is 1: 2:  n  (5 × 10−6 m) · (10,000 cm2 /m2 ) Ri = (500 A) ηR = i A (0.3 × 8.3 · m)(500 cm2 ) j=1   (51 × 10−6 ) × 10,000 (10 × 10−6 ) × 10,000 0.03 · cm2 + + + 8.3 × 500 0.35 × 8.3 × 500 166.6 cm2 Resulting in: η R = 0.205 V (b) We can simply compare the electrical power at a condition with no losses to the condition including our calculated ohmic losses: P1 = I V = 1.25 V · 500 A = 625 W P2 = I V = 1.044 V · 500A = 522.0 W (625 − 522) = 16.48% Wasted = 625 COMMENTS: At a relatively high current density of 1 A/cm2 , we see that the ohmic losses are very significant. For a PEFC, the ionic conductivity of the electrolyte is a strong function of humidity. Lower humidity values greatly increase the impact of ohmic losses, steepening the slope of the ohmic drop on a polarization curve. Returning to our ultimate goal of being able to analytically describe the fundamental physics of the polarization curve, we now have an expression that includes the starting equilibrium voltage, the departure from this voltage resulting from activation overpotential at each electrode, and the ohmic polarization:     (4.79) E cell = E ◦ (T, P) − ηa,a − ηa,c  − ηr −ηm,a − ηm,c  − ηx
  Can now solve

The only remaining major losses are a result of reactant crossover and concentration polarization, discussed in the following sections.

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4.4

REGION III: CONCENTRATION POLARIZATION Concentration polarization is caused by a reduction in the reactant surface concentration, which reduces the thermodynamic voltage from the Nernst equation and the exchange current density from the BV equation. Figure 4.33 illustrates the transport of reactants from the flow channel to the reaction surface in a PEFC. The transport of species in the fuel cell is discussed in detail in Chapter 5. For now, we consider the effects of reduced reactant availability at the surface. At the electrode surface, reaction consumes fuel and oxidizer at the rate determined from Faraday’s law. A rate of transport of reactant must be at least equal to this or concentration polarization will develop: n˙ consumed =

iA ≤ n˙ transport nF

(4.80)

Restriction of the rate of transport to the electrode can occur for a variety of reasons: 1. Gas-Phase Diffusion Limitation The diffusion of reactant in the gas phase is limited to some value. In principle, we can imagine that there is a maximum rate that perfume can diffuse from the front of a room to the back of the room. Now consider the perfume is being consumed at the back of the room. The consumption rate would be limited to the maximum perfume diffusion rate, as the reaction rate is limited by reactant availability. At the double layer, a greater polarization will be required to attract the required adsorbed species for reaction in a limiting condition. 2. Liquid-Phase Accumulation and Pore Blockage Limitation In low-temperature fuel cells such as the PEFC, liquid water accumulation and blockage in the pores of the electrolyte, diffusion media, or flow channels of the anode or cathode can reduce the transport rate of reactant to the catalyst. Voltage loss by this phenomenon is generically termed flooding. This topic is discussed in greater detail in Chapters 5

Figure 4.33

Schematic of path through diffusion media to catalyst layer in PEFC.

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and 6. In liquid electrolyte systems such as the MCFC or PAFC, improper electrolyte control can also restrict reactant access to catalyst sites. 3. Build-up of Inert Gases This is also a gas-phase limitation but is a result of the accumulation of nonparticipating inert species such as nitrogen. As the oxygen is consumed in an air cathode, the nitrogen mole fraction increases. Near the electrode, the nonparticipating species can form an inert boundary-layer-restricting reaction. 4. Surface Blockage by Impurity Coverage In this case, some impurity becomes adsorbed on reaction sites, preventing adsorption of the desired reactant. This is commonly seen in low-temperature fuel cells when a CO impurity is present. Carbon monoxide preferentially adsorbs on platinum catalyst sites in the anode and has a very high polarization for oxidative removal. In Chapter 3, we learned that the Nernst equation could be used to predict the change in equilibrium voltage from concentration changes of the reactants and products. At the time, we noted that there was also a kinetic effect of the concentration. Once there is reaction at the electrode, the system is not in thermodynamic equilibrium and these effects must be considered. From a combination of the thermodynamic (Nernst) and exchange current density dependency [Eq. (4.31)], the voltage adjustment as a result of the change in oxygen concentration from the reference value (1 atm) on the cathode can be shown as
Vs,ref =

    CO2 ,s 1/2 Ru T CO2 ,s γO2 Ru T ln ln + 2F CO2 ,ref F CO2 ,ref

(4.81)

where γ is the ORR order with respect to O2 partial pressure at constant overpotential and ranges between 0.6 and 0.75 for a PEFC [9]. Assuming γ ∼ 0.75, the two can be combined into the following:
Vs,ref

  CO2 ,s Ru T ln = F CO2 ,ref

(4.82)

This predicts a 47-mV gain in potential for switching from dry air (21% O2 ) to pure oxygen at 353 K, a value that matches experimental data well [9]. On the anode, we can write
Vs,ref =

    CH2 ,s CH2 ,s γH2 Ru T Ru T ln ln + 2F CH2 ,ref F CH2 ,ref

(4.83)

where the reaction order for hydrogen is 0.25–1.0. In practice, the anode hydrogen concentration effect is often neglected for several reasons: 1. The diffusivity of hydrogen is much more rapid than oxygen, especially in higher temperature fuel cells, so that transport limitation is rare. 2. The HOR kinetics are facile compared to the cathode so that the cathode polarization typically dominates. 3. In PEFCs, liquid blockage (electrode flooding) occurs more frequently on the cathode, so that two-phase effects can be mostly ignored for low-temperature fuel cells at the anode and completely ignored for high-temperature fuel cells.

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iA nF

Porous diffusion layer Catalyst layer electrode

into electrode

Figure 4.34

Land iA nF

Suction of

Schematic of channel flow suction into catalyst layer of fuel cell.

Equations (4.81) and (4.83) can be used for any fuel and oxidizer reaction with different reaction orders. Considering flow through a fuel cell channel, there is a flux of products away from the catalyst, a suction of reactants to the catalyst surface due to reaction, and inert species not participating in the reaction, as shown in Figure 4.34. At higher current densities, the mass transport limitations can reduce the concentration of the reactants at the catalyst surface to well below the flow field channel concentration and cause a sharp decline in the output voltage. This concentration loss can be precipitous and corresponds to (region III in Figure 4.1). This region of the polarization curve is really a combined thermodynamic- and kinetic-related phenomenon that occurs independently at both electrodes. To determine an expression for ηm,a and ηm,c, the mass concentration polarizations at each electrode, consider Eqs. (4.81) and (4.83). From these, a general form of the voltage change at an electrode for concentration changes in reactant R from some state 2 to state 1 can be written as   C R,s,2 Ru T ln (4.84)
VC2 −C1 = ηc = VC2 − VC1 = (n + γ ) F C R,s,1 Example 4.10 Kinetic and Thermodynamic Effect of Change in Oxygen Concentration Determine the change in voltage expected for an increase in oxygen mole fraction from a fully humidified state at 90◦ C, 1.5 atm, to a fully humidified state at 70◦ C, 1.5 atm pressure. Assume an ORR order γ of 0.75. For this example, ignore changes in exchange current density with temperature. SOLUTION In this example, we are considering increasing the operating temperature of the fuel cell at constant relative humidity. This will have a positive effect in terms of the exchange current density (ignored here) but will also decrease the available oxygen mole fraction since the saturation pressure is strongly related to temperature, as we have discussed in Chapter 3. First we need to calculate the mole fraction of oxygen in both cases. From Chapter 3 Psat (T )(Pa) = −2846.4 + 411.24 T (◦ C) − 10.554 T (◦ C)2 + 0.16636 T (◦ C)3 Evaluation gives Psat (70) and Psat (90) = 0.31 and 0.69 atm, respectively. From RH =

Pv yv Ptotal = Psat (T ) Psat (T )

we find that yv (70) =

1 × 0.31 = 0.21 1.5

yv (90) =

1 × 0.69 = 0.46 1.5

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Next we need to covert the vapor mole fraction to the oxygen mole fraction. The ratio of oxygen to nitrogen in dry air is constant in humidified air at yO2 ,dry = 0.21. For the moist air at 70◦ C yair,70 = 1 − yv,70 = 0.79

yO2 = 0.21yair = 0.166

For the moist air at 90◦ C yair,90 = 1 − yv,90 = 0.54

yO2 = 0.21yair = 0.113

From simplification of Eq. (4.84) at 70 and 90◦ C, with γ = 0.75, we have
V70−90

  Ru T Co2 ,70 = ln F Co2 ,90

Finally: V70 − V90 =

Ru T ln (0.166) Ru = [343 ln (0.166) − 363 ln (0.113)] = 15 mV F ln (0.113) F

So decreasing the temperature from 90 to 70◦ C actually increases the expected voltage by 15 mV for a fully humidified system because the oxygen mole fraction will increase. There will also be an expected decrease in the exchange current density which can partially or completely offset this trend. However, this example illustrates another issue with operating PEFCs at elevated temperatures where the oxygen mole fraction in a moist system is decreased. COMMENTS: High-temperature PEFC operation has several disadvantages, including: (a) electrolyte material limitations (conventional electrolyte materials are limited to <120◦ C), (b) reduced oxygen mole fraction for humidified conditions, and (c) need for larger humidification system. The ideal operating temperature depends on the trade-offs between enhanced kinetics and decreased reactant concentration, humidification requirements, and longevity. For high-temperature fuel cell operation, an elevated pressure sometimes is preferred since it reduces the oxygen mole fraction decrease with temperature for humidified flow. Mass-Limiting Current Density We previously examined ohmic limiting current density. Now we consider the case of mass transfer limiting current density il . At the mass transport limiting current density, the rate of mass transport to the reactant surface is insufficient to promote the rate of consumption required for reaction. In this case, the local concentration of reactant will be reduced to zero, which, from Eq. (4.84), must also reduce the cell voltage to zero.3 Assuming the surface concentration (CR ) is zero at the limiting state (il )

3 Small

localized areas of fuel or oxidizer starvation in the fuel cell can exist, but if a significant area is depleted of fuel or oxidizer, the local voltage potential is reduced to zero, and since the catalyst layers are conductive, the voltage of the entire cell will be reduced to zero. Thus, when we operate a fuel cell, the flow stoichiometry of the anode and cathode must always be greater than unity to enable operation at sufficient voltage.

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and decreases linearly from state 1 to state 2, we can show that C R,s,2 = C R,s,1 − C R,s,1

  i i = C R,s,1 1 − il il

(4.85)

which we can plug into Eq. (4.84) and show that
VC2 −C1 = ηm = −

  i Ru T ln 1 − (n + γ ) F il

(4.86)

If we assume the reaction occurs only at the catalyst layer interface, which is true for high-current-density mass-transport-limited reactions, and we neglect kinetic effects, we are left with the Nernst equation at each electrode:   i Ru T ln 1 − ηm = − nF il

(4.87)

In practice, the concentration loss is more gradually observed than predicted by Eqs. (4.87) or (4.86), but the qualitative result of the equation holds (see Figure 4.35). The deviation from predicted values is a result of the dependence of the kinetics on reactant concentration, the accumulation of liquid water or the accumulation of inert species such as nitrogen, which cannot be easily predicted without inclusion of fuel cell geometry, material, and other parameters. To account for this deviation, a semiempirical approach is often used where Eq. (4.87) is changed slightly to include a constant (B) to better fit with experimental data:   i ηm = −B ln 1 − il

(4.88)

Figure 4.35 Comparison of concentration polarization predicted with Nernst equation and that predicted with semiempirical modification with B factor of 0.05 V at 353 K and il = 2.5 A/cm2 .

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Region III: Concentration Polarization

Therefore, the total concentration polarization of the fuel cell can be written as     i i ηm,a + ηm,c = −Ba ln 1 − − Bc ln 1 − il,a il,c

173

(4.89)

Each electrode will have this loss (and a separate limiting current density), although the anode loss is typically negligible for a hydrogen feed due to the high concentrations and mass diffusivity, so that a single expression is often used to represent concentration polarization. If the anode contribution to the concentration and activation polarization is ignored, little error would result for air–H2 systems. This is not the case for fuel cells without neat hydrogen as fuel or with significant dilution or impurities in the anode side, such as when the hydrogen gas from a fuel reformer is used. It is important to understand that each electrode has a different mass transport limiting current density, which can be approximated with the concepts discussed in Chapter 5. However, the minimum value of limiting current density between the electrodes will be the determining value on the fuel cell polarization curve. Example 4.11 Determine Concentration Polarization Given the anodic mass-transportlimited current density is 15 A/cm2 and the cathode mass-transport-limited current density is 2.5 A/cm2 , determine the anode and cathode concentration polarization at 0.1 and 1.0 A/cm2 . Assume the B factor is 0.045 V on both electrodes and Eq. (4.88) is appropriate and is determined from curve-fit of several polarization curves. SOLUTION

On the anode ηm,a

  i = −0.045 ln 1 − 15

which is 0.3 and 3.1 mV for 0.1 and 1.0 A/cm2 , respectively. On the cathode   i ηm,c = −0.045 ln 1 − 2.5 which is 1.8 and 23.0 mV for 0.1 and 1.0 A/cm2 , respectively. COMMENTS: The fuel cell maximum current density would be limited by the cathode il in this case. It would also be possible that the maximum current density is limited by kinetic or ohmic effects as well. Alternate Empirical Approach Another completely empirical approach to describe the overall fuel cell concentration polarization has been proposed [18–20]: ηm = m exp (ni)

(4.90)

If this equation is used, the constants m and n are typically fit from several polarization curves, and the total (anode + cathode) concentration polarization is included in this single expression. According to [20], typical values of the m constant are around 3 × 10−5 V, and the n constant is around 8 × 10−3 cm2 /mA for a PEFC. Although this expression completely loses physical meaning, it can be used to simply model the complex fuel cell stack mass transport limitations if plentiful polarization curve data are available.

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Functionally, the mass-limiting current density at each electrode depends on: 1. Fuel cell design (discussed in other chapters for various fuel cells) 2. Operating conditions and stoichiometry 3. Mass transport to the catalyst layer (discussed in Chapter 5) (a) Thickness and porosity of the diffusion media (PEFC and AFC) and catalyst layer (b) Transport mode to electrode (diffusion, forced convection) (c) free-stream concentration, temperature, pressure 4. Impurities/blockage/water accumulation/flooding or liquid electrolyte can cover the catalyst, hindering access to the catalyst Flow Stoichiometry Until now, we have discussed the flow into a fuel cell and not explored the fact that the concentration of reactant is depleted inside the fuel cell from consumption of reactant. Flow comes into a fuel cell with a molar flow rate of reactant shown in Chapter 2: n˙ in = λ

iA nF

(4.91)

The reactant consumed can be determined from Faraday’s law: n˙ consumed =

iA nF

(4.92)

Therefore the amount of reactant out of a fuel cell is n˙ in − n˙ consumed = (λ − 1)

iA nF

(4.93)

We can see now why the flow stoichiometry must always be greater than unity in a fuel cell, since in a unity condition, the flow leaving the fuel cell would contain no reactant, automatically assuring that the catalyst layer in this region would have no reactant and, according to the Nernst equation, zero voltage. It is important to understand that the entire fuel cell need not suffer reactant depletion. Since the fuel cell catalyst layer is electrically conductive, any significant region devoid of reactant can induce zero fuel cell voltage for a single cell. Even smaller, locally starved regions can reduce performance and accelerate degradation. If the cell is in a stack, then the individual fuel cell in series with severe reactant depletion can suffer voltage reversal. Voltage reversal can result in rapid degradation of the catalyst and support, and therefore local reactant depletion should be avoided. To avoid depletion, the minimum requirement is an inlet anode and cathode stoichiometry greater than unity. In a combustion engine, this would be like having a requirement that the engine have unburned gasoline and air in the exhaust. For both an internal combustion engine and a fuel cell this is obviously wasteful. If not recycled, the fuel cell loses the potential for the energy released by the reaction of the unreacted fuel and oxidizer, in addition to being a possible safety risk if released to the environment. In fuel cell stacks, the hydrogen or other fuel used is typically recycled back into the anode, which carries a parasitic energy penalty. In the cathode, since air is usually used, recycling is not neccesary.

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Some fuel cell designs have attempted to boost fuel utilization and reduce system parasitic losses with a dead-ended hydrogen fuel compartment. That is, the hydrogen flow channels have no exit, and fuel is either continuously or sporadically supplied at the consumption rate required for suitable performance. A major drawback of this approach is that inerts and poisons in the flow stream build up in the dead end over time, and at least periodic purging is needed. In low-temperature systems, liquid accumulation is also a common problem, and some flow in the channels is beneficial to remove liquid droplet accumulations [20]. Returning to our ultimate goal of being able to analytically describe the fundamental physics of the polarization curve, we now have an expression that includes the starting equilibrium voltage, the departure from this voltage resulting from activation overpotential at each electrode, the ohmic polarization, and concentration polarization:     (4.94) E cell = E ◦ (T, P) − ηa,a − ηa,c  − ηr − ηm,a − ηm,c  −ηx
  Can now solve

Only the crossover and shorting polarization losses need to be modeled, which are covered in the next section.

4.5 REGION IV: OTHER POLARIZATION LOSSES The final piece of the polarization curve to be modeled is the departure from the expected OCR given by the Nernst equation. For low-temperature PEFCs, the OCV is predicted to be around 1.2 V, but in practice, only about 1.0 V is observed. For a high-temperature SOFC, however, the actual OCV can be very close to the theoretical OCV. For the PEFC, the 0.2 V represents an incredibly significant efficiency loss before any useful current is even drawn. The departure from the theoretical OCV is typically a result of two phenomena: 1. Electrical short circuits in the fuel cell 2. Crossover of reactants through the electrolyte and subsequent mixed-potential reaction at the opposite electrode Electrical Shorts Electrical short circuits can happen if the cell is poorly designed or assembled or, more commonly, the electrolyte is not completely insulating for electrons. For low-temperature fuel cells, this is usually not a major problem, but for higher temperature fuel cells, especially SOFCs, the electrolyte phase can have a mixed conductivity for electrons that is dependent on material properties, temperature, and oxygen partial pressure. The transference number (ti ) is the ratio of electrolyte ionic conductivity to the total conductivity (ionic plus electronic), defined as [22] ti =

σi σi + σe

(4.95)

Obviously, a transference number close to unity is desired, and a value greater than 0.9 is found in conventional SOFCs. When a significant electrical conductivity exists in the

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electrolyte, current is short circuited through the electrolyte, causing a departure from the Nernst potential at open-circuit conditions, as well as additional losses throughout the entire polarization curve. At an open circuit, the current passed as a result of the electronic leakage equals the ionic exchange, and the following equation can be developed: E OCV = E ◦ (T, P)Nernst ×

σi = E ◦ (T, P) × ti σi + σe

(4.96)

One goal of SOFC research is the development of electrolyte structures with high ionic conductivity at low operating temperatures [22–26]. A problem with achieving this goal has been the mixed conductivity of the electrolyte. Ironically, a long-term goal of PEFC operation in to increase the operating temperature to provide tolerance to impurities and better heat rejection, while a long-term goal of SOFCs is to reduce operating temperature so that less expensive materials can be used. Phosphoric acid fuel cells do operate at an intermediate temperature but have power density and cost limitations. In fuel cells with coolant flow, ionic impurities which accumulate in the coolant over time can also cause short currents through the coolant to develop. Species Crossover In a high-temperature SOFC, the Nernst potential is reduced compared to a low-temperature PEFC, as discussed in Chapter 3. However, the normally observed OCV of a SOFC and a PEFC are similar, due to crossover losses in the PEFC. Crossover of reactants through the electrolyte can be a major issue degrading the performance of a PEFC. The 0.2-V loss typically suffered at the open circuit in a PEFC represents ∼20% efficiency loss without a useful electron being drawn. In a DMFC, the effect is even more extreme, since the liquid solution used as a fuel has a higher molecular density, thus crossing over more readily. For the DMFC, an actual OCV of 0.7 V (∼1.2 V is predicted) is normally observed due to this loss. Intensive research and development has been invested to lessen the crossover effect in DMFCs while not sacrificing operating performance. Physically, a large concentration gradient in the reactant between the anode and cathode sides acts as a driving force for diffusion of reactants across the electrolyte that compete with the opposing electrode reactions (Figure 4.36). Recall that with the Nernst equation we establish the thermodynamic equilibrium potential between the two electrodes. With crossover, the Nernst potential will be altered by slightly changing the surface

H2 O2 Anode

Cathode

Thin-film electrolyte

Figure 4.36

Reactant crossover in PEFC.

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concentrations at the catalyst surface, but this effect is negligible. The major effect of crossover on OCV is due to kinetics. At the hydrogen electrode, the exchange current density is typically orders of magnitude higher for the hydrogen electro-oxidation than for any reaction with crossover oxygen, despite the high reduction potential (see Table 4.1). Therefore, there is little interference from oxygen crossover at the anode, and a nearly true equilibrium can be established. However, at the cathode, the hydrogen crossover typically has a much higher exchange current density for oxidation than the ORR, which is very slow. At the cathode, a true thermodynamic equilibrium cannot be established due to hydrogen crossover oxidation reaction and relatively slower oxygen reduction kinetics, resulting in a mixed reaction and lowered OCV. It should be noted that, although the oxygen crossover to the anode has a small impact on the OCV departure, it does have an important impact on PEFC durability, discussed in Chapter 6. Because of these reasons, we seek to eliminate crossover of reactants in PEFCs and other fuel cells in general. From concepts discussed in the next chapter, the crossover can be related to the diffusion coefficient, thickness, and concentration gradient across the electrolyte through the one-dimensional version of Fick’s law [27]: n  − D

∂C ∂x

(4.97)

where D is a mass diffusivity coefficient, C is the molar concentration, and x is the length scale in the direction of transport. Even a very small amount of reactant crossover can have a large impact on OCV. Several approaches have been used to limit reactant crossover: Ĺ Change in Material Properties of Electrolyte If the PEFC electrolyte is made less permeable to the reactants [e.g., D in Eq. (4.97) is reduced], crossover losses will be reduced. However, this approach has the severe limitation of reducing the reactant transport to the catalyst, where it is needed, resulting in severe mass transport losses. From the concept of the reaction surface of Chapter 1, some diffusion of reactants through the electrolyte covering catalyst particles is needed for adequate performance. Other alterations of the electrolyte material porosity or use of composite structures have been tried with some success. Figure 4.37 shows the measured hydrogen crossover current density for several PEFC membranes. Notice that the thicker membrane limits crossover, as expected. Experimentally, the hydrogen crossover is oxidized until a mass transfer limiting condition is reached, which is proportional to the rate of hydrogen crossover. The equivalent current density produced by the crossover hydrogen can be solved from Faraday’s law, that is, i x = n˙ x 2F/A Ĺ Use of Thicker Electrolyte From Eq. (4.97), the longer the distance of diffusion, the lower the flux. This approach has been used extensively in the DMFC and other alcohol-based liquid solution fuel cells. Although this is effective to reduce crossover, the ohmic losses are directly proportional to electrolyte thickness, which limits the use of this technique in high-power applications. Ĺ Alteration of Morphology or Structure of Porous Media and/or Catalyst Layers to Limit Diffusion Through Electrolyte This approach is favored in DMFC applications because this approach allows the use of high-methanol-concentration

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Figure 4.37 Measured hydrogen crossover current density with different electrolyte structures [28]. The crossover current density is measured directly with a hydrogen anode and an inert humidified cathode compartment. The limiting current density of hydrogen oxidation at the cathode is determined to be the crossover current density.

solution. A very simple concept, a diffusion barrier is put between the catalyst layer and the diffusion media, causing a sharp diffusion gradient across this boundary which does not add to overall ionic impedance since it is not in the electrolyte. Since the methanol reaction is kinetically limited, the goal of this approach is to tailor the diffusion barrier to permit only the amount of methanol to reach the catalyst layer as is needed for the electrochemical oxidation reaction, since additional methanol is assumed to cross to the cathode: n CH3 OHcatalyst − n CH3 OHreacted = n CH3 OHcrossover

(4.98)

Ĺ Alteration of Electrolyte Composition to Consume Crossover before Reaching Electrode A novel approach by Wantanabe [29] was used where platinum particles were embedded within the PEFC electrolyte (Figure 4.38). The concept was designed to react the crossover hydrogen with crossover oxygen within the electrolyte to generate water and maintain high membrane humidity levels while reducing crossover losses. This approach is more costly since it involves additional platinum, and it may also lead to reduced durability. Ĺ Recirculation of Liquid Electrolyte In fuel cells with a liquid electrolyte, such as an alkaline fuel cell, recirculation of the electrolyte can be used to filter impurities and prevent crossover. This adds ancillary equipment and other system-related difficulties. Obviously, each approach has design limitations that result in a balance depending on the application. For example, for reduced ohmic losses, the ideal electrolyte thickness is infinitely thin. However, in this limit electrical shorts and crossover dominate. Some thickness is required to provide a physical separation barrier. Ultimately, since a very small amount (even milliamperes per cubic centimeter) of crossover will cause a large decrease

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Figure 4.38 Schematic of embedded catalyst for crossover elimination and internal water generation based on concept of Wantanabe [29].

in OCV, it is nearly impossible to completely eliminate this problem in polymer electrolyte systems. Modeling Crossover Losses There are several approaches used to empirically, semiempirically, or analytically account for the noted OCV deviation caused by internal currents or reactant crossover. For electrical conductivity effects, if the transference number (ti ) is known, it is a simple matter to add this effect to the performance deviation, since it can be modeled as a short circuit in parallel with the external current, whose resistance is Rshort =

δelectrolyte Aσe

( )

(4.99)

where δ electrolyte is the electrolyte thickness and A is the geometric area of the electrolyte. For mass crossover losses, several approaches have been taken, with different levels of accuracy and physicochemical relevance. The first approach is purely empirical, based on experimental data only. This is particularly useful for computational modeling that is not overly concerned with conditions at OCV. The difficulty with this approach is it may not be accurate and does not take into account the many related phenomena on OCV. From the Nernst equation with unity reactant activity we can show the theoretical equilibrium potential, which is close to accurate for the SOFC but assumes zero crossover and only accounts for equilibrium effects. From experimental observation of a hydrogen PEFC, Parthasarathy and co-workers [30] found that OCV (cathode potential vs. RHE) = 0.0025T + 0.2329

(4.100)

where T is in Kelvin. From the Nernst equation, the OCV decreases with temperature, while experimentally, the OCV is determined to increase slightly with the OCV for a PEFC. This is due to crossover losses. As the temperature increases, the exchange current density on the cathode increases dramatically, reducing the mixed potential effect of the crossover hydrogen. The empirical trend is only valid over the low-temperature range of PEFCs (up to ∼100◦ C), however, and should also be a function of catalyst, electrolyte thickness and material, age, and other factors not included in this simple fit. However, Eq. (4.100) has been used conveniently in modeling studies to simplify calculation. Other empirical forms can be derived based on experimental or theoretically determined data as needed.

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On a semiempirical basis, the crossover current density ix can be modeled as a base current density that occurs even under open-circuit conditions. In this approach the current density at the cathode is modeled as i + ix . At OCV, the external current i = 0, but ix is still active. For instance, if a Tafel kinetics approach is used on the cathode, we would model the cathode kinetic overpotential in the absence of concentration affects as ηa,c = −

  i + ix Ru T ln αc F i o,c

(4.101)

This has the desired effect of decreasing the OCV to observed levels but is really not an accurate representation of the true mixed potential reaction, in part because the exchange current density on the cathode for the ORR is different than for the HOR on the cathode. If a full analytical model of the surface is desired, the mixed potential must be properly accounted for and include separate terms to account for the kinetic losses associated with the individual reactions present on the particular electrode. Except in the cases where detailed analysis of the OCV effects is desired, this is often not necessary, since the OCV departure affects the starting potential at zero current but has little effect beyond the OCV loss. Example 4.12 Calculating Crossover Losses In ref. [9], the authors noted a hydrogen crossover loss of 3.3 mA/cm2 for their automotive H2 PEFC applications. Calculate the mass crossover rate of hydrogen through the membrane. Also, calculate and plot the cathode activation overpotential loss at open circuit and 1 A/cm2 as a function of cathodic exchange current density. Assume the cathodic charge transfer coefficient at the cathode is 1.5 at a temperature of 353 K, and the fuel cell has a 50 cm2 geometric area. SOLUTION The mass flux of hydrogen can be calculated from Faraday’s law and a unit conversion using the molecular weight of hydrogen. Note the need to keep consistent units of current density in the expression: nx =

3.3/1000 × 50 ix A = = 8.55 × 10−7 mol/s nF 2 × 96,485

To convert to mass crossover rate, we use the MW: m˙ x = n x · MWH2 = (8.55 × 10−7 mol/s)(2 g/mol = 1.71 × 10−6 g/s We can assume Tafel kinetics at the cathode; then ηa,c = −

    i + 0.0033 i + ix Ru T = −0.0203 ln ln αc F i o,c i o,c

At OCV this becomes ηa,c = −

    0.0033 ix Ru T = −0.0203 ln ln αc F i o,c i o,c

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Plotting the activation losses as a function of cathodic exchange current density, we find:

COMMENTS: Even a very small crossover results in an extremely significant polarization loss near an open circuit. In the PEFC at low temperatures, 0.1–0.2 V is typically sacrificed to crossover. At high current density, the added effect of the crossover is minimal, though, as i >> ix .

4.6 POLARIZATION CURVE MODEL SUMMARY Returning again to our overall model, we now have a complete representation of the polarization curve. If we know several key paramaters relating to the kinetic, ohmic, and mass transfer processes, we can predict the overall polarization curve of the fuel cell. Much more complex models exist in the literature to cover multidimensional, multiphase, and transient aspects as well as approach the problem from various length scales from molecular to full-size stack simulation. However, the approach taken here does include the most important physicochemical phenomena that affect fuel cell performance:     (4.102) E cell = E ◦ (T, P) − ηa,a − ηa,c  − ηr − ηm,a − ηm,c  − ηx Extension of these relations into multi-dimensional is a matter of additional mathematics, not fundamental understanding. From Chapter 3 

υoxidizer   Pfuel υfuel PO2 Ru T
G ◦ + ln E (T, P) = − (4.103) ∗ nF nF Pfuel PO∗2 The anode and cathode activation polarization losses (ηa,a and ηa,c ) for most fuel cell reactions can be determined from Eq. (4.35), the BV equation or a simplified form [i.e., Eqs. (4.52)–(4.55)].

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The ohmic polarization, ηr can be determined from Eq. (4.71), including contact, ionic, and electronic resistances. The concentration polarization values, ηm,a and ηm,c from Eq. (4.86), and the crossover losses can be included by adding either the fuel crossover current density to the cathode current (mass transfer) or an internal short resistor for the case of a mixed conductivity in the electrolyte. We still cannot fully investigate the concentration polarization without the tools of Chapter 5, which will allow us to predict the mass transfer limiting current density. Alternative Simplified Empirical Model The complexity of the model shown requires calculation or estimation of many parameters that are themselves functions of operating conditions. Additionally, due to the many complexities and material, geometry, fluid manifolding, and so on, not included in our bulk model, the calculated results often have a large deviation from experimental results. As stated, much more complex computational models exist, but even these have significant deviations from measured results because not every phenomenon can be accurately modeled and many of the transport parameters needed still have significant uncertainty in their values. It must be emphasized that the basic model presented in this chapter is a mere starting point and is not intended as a quantitative or exact solution for all operating fuel cells. Instead, it serves to promote understanding of the underlying physicochemical phenomena that control performance, so that an understanding of the engineering trade-offs in design optimization can be achieved based on the qualitative trends predicted. Given the error and experimental effort associated with estimation of all the parameters in the analytical model and the complexity and time required for computational simulation, which, ultimately, still relies on the accuracy of the input parameters, there is a need for an entirely empirical approach to quickly characterize performance of fuel cells and stack designs. The following semiempirical model can be used to quickly glean some comparative information:   i (4.104) E cell = E OCV − A ln (i) − i R − B ln 1 − il or, using Eq. (4.90) [20], E cell = E OCV − A ln (i) − i R − m exp (ni)

(4.105)

where A, R, B, il , m, and n, are parameters taken from curve-fits of experimental data. Each form has fit parameters for activation, ohmic, and concentration polarizations. For the OCV, an empirical equation or constant can be used based on experimental data. This approach is useful to quickly model real fuel cell performance, and by comparison with other similar curve its, the relative impact of the ohmic, concentration, and activation polarizations between different designs can be compared. Example 4.13 Predicting Change in Polarization Curve Based on our understanding of fuel cell polarizations, we can now diagnose and predict basic polarization curve behavior as a function of the relevant parameters. We should be careful not to generalize too much, as many other minor effects and differently combined variables can lead to similar bulk

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Summary

183

polarization curve results. Nevertheless, at this stage basic conclusions and predictions can be made based on the understanding of this chapter: (a) Sketch a typical hydrogen PEFC polarization curve with electrolyte A. Then, sketch a polarization curve with the same operating conditions, but with a thicker electrolyte B. Be sure to think about all of the effects of this change. (b) Sketch a typical high-temperature fuel cell (SOFC, MCFC) polarization curve operating at temperature A. Then, sketch a polarization curve B with elevated temperature conditions. Be sure to think about all of the effects of this change. (Ignore the effects on mass transport region until Chapter 5.) (c) Sketch the shape of the anode and cathode electrode polarizations versus current for the hydrogen PEFC. SOLUTION

COMMENTS: When thinking about changes in operating conditions, the effects on all the regions of the polarization must be considered. Some of these we cannot yet fully understand (without Chapter 5, that is). Note that in many cases what seems like a completely positive effect has other limitations that require an engineering optimization.

4.7 SUMMARY This chapter presents a fundamental background in the various polarization losses on a fuel cell system. The main figure of merit for a fuel cell system is the polarization curve, shown in Figure 4.1. Starting at the maximum (unobtainable) thermal voltage E◦◦ , the potential is reduced to the predicted Nernst open circuit potential due to entropy and concentration effects. From this initial maximum possible starting point, four main modes of polarization occur: 1. Activation polarization dominates at low current density and occurs at each electrode. 2. Ohmic polarization occurs throughout the polarization curve as a result of ionic and electronic bulk and contact resistance through all components of the fuel cell, but typically is dominated by the electrolyte ionic transfer resistance. 3. Concentration polarization dominates at high current density and occurs at each electrode. 4. Crossover or mixed-conductivity polarization is mainly responsible for the departure from the expected Nernst potential at open-circuit conditions.

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The activation polarization is commonly modeled with the BV expression, which assumes the electrochemical reaction is rate limited by a charge transfer process:      αa F −αc F i cell = i o exp η − exp η Ru T Ru T Several simplifications that allow explicit calculation of the activation overpotential are possible from this expression, including: 1. Tafel kinetics for high polarization (branch ratio 10 : 1):   i Ru T ln η=± αj F io 2. Linerarized kinetics for low polarization (α i Fη/Ru T < 0.15): η=

i Ru T i Ru T = i o (αa + αc ) F io n F

3. A sinh simplification for the case where the anodic and cathodic charge transfer coefficients are equal:   i cell Ru T sinh−1 η= αF 2i o In electrochemical reactions, the dominating kinetic parameter is the exchange current density io , which is a strong function of temperature and reactant concentration. The exchange current density is not an intrinsic parameter of a catalyst and is also a strong function of the morphology of the electrode structure:    CR γ Ea i o (T, C R ) = i o,ref exp − Ru T C R,ref The ohmic polarization loss can be represented symbolically as n

 nr = i A rk k=1

where the summation is performed over the contacts and bulk ionic and electronic resistances of all components. The losses are typically dominated by ionic resistance in the electrolyte, which is discussed in Chapter 5. The concentration polarization is a result of decreasing surface concentration of reactant. The restriction can be a result of gas-phase transport limits, impurity absorption at the catalyst surface, liquid blockage in low-temperature fuel cells, or other reasons. The thermodynamic (Nernst) and kinetic concentration polarization at an electrode can be written as   i ηm = −B ln 1 − il

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185

where B is an empirical constant and il is the mass transfer limiting current density at that electrode. Another approach is to use an empirically derived expression: ηm = m exp (ni) The departure from Nernst OCV is a result of reactant crossover through the electrode and mixed reaction potential, or electrical shorts from mixed electrolyte conductivity. For most fuel cell systems, the major concern is reactant crossover, although high-temperature SOFC systems suffer from some electrical conductivity in the electrolyte. For the mass crossover case, the effect can be modeled by inclusion of the crossover current density with the fuel cell current density activation overpotential at the electrode with the mixed potential reaction. The various polarization losses are summarized in the following equation for fuel cell voltage as a function of current density:     E cell = E ◦ (T, P) − ηa,a − ηa,c  − ηr − ηm,a − ηm,c  − ηx where E◦ (T, P) is solved from the Nernst equation.

APPLICATION STUDY: POLARIZATION CURVE LOSSES Now that this chapter is completed, we have some real analytical tools to work with to describe fuel cells in operation. The methods shown in the chapter can be applied to any fuel cell system, given appropriate transport and electrochemical parameters. First, the empirical method can be used to curve-fit any experimental polarization curve and to understand a little about the general performance of a fuel cell. The basic analytical model we described can be applied to more fundamentally understand the roles of particular types of materials and geometry on the performance, provided all of the unknown quantities can be properly fit or estimated from existing resources. Fortunately, there are a lot of existing data available that are continuously updated in technical journals, which can be used as a starting point for evaluation of polarization behavior. For this assignment: (a) Find a recent fuel cell technical journal article or publication with some experimental polarization curves in it at different experimental conditions for either a fuel cell or stack. Perform an empirical curve fit of the form of Eq. (4.105). Find a best-fit kinetic, ohmic, and mass transfer parameter fit. (b) Try to estimate (or use vales provided) for a more complete analytical model from this chapter. Use given parameters where available and reasonable assumptions or approximations where there is not enough information. (c) Use the results of parts A and B to estimate fuel cell performance at different operating conditions. Discuss how reasonable the results are and what would be needed to have a more accurate predictive tool. Some good journals to refere to are the Journal of Power Sources, Journal of the Electrochemical Society, Electrochimica Acta, and others your professor can provide. Your school

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library likely has online access to some of these resources or can get the relevant texts for you. The websites of these journals provide free topical searches and abstracts to get you started. In lieu of these data, you can also use the data provided in the table below for a PEFC operating at 65◦ C, 1 atm back pressure, 100% RH inlets, anode and cathode stoichiometry of 1.5 and 2.0, respectively.

Current Density (A/cm2 )

Voltage (V)

0.0000 0.0539 0.1817 0.4129 0.6944 0.9132 1.0850 1.2894 1.4452 1.5612 1.6509 1.7300

0.9317 0.8493 0.7995 0.7490 0.6992 0.6493 0.5989 0.4993 0.3988 0.2990 0.1987 0.0000

PROBLEMS Calculation/Short Answer Problems 4.1 Draw a typical polarization curve and label the regions dominated by activation polarization (A), ohmic polarization (B), and concentration polarization (C). Also label the specific locations of the OCV (D), Mass-limiting current density il (E), heat-generating region (F), and useful electric region (G). Discuss the factors that result in the various polarizations (e.g., the catalyst choice has a strong effect on the activation region, as do many other factors). 4.2 (a) Consider a fuel cell stack with poor overall compression. What region of the polarization curve would be most affected? (b) Consider a poor catalyst layer. What region of the polarization curve would be most affected? (c) Consider the electrolyte becomes very dry in a PEFC and the ionic conductivity decreases. What region of the polarization curve would be most affected? 4.3 Describe what is happening when a low-temperature H2 –O2 PEM fuel cell is “flooded” and what region of the polarization curve in Problem 4.1 (A, B, or C) would be most affected?

4.4 Explain why the operating stoichiometry of a fuel cell reactant can never be equal to or less than 1 (without recycling effluent gas). 4.5 Consider a hydrogen fuel cell with 80% H2 and 20% water vapor in the anode at 2 atm total pressure. If the hydrogen mole fraction is reduced to 70% because the water content has increased to 30%, what must your anode total pressure be to offset the effect of the increased water content on expected OCV? Consider Nernst and kinetic effects with a hydrogen reaction order of 1. 4.6 Fill out the plot for a typical PEFC. The plot is of fuel cell voltage at a given steady-state current versus compression pressure:

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Problems 4.7 Consider the following typical polarization curve for a fuel cell. Be careful to consider all the effects of what the question poses!

187

4.10 Consider a hydrogen fuel cell with 75% N2 , 19% oxygen, and 6% H2 O in the cathode at 1 atm total pressure. If the oxygen mole fraction is reduced because water vapor has been added to the cathode (new balance 15% O2 , 25% H2 O, and 60% N2 ), the expected OCV will fall. To counter this loss, you suggest changing the cathode pressure. To what value must your cathode total pressure be changed to in order to maintain the OCV? Conditions on the anode are not to be changed. 4.11 Given the table below of parameters for a 50-cm2 active-area fuel cell, solve the following:

(a) Consider the case where we have half the thickness of the electrolyte. Draw the expected polarization curve. Label the curve A. (b) Consider the case where we increase the exchange current density of both electrodes. Draw the expected polarization curve. Label the curve B. (c) Consider the case when we increase the temperature of operation in reference to the baseline case already drawn. Label the curve C. 4.8 Consider the polarization curve of an electrode below. If we decrease the activity of this electrode by using a worse catalyst, what will the same curve look like? Redraw the curve below with a worse catalyst.

ηactivation

log i

4.9 On the single-electrode polarization plot below indicate the regions where (a) Butler–Volmer kinetics, (b) Tafel kinetics, (c) the sinh solution, and (d) facile kinetics (linearized Butler–Volmer) apply.

ηactivation

log i

(a) Using the appropriate kinetics, calculate the cathodic activation overpotential ηa,c at 0.8 A/cm2 . (b) Calculate the total ohmic overpotential ηR at 0.5 A/cm2 , including contact resistance.

Parameter

Value

Unit

T cell Ionomer fraction, anode Ionomer fraction, cathode Anode thickness Cathode thickness Average electrolyte conductivity Electrolyte thickness Anode GDL thickness Cathode GDL thickness α a (for anode) α c (for anode) α a (for cathode) α c (for cathode) E(T,P) Anode GDL porosity Cathode GDL porosity Anode io Cathode io Anode pressure Cathode pressure B (replaced RT/nF in concentration loss) n anode elementary reaction n cathode elementary reaction R contact, total for cell Landing to channel width ratio I n (crossover) gO2 average mole fraction yH2 average mole fraction

340 0.4 0.3 30 20 7.0

K — — µm µm S/m

50 250 300 0.6 Solve Solve 0.4 1.15 0.3 0.4 1.5 5.0 × 10−4 101,325 300,000 0.05

µm µm µm — — — — V — — A/cm2 A/cm2 Pa Pa V

1 2 35 1:1 3.0 0.15 0.75

— — m ·cm2 Unitless mA/cm2 Unitless Unitless

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4.12 Do you expect the voltage of a hydrogen–air fuel cell to increase, decrease, or stay the same if the anode and cathode pressures are both doubled. 4.13 Given the table of parameters included in problem 11 for a 100-cm2 -active-area fuel cell, determine the following: (a) Using the appropriate kinetics, calculate the anodic activation overpotential ηa,a at 0.5 A/cm2 . (b) Using the appropriate kinetics, calculate the cathodic activation overpotential ηa,c at 0.5 A/cm2 . (c) Calculate the total ohmic overpotential ηR at 0.5 A/cm2 . 4.14 (a) Discuss under what conditions the Butler–Volmer kinetics model is valid. (b) Discuss under what conditions the Tafel kinetics model is valid. (c) Discuss under what conditions the linearized Butler–Volmer model is valid. (d) Discuss under what conditions the sinh solution to the Butler–Volmer model is valid. (e) Define and discuss the meaning of the charge transfer coefficient. (f) Define the exchange current density and list what factors affect it. (g) Define and discuss the basic assumptions of the Temkin and Langmuir kinetics model in contrast to the Butler–Volmer model. 4.15 Consider you are designing a 50-cm2 -active-area hydrogen–oxygen PEM fuel cell system to operate at a nominal current density of 1.2 A/cm2 at 100◦ C. The current collector landing–channel width ratio is 1 : 2 on the anode and cathode sides. (a) In order to enhance power output, you would like to increase operating pressure from 1 to 3 atm on the cathode with 1 atm constant on the anode. However, in doing so, the contact resistance between the cathode and gas diffusion layer increases by 30 m ·cm2 . What is the net effect of changing the anode from 1 to 3 atm pressure on voltage at 1.2 A/cm2 ? (b) Determine the operating current density at which the positive effect of the pressure increase is exactly offset by the negative impact from the increased contact resistance.

4.16 Consider a fuel cell with 100 cm2 superficial active area and a measured contact resistance of 20 m · cm2 at the anode and 10 m · cm2 at the cathode. Consider the Nafion 115 (0.005-in.thick) electrolyte as fully saturated with moisture everywhere. Consider the anode and cathode electrodes to be 20 and 30 µm thick, respectively, and 25 and 30% equivalent ionomer fraction. Find the fraction of the total potential power lost at 1.2 A/cm2 current density from ohmic losses if E◦ = 1.25 V. Since the ionic resistance is much greater than the electronic resistance, you may neglect the electronic resistance. Assume the area ratio is 1 : 1.3 between the landing and channel. 4.17 In Equation (4.96), it was shown that E OCV = E (T, P)Nernst ×

σi = E ◦ (T, P) × ti σi + σi

Derive this relationship. Recall it is for open-circuit conditions where the ionic and electronic current exchange is equivalent. That is, ie = ii . 4.18 Sketch a typical hydrogen PEFC polarization curve with electrolyte A. Then, sketch a polarization curve with the same operating conditions, but with a thicker electrolyte B. Be sure to think about all of the effects of this change. 4.19 Sketch a typical high-temperature fuel cell (SOFC, MCFC) polarization curve operating at temperature A. Then, sketch a polarization curve B with reduced temperature conditions. Be sure to think about all of the effects of this change. (Ignore the effects on mass transport region until Chapter 5.) 4.20 Sketch the shape of the anode and cathode electrode polarizations versus current for the hydrogen PEFC on the same plot as a DMFC. 4.21 Using total kinetics, plot the ORR over potential versus current density for a PEFC with a PT-C catalyst at 300 K, 1 atm for roughness factors of 1 (smooth electrode), 500, and 2000.

Computer Problems 4.22 Using a spreadsheet or other computer program, put together a basic fuel cell model program for a chosen fuel cell system that includes the various terms and parameters discussed in this chapter for the activation, ohmic, concentration, and crossover polarization losses. For now, use reasonable parameters for the unknown quantities based on the examples in this chapter. After Chapters 5–7, more specific parameters for a given fuel cell can be added.

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References (a) Select appropriate anodic and cathodic kinetics based on the fuel cell chosen and plot the activation polarization for each electrode as a function of current density for each electrode. Check your code by a hand calculation at a given current density. The act of checking the computed values with hand calculations or exact analytical solutions is called model verification and is a necessary step every time a computer model is used. (b) Plot the ohmic polarization as a function of current density. Check your code by a hand calculation at a given current density. (c) Plot the concentration polarization as a function of current density for both electrodes. Check your

189

code by a hand calculation at a given current density. (d) Now add crossover to the calculation and show a plot of the OCV as a function of crossover flux. Check your code by a hand calculation at a given current density. (e) Plot the polarization curve for this fuel cell. 4.23 Using a spreadsheet or other computer program, find a polarization curve for a given fuel cell from the literature and curve fit the results using the empirical fuel cell model. Discuss the meaning of the mass transfer, kinetic, and ohmic parameters. How could this model be expanded to use for other test conditions? Hint: Your professor can help you find some typical polarization curves to use.

REFERENCES 1. A. J. Bard and L. R. Falkner, Electrochemical Methods, Fundamentals and Applications, 2nd ed., Wiley, New York, 2001. 2. T. E. Springer, T. A. Zawodzinski, M. S. Wilson, and S. Gottesfeld, “Characterization of Polymer Electrolyte Fuel Cells Using AC Impedance Spectroscopy,” J. Electrochem. Soc., Vol. 143, No. 2, pp. 587–599, 1996. 3. P. M. Gomadam and J. W. Weidner, “Analysis of Electrochemical Impedance Spectroscopy in Proton Exchange Membrane Fuel Cells,” Int. J. Energy Res., Vol. 29, pp. 1133–1151, 2005. 4. R. S. Berry, S. A. Rice, and J. Ross, Physical Chemistry, Oxford University Press, New York, 2000. 5. K. Eguchi, “Internal Reforming,” In Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1057–1069. 6. X. Li, Principles of Fuel Cells, Taylor and Francis Group, New York, 2006. 7. J. O’M. Bokris and S. Srinivasan, Fuel Cells: Their Electrochemistry, McGraw-Hill, New York, 1969. 8. S. H. Chan, K. A. Khor, and Z. T. Xia, J. Power Sources, Vol. 93, pp. 130–140, 2001. 9. H. A. Gasteiger, W. Gu, R. Makharia, M. F. Mathias, and B. Sompalli, “Beginning-of-Life MEA Performance—Efficiency Loss Contributions,” In Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 593–610. 10. J. Tafel, Z. Physik. Chem., Vol. 50A, p. 641, 1905. 11. T. E. Springer, T. Rockward, T.A. Zawodzinski, and S. Gottesfeld, “Model for Polymer Electrolyte Fuel Cell Operation on Reformate Feed—Effects of CO, H2 Dilution, and High Fuel Utilization,” J Electrochem. Soc., Vol. 148, No. 1, pp. A11–A23, 2001. 12. E. Gileadi, Electrode Kinetics for Chemists, Chemical Engineers and Materials Scientists, WileyVCH, New York, NY, 1993. 13. S. Park, R. J. Gorte and J. M. Vohs, “Applications of heterogeneous catalysis in the direct oxidation of hydrocarbons in a solid-oxide fuel cell,” Appl. Catal., A, Vol. 200, p. 55, 2000.

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Performance Characterization of Fuel Cell Systems 14. M. L. Perry, J. Newman, and E. J. Cairns, “Mass Transport Gas-Diffusion Electrodes: A Diagnostic Tool for Fuel-Cell Cathodes”, J. Electrochem. Soc., Vol. 145, p. 5, 1998. 15. C. Boyer, S. Gamburzev, O. Velev, S. Srinivasan, and A.J. Appleby, “Measurements of Proton Conductivity in the Active Layer of PEM Fuel Cell Gas Diffusion Electrodes,” Electrochim. Acta, Vol. 43, p. 3703, 1998. 16. J. Scott, The Development and Operation of a 466 cm2 Direct Methonol Fuel Cell, M. S. Thesis, The Pennsylvansa State University, University Park, PA, 2002. 17. M. F. Mathias, J. Roth, J. Fleming, and W. Lehnert, “Diffusion Media Materials and Characterization,” In Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 517–537. 18. J. Kim, S-M. Lee., S. Srinivasan, and C. E. Chamberlin, “Modelling of Proton Exchange Membrane Fuel Cell Performance Using An Empirical Equation,” J. Electrochem. Soc., Vol. 142, No. 6, pp. 1895–1901, 1995. 19. F. Laurencelle, R. Chahine, J. Hamelin, T. K. Bose, and A. Laperriere, “Characterization of a Ballard MK5-E Proton Exchange Membrane Stack,” Fuel Cells, Vol. 1, No. 1, pp. 66–71, 2001. 20. J. Larmine and A. Dicks, Fuel Cell Systems Explained, 2nd ed., Wiley, New York, 2003. 21. E. C. Kumbur, K. V. Sharp, and M. M. Mench, “Liquid Droplet Behavior and Instability in a Polymer Electrolyte Fuel Cell Flow Channel,” J. Power Sources, Vol. 161, pp. 335–345, 2006. 22. N. Q. Minh and T. Takahashi, Science and Technology of Ceramic Fuel Cells, 2nd ed., Elsevier, New York, 2005. 23. R. Doshi, V. L. Richards, J. D. Carter, X. Wang, and M. Krumpelt, “Development of Solid-Oxide Fuels That Operate at 500◦ C,” J. Electrochem. Soc., Vol. 146, No. 4, pp. 1273–1278, 1999. 24. J. M. Ralph, C. Rossignol, and R. Kumar, “Cathode Materials for Reduced-Temperature SOFCs,” J. Electrochem. Soc., Vol. 150, No. 11, pp. A1518–A1522, 2003. 25. T. Hibino, A. Hashimoto, T. Inoue, J. Tokuno, S. Yoshida, and M. Sano, “Single-Chamber Solid Oxide Fuel Cells at Intermediate Temperatures with Various Hydrocarbon-Air Mixtures,” J. Electrochem. Soc., Vol. 147, No. 8, pp. 2888–2892, 2003. 26. O. Yamamoto, “Low Temperature Electrolytes and Catalysts,” In Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds.,Wiley, New York, 2003, pp. 1002–1014. 27. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., Wiley, New York, 2002. 28. M.-K. Song, Y.-T. Kim, J. M. Fenton, H. R. Kunz, and H.-W. Rhee, “Chemically-Modified R /Poly(vinylidene fluoride) Blend Ionomers for Proton Exchange Membrane Fuel Cells,” Nafion J. Power Sources, Vol. 117, pp. 14–21, 2003. 29. M. Watanabe, H. Uchida, Y. Seki, M. Emori and P. Stonehart, “Self-Humidifying Polymer Electrolyte Membrane for Fuel Cells,” J. Electrochem. Soc., Vol. 143, pp. 3847–3852, 1996. 30. A. Parthasarathy, S. Srinivasan, A. J. Appleby, and C. Martin, “Temperature Dependence of the R Interface-A Microelectrode Electrode Kinetics of Oxygen Production of the Platinum/Nation Investigation,” J. Electrochem. Soc., Vol. 139, pp. 2530–2537, 1992.

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Fuel Cell Engines Matthew M. Mench

5

Copyright © 2008 by John Wiley & Sons, Inc.

Transport in Fuel Cell Systems General Motors absolutely sees the long-term future of the world being based on a hydrogen economy. Forty-five percent of Fortune 50 Companies will be affected, impacting almost two trillion dollars in revenue. —Larry Burns, Vice President of R&D and Planning, General Motors Corporation, February 2003

In the previous chapter we discussed the polarization curve and all of the losses associated with the generation of current that result in decreased operating efficiency and generation of heat. At a fundamental level, all of these polarizations are a result of transport limitations. The ohmic polarization is a result of ion and electron transport losses, and the concentration and activation polarization is a result of mass transport limitations of the reactant to the catalyst surface and charged particles across the double layer, respectively. Even the crossover and internal short current loss from the expected Nernst potential is a result of transport. Optimization of the fuel cell design therefore must include an optimization of the (desired) modes of transport and minimization of the undesired modes of transport. In this chapter, the modes of transport relevant to fuel cells are described in greater detail.

5.1 ION TRANSPORT IN AN ELECTROLYTE Ion transport in an electrolyte is necessary for current flow. Because the ions carry charge, the net rate of ion transport through the electrolyte is directly proportional to the current flow: i = n˙ j z j F

(5.1)

where n˙ j is the molar rate of transfer of the ion through the electrolyte, F is Faraday’s constant, and z j is the charge number of the ion (e.g., for H+ , z = 1, and for O2− , z = −2). Transfer of ions through the electrolyte occurs through several mechanisms of electrical, chemical, and thermodynamic origin. 1. Mass Diffusion Mass transfer of ions (and any other species) occurs as a result of a concentration gradient in the material. Figure 5.1 shows diffusion of oxygen and 191

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Transport in Fuel Cell Systems H2

H2

H2

H2

H2 H2

H2

H2

H2

H2

H2

H2

H2

H2 H2

H2

H2

Net H2 diffusion direction Figure 5.1

Net O2 diffusion direction

O2

Diffusion mass transfer results from concentration gradient.

hydrogen into each other: n˙

j,i




mol s · cm2

 = −D j,i

∂C j ∂ xi

(5.2)

where n˙

j,i is the mass flux rate of the j ion in the x, y, and z directions, and Cj represents the molar concentration of species j. The net hydrogen motion is a result of collisions with other hydrogen molecules (self-diffusion) and collisions with oxygen molecules. Equation (5.2) therefore represents a total of three scalar equations. That is, n˙

j,x = −D j,x

∂C j ∂x

n˙

j,y = −D j,y

∂C j ∂y

n˙

j,z = −D j,z

∂C j ∂z

The negative sign represents the fact that mass transport of j will occur in this mode in the direction of decreasing concentration of j. Here, Dj,i is the mass diffusivity coefficient of j in the i direction and ∂C j /∂ xi is the concentration gradient of j in the i direction. 2. Convection Mass transfer of ions (and any other species) occurs as a result of the net motion of the electrolyte (e.g., stirred liquid solutions). Forced convection is a result of externally controlled fluid motion, and natural convection is a result of buoyancy forces resulting from a density gradient. Figure 5.2 illustrates convective

H2

H2

H2

H2

H2

H2 H2

H2

H2

H2

H2 H2

H2

H2 H2

H2 H2 H2

H2

Net H2 diffusion direction

H2 cit Velo Flow

y

H2

H2 H2

H2

Net O2 diffusion direction

Figure 5.2 Convection mass transfer results from net motion of fluid.

O2

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5.1

E-

193

E+

-

+

+ -

+

+ Figure 5.3 gradient.

Ion Transport in an Electrolyte

+

Migration mass transfer results from charged particles subjected to potential field

mixing of hydrogen into oxygen by a velocity field:
 mol = C j vi n˙

j,i s · cm2

(5.3)

where vi is the solution velocity field vector. Equation (5.3) represents a total of three scalar equations, one in each direction. 3. Migration Mass transport of charged species is driven by an electrical potential difference (Figure 5.3). In a fashion that is similar to diffusion mass transfer driven by a concentration gradient and heat transport driven by a temperature gradient, charged species will be driven by an electrical potential gradient:
 zjF mol ∂φ

D j,i C j =− n˙ j,i (5.4) 2 s · cm Ru T ∂ xi Here ∂φ/∂ xi is the electrical field gradient in all directions. Simply stated, a negative ion will migrate toward the positively charged electrode under a potential field gradient. The negative sign represents the fact that mass transport of positive ion j will occur in the direction of decreasing electrical potential. By putting all the relevant modes together, we have the Nernst–Planck equation governing ion transport: n˙

j,i = −D j,i

∂C j zjF ∂φ D j,i C j + C j vi − ∂ xi Ru T ∂ xi

(5.5)

which reduces to simple diffusion and convection in the absence of a potential gradient, as it must. In an electrolyte with no convection or concentration gradient, Eq. (5.5) reduces to Ohm’s law. Thus, as discussed in Chapter 4, Ohm’s law is not strictly valid in electrolytes unless there is no concentration gradient or motion, which is not always the case. If there is a concentration gradient in the electrolyte, then an additional ohmic concentration polarization will exist. Convective flow enhances mixing and reduces any concentration ohmic polarization. In most fuel cell systems (or as part of an introductory analysis), this additional effect is neglected or is minor. Equation (5.5) is in compact form and expands to

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Transport in Fuel Cell Systems

the following three equations in the x, y, and z directions: n˙

j,x = −D j,x

∂C j zjF ∂φ + C j vx − D j,x C j ∂x Ru T ∂x

(5.6)

n˙

j,y = −D j,y

∂C j zjF ∂φ + C j vy − D j,y C j ∂y Ru T ∂y

(5.7)

n˙

j,z = −D j,z

∂C j zjF ∂φ + C j vz − D j,z C j ∂z Ru T ∂z

(5.8)

where the electrolyte velocity vector of the fluid is v = vx i + v y j + vz k

(5.9)

From Eqs. (5.1) and (5.5), we can show in general that
 ∂C j zjF ∂φ i = −D j,i zjF D j,i C j + C j vi − ∂ xi Ru T ∂ xi

(5.10)

The mobility uj of ion j in the electrolyte is an important parameter related to the diffusion coefficient Dj through the Nernst–Einstein relation [1]:    z j F2 Dj    uj =  Ru T 

(5.11)

The ion mobility is a function of the ionic charge and the operating temperature, pressure, and ionic concentration and ion size. Despite the form of Eq. (5.11), the mobility typically increases with temperature due to a decrease in the viscosity of the electrolyte, which increases diffusivity. The ionic mobilities of various ions in solution are highly varied and available in various literature, but generally on the order of 10−3 –10−4 (cm2 /Vs) at 25◦ C. The absolute value is necessary in Eq. (5.11) due to the charge on the ionic species j since mobility is always a positive quantity. Using ionic mobility, Eq. (5.10) can be written as i = −z j F D j,i

∂C j ∂φ + z j FC j v i − u j C j ∂ xi ∂ xi

(5.12)

This is a general form appropriate for all electrolyte systems. In static electrolyte systems, the electrolyte velocity vector reduces to zero, and only diffusion and migration terms remain. At open-circuit conditions in a static electrolyte, the diffusion and migration transport will balance each other, so there is no net current. Liquid viscosity (µ) is a function of temperature [2]: µ =a+b ln µo




To T




+c

To T

2 (5.13)

Values for the empirically derived constants can be found in various resources, and mixture relations can be used to estimate solution viscosities. For water, a = −1.94, b = −4.80, and c = 6.75 with To = 273.16 K and µo = 0.001792 kg/(m · s).

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5.1

Ion Transport in an Electrolyte

195

Conductivity A convenient relationship exists between the ionic conductivity (σ j ), mobility (u j ), and ion concentration (C j ) in a single ion carrier electrolyte [1]: σ j = F|z j |u j C j

(5.14)

This expression provides physical insight into the ion conduction process in an electrolyte: 1. As the charge number zj is increased, the total current carried per ion increases proportionally, increasing the effective conductivity. 2. As the mobility of the charge carriers increases, the conductivity increases. 3. As the concentration of charge carriers (participants in the ion exchange) increases, the ionic conductivity increases, although this trend does not hold for highly concentrated solutions. Plugging in our expression for mobility, Eq. (5.11), we can glean a little more physical insight into the ion transport process. σj =

F2 2 z DjCj Ru T j

(5.15)

From this expression, we can see that the conductivity of an electrolyte is strongly related to the diffusivity, ion concentration, and charge number. This relationship predicts a monotonically increasing ionic conductivity for electrolyte solutions as ion concentration is increased. This trend is not actually seen in strong solutions, however, due to ion–ion interactions. The model in Eq. (5.14) is derived for dilute solutions with low ion–ion interaction. Concentrated solution theory is treated in other electrochemistry texts, such as [1]. Ion conductivity is a different phenomenon than electrical conductivity. In electrical conductivity, the valence electrons have a very high relative mobility along the surface of an electrical conductor. In contrast, ion conductivity relies on the mobility of all ions in the electrolyte with a much lower relative charge carrier concentration compared to electron conductors. Not all molecules in an electrolyte are charge carriers. Almost all molecules in a metal are participants and are very closely packed. In most types of fuel cells, ohmic losses are dominated by ionic conductivity losses through the electrolyte. Contacts and electrical conductivity typically play a small, although significant, overall role in the ohmic polarization. The electrolyte is also responsible for many of the durability limitations and overall system cost. 5.1.1 Solid Polymer Electrolytes In a solid polymer electrolyte, such as used in the PEFC, ion mobility is a result of an electrolyte solution integrated into an inert polymer matrix. Early electrolyte membranes developed for the United States space program consisted of treated hydrocarbons, which resulted in poor longevity due to the relatively weaker hydrocarbon bonds [3]. Most modern solid electrolytes are perflourinated ionomers with a fixed side chain of sulphonic acid bonded covalently to the inert, but chemically stable, polymer polytetrafluoroethylene (PTFE) structure.1 As a result, the membrane consists of two very different sub-structures: 1) a hydrophilic and ionically conductive phase related to the bonded sulphonic acid groups 1 Additional

details on membrane manufacturing can be found in [3].

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Transport in Fuel Cell Systems H+ O-

Sulfonated side chain

O

S

O

F

C

F

F

C

F

O

PTFE F

F

F

F

F

F

F

F

F

F

F

F

C

C

C

C

C

C

C

C

C

C

C

F

F

F

F

F

F

F

F

F

F

F

F

C

F

C

F F

F

F

F

F

F

F

F

F

O

F

F

F

F

F

F

F

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

F

O

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

C

F

C

F

F

F

F

C

C

C

C

C

F

O

F

F

F

F

F

C

F

F

F

C

F

O

O

F

C

F

F

C

F

C

F

F

C

F

O

S

O

O

S

O

O-

Repeating

H+

O-

F

H+

Figure 5.4 Schematic of sulfonated polytetrafluoroethylene (PTFE) structure used as ionconducting electrolyte in PEFCs.

that absorbs water, and 2) a hydrophobic and relatively inert polymer backbone that is not ionically conductive but provides chemical stability and durability. Perhaps the most ubiquitously studied perflourinated ionomers for fuel cells is NafionR , developed by E. I. DuPont de Nemours and Company. Many other companies such as W. L. Gore and Associates, Asahi Glass Co, Ltd., Dow Chemical, and 3M have developed ionically conductive solid polymers as well. Due to the desire for higher temperature operation and low humidity high durability capabilities, many other alternative electrolyte technologies have emerged [4]. In this text, for the purposes of understanding and brevity, we will focus on understanding the fundamental transport modes and known transport parameters for Nafion that can be used as a starting point for advanced study. Transport in other polymer membranes used in fuel cells is generally similar to that of Nafion, but material-specific relationships for most of the transport parameters discussed here are available in the literature. Nafion, like other perflourinated ionomers is created by sulphonation (SO3 − ) of the basic PTFE structure, as shown in Figure 5.4. When the structure is hydrated, H3 O+ -SO3 − groups enable motion of H+ ions. Dry perflourinated ionomers are almost completely non-conductive, so PEFCs typically operate with humidified reactant flow to boost conductivity and reduce ohmic losses. Studies of the fundamental nature of proton transport in the ionomer have suggested that two modes of transport exist, as illustrated in (Figure 5.5): 1. Under low water content, the ionically conductive hydrated portion of the membranes behave as nearly isolated clusters, and proton transport is dominated by a vehicular mechanism or diffusion, where proton transport is direct, and by purely physical means.

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5.1

SO3SO3SO3SO3 H2O SO3H+ -

SO3SO3-

SO3 SO

3

SO

3

SO

SO3-

SO3

SO3-

SO3SO3-

SO3-

SO3SO3-

SO3-

SO3 SO3-

SO3

-

SO3 SO3-

SO3SO3-

SO3-

SO3SO3-

SO3SO3SO3-

H3O+ -

197

SO3-

SO3-

SO3-

SO3-

3

SO3- SO3- SO3- SO3-

H2O

SO3 SO3-

SO3-

Ion Transport in an Electrolyte

-

SO3-

3

SO

SO3-

3

SO

SO3SO3-

Figure 5.5 Schematic of connected sulfonated side chains which enable proton conduction through (a) Grotthuss and (b) vehicular mechanisms in wet and dry PEFC electrolyte membranes, respectively. (Adapted from Weber and Newman [5].)

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Transport in Fuel Cell Systems

2. With high hydration in the electrolyte, a proton hopping, or Grotthuss mechanism [5] is observed, with concomitantly higher effective proton conductivity. In this mode of transport, protons “hop” from one H3 O+ to another along a connected pathway in the ionomer structure. The ionic conductivity of the electrolyte is related to the clustering of the sulfonic acid side groups and hydration level. The structural relationship between the non-conductive polymer backbone and the conductive side chains is the critical factor in the electrolyte water uptake, conductivity, and swelling behavior. A measure of this structural relationship is the equivalent weight (EW) of the ionomeric membrane [3]:
 g = 100 × k + 446 (5.16) EW eq Where k is the number of tetraflouroethylene groups per polymer chain. The higher the EW, the higher the amount of inert backbone relative to conducting side chains. A higher EW should then theoretically lead to: 1. higher durability through a greater fraction of inert structure, 2. lower ionic conductivity due to reduced conducting acid content, 3. reduced membrane water uptake and swelling due to reduced hydrophilic sulfonic acid side chain clusters, and 4. higher reactant solubility due to reduced water content [6]. The EW for fuel cell electrolytes is typically from 800–1200. The most commonly used electrolyte is Nafion, 11×, representing an EW of 11 × 100, or 1100. The last number in the Nafion designation represents dry electrolyte thickness in thousandths of an inch. That is, Nafion 112 represents a 0.002

(51 µm) thick dry membrane with 1100 EW. In general, lower EW electrolytes tend to have better low-humidity performance due to higher moisture uptake, but suffer increased swelling in moist environments. At very low EW (EW < 800), these membranes suffer reduced ionic conductivity from excessive dilution of the acid. Swelling of the electrolyte in the PEFC can cause mechanical stresses in the membrane, and lead to more rapid degradation. Water Uptake Water uptake, λ, is commonly referenced in terms of water molecules per sulfonic acid site: λ=

H2 O SO3 H

(5.17)

Water-soaked values range from ∼30 for an EW of 900, to ∼20 for an EW of 1100 (see Table 5.1). Additional data for commonly used Nafion electrolytes is given in Table 5.2. Note that these values are for a membrane soaked in liquid water solution and represents a maximum value. For membranes in a low humidity environment, the water uptake is much lower. For contact with a gas-phase flow stream, the water uptake of Nafion 1100 EW at 30◦ C has been correlated as [7]: λ = 0.043 + 17.18a − 39.85a 2 + 36.0a 3

for 0 < a ≤ 1

(5.18)

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Ion Transport in an Electrolyte

Table 5.1 Water Uptake, Swelling, and Ionic Conductivity versus EW in a PEFC EW (g/eq)

Water Uptake (wt %)

Effective Ionic Concentration

Ionic Conductivity at 23◦ C (S/cm)

13.3 19.4 21.0 25.0 27.1 53.1 79.1

1.245 1.338 1.492 1.591 1.764 1.761 1.539

0.0123 0.0253 0.0636 0.0902 0.1193 0.1152 0.0791

1500 1350 1200 1100 980 834 785 Source: Adapted from [8].

Table 5.2 Water Uptake, Weight Percent, and Swelling for Nafion Membranes Nafion Designation 112 115 117 105

Water Uptake, λ (H2 O/SO3 H)

Water Weight Percentage (%)

Thickness Strain from Water Uptake, twet /tdry

21–22 21–22 21–22 27–28

24–26 24–26 24–26 32–33

14–21 14–18 13–15 26–30

Source: Adapted from [9].

where a is water vapor activity, which is the relative humidity RH: a = RH =

yv P Psat (T )

(5.19)

The relationship in Eq. (5.18) has a maximum value at fully humidified conditions of λ = 14. Although the relationship in Eq. (5.18) was derived for 30◦ C, it has been commonly applied with little reservation for modeling fuel cells at much higher temperatures. However, although the qualitative shape of the uptake curve is similar, the maximum λ achievable actually decreases with increasing temperature, to a value around λ = 10 at 80◦ C. A more rigorous treatment of the water uptake including temperature and EW effects is given in the literature [10]. When equilibrated with liquid water, the water uptake for expanded form Nafion2 is much higher, and nearly invariant over the range of normal PEFC operating temperatures at a value of around λ = 22. Other forms of Nafion also show an abrupt increase in water content when equilibrated with liquid water, although the maximum value decreases with increasing temperature. The sharp difference in water uptake between a membrane equilibrated with vapor and liquid water is known as Schroeder’s paradox. This important phenomenon is of 2 Perflourosulfonic

acid membranes such as Nafion can be oriented in three basic forms of S (Shrunken) N (Normal) and E (Expanded) types, depending on the pretreatment and environment [11]. The E form of the membrane uptakes the most water for its EW, and is the most conductive and is normally what is in operation in the fuel cell.

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critical importance, since the abrupt change in water content results in a similarly abrupt variance in ionic conductivity, swelling, and other important transport parameters. The physicochemical reason for this phenomenon is still subject of debate. A recent attempt to explain the phenomena based on physical considerations is given by Weber and Newman in [5]. If the membrane itself is partially in contact with liquid and vapor, as can commonly be the case in an operating fuel cell, the water content and uptake in the membrane can vary with location, although in equilibrium the water content in the membrane will become homogeneous with uptake depending on the overall water availability. Transport in this case can be modeled as occurring in parallel between gas and liquid equilibrated modes, with a suitable fraction denoting the liquid and gas phase fractions of contact with the membrane. Example 5.1 Water Uptake in Nafion Plot the expected water uptake in Nafion as a function of RH and include Schroeder’s paradox uptake value of 22 at 80◦ C and a water activity of one for liquid water. SOLUTION

Using Eq. (5.18), we can plot:

The uptake of Nafion when equilibrated with liquid water illustrates Schroeder’s paradox, whereby a water content of up to λ = 22 has been measured in elevated temperature environments [7]. COMMENTS: There is a sharp change in the slope of the uptake curve beyond a RH value of 0.6. This is believed to be a result of the changing structure of the water distributed in the membrane. At low water activity, the water is strongly bound to the sulfonic acid

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Figure 5.6

Ion Transport in an Electrolyte

201

Calculated Nafion ionic conductivity (σ i ) at different RH values at 80◦ C.

side chains. With increasing water activity in the membrane, the bonding is weak and the water behavior approaches unbounded water in a dilute solution. Nafion Ionic Conductivity Because the conductivity of the membrane is related to the uptake of water in the membrane, the ionic conductivity is strongly related to the hydration level of the membrane. Fundamentally, the water provides the ion conduction pathways, so that increased water content increases the ionic concentration, increasing the conductivity for dilute solutions. Like other electrolytes, temperature also affects conductivity. The ionic conductivity of Nafion 1100 EW ionomer was correlated based on measurements of conductivity over 25–90◦ C and a full humidity range [12], and is shown as:
 
 S 1 1 (0.005193λ − 0.00326) = exp 1268 − (5.20) σi cm 303 T σe ≈ 0 (5.21) where T is in Kelvin. Schroeder’s paradox also effects the conductivity of the membrane, as the jump in water uptake from contact with liquid water is included implicity in Eq. (5.20) through λ. Plots of the ionic conductivity as a function of water uptake and temperature are shown in Figures 5.6 and 5.7. Note the high impact of humidity on the conductivity especially above RH = 60%. One of the major limitations of perflourinated ionomers is the high hydration level needed to sustain performance. At high temperatures, the water vapor mole fraction becomes excessively large in the gas-phase which can limit reactant transport. For a well-hydrated PEFC membrane, typical conductivities are around 10 S/cm. Example 5.2 Determine the ohmic drop through a Nafion 112 electrolyte in a 50% RH environment at 80◦ C, 1A/cm2 .

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Figure 5.7 100% RH.

Calculated Nafion ionic conductivity (σ i ) at different temperature values at 50 and

SOLUTION Nafion 112 is 0.002

, or 51 µm thick in a dry state. In a wet state, from Table 5.1, we estimate the thickness to be approximately 60 µm. Then from Eq. (5.18), we calculate: 
H2 O λ = 0.043 + 17.81a − 39.85a 2 + 36.0a 3 = 3.49 SO3 H where a = RH = 0.5 from Eq. (5.19).
 

 S 1 1 S (0.005193λ − 0.00326) = 0.0268 = exp 1268 − σi cm 303 353 cm Then from Ohm’s law:


 cm l 60 × 10−6 (m) A   V = i A × = 0.224 (V) × 100 =1 1 σA cm2 m 0.0268 ·cm

COMMENTS: Notice the active area cancels out of the relationship. For this system, we lose 224 mV at 1 A/cm2 through the electrolyte. There are additional ohmic losses in the contacts and through the electrolyte in the catalyst layers, as discussed in Chapter 4. 5.1.2

Ceramic Electrolytes Solid Oxide Fuel Cell In contrast to the PEFC, in the SOFC O2− ions are passed from the cathode to the anode via oxygen vacancies in the electrolyte molecular matrix (see Figure 5.8). In ceramic electrolytes, the ionic mobility is usually two to three orders of magnitude lower than polymer or liquid electrolytes, at around 10−11 m2 /s. Due to acceptable performance, availability and low cost, the most commonly used SOFC electrolyte is yttria(Y2 O3 -) stabilized zirconia (ZrO2 ), termed YSZ. Besides yttria, several other aliovalent oxide materials have been used to dope YSZ, such as Yb2 O3 , Nd2 O3 , and Sc2 O3 [13]. Doped YSZ conducts negative O2− ions, which are transported through oxygen vacancies in the zirconia structure. Yttria is typically added in 8–10 mol % to the ZrO2 to stabilize

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203

Oxygen Vacancies O 2Zr

4+

Y 3+ Zr

H2+O2-

H2O+2eO 2-

O 2-

Anode

O

Zr 4+ 2-

4+

Zr 4+

Y 3+

2Y 3+ O Zr 4+

O 2O

2-

O

2-

Zr

4+

O 2-

O 2-

Y 3+

Y 3+ O 2- Zr

4+

24+ O Y 3+ O 2- Zr

Zr 4+

Y 3+

Y 3+

Zr 4+

O 22-

Zr 4+

O 2-

O2+4e-

202-

Zr 4+

O O 24+ 4+ 2- Zr O 2- Zr O 2- Zr 4+ O 2Zr 4+ 2- 4+ O Zr O 2- Zr 4+ O Y 3+ Y 3+ O 2- Y 3+ Zr 4+ Y 3+ O 2Zr 4+ Zr 4+

O2

Zr 4+

O 2-

Cathode

Electrolyte Figure 5.8

Illustration of oxygen ion transport in ceramic SOFC electrolytes.

ZrO2 in a cubic fluorite structure and maximize oxygen vacancies, as pure YSZ in not a suitable ion conductor. High electrolyte temperature is required to ensure adequate oxygen ion conductivity in the solid-state ceramic electrolyte, as oxygen ion mobility is nearly zero below a critical light-off temperature in the electrolyte. As a result, conventional SOFCs will not produce any significant current until being externally heated to the light-off temperature. Commonly used electrolyte conductivity is nearly zero until around 650◦ C [14], although low-temperature SOFC operation at 500◦ C using doped ceria (CeO2 ) ceramic and other electrolytes has shown feasibility [13]. The YSZ has a mixed (electrical and ionic) conductivity, but the electrical conductivity is nearly negligible for typical operating conditions in the SOFC. The ionic and electrical conductivity of 8% mole fraction yttria YSZ, (ZrO2 )0.92 (Y2 O3 )0.08 , has been well studied [14]:
 
S −0.79 eV 2 = 1.63 × 10 exp (5.22) σi cm kB T
 
S −3.88 eV 7 = 1.31 × 10 exp PO−0.25 σe (5.23) 2 cm kB T where kB is the Boltzmann constant (8.617339 × 10−5 eV/K = 1.3807 × 10−23 J/K). A plot of the ionic conductivity of (ZrO2 )0.92 (Y2 O3 )0.08 as a function of temperature is given in Figure 5.9. The electronic conductivity from Eq. (5.23) is very low for all normal values of oxygen partial pressure, resulting in an ionic transference number (see Chapter 4) of approximately unity. The boundary where electrical conductivity becomes nonzero is evident around 600◦ C. As mentioned, other electrolyte materials do show better ionic conductivities at lower temperature operation but have other limitations such as intrinsic cost, stability, or finite electrical conductivity. Example 5.3 Ohmic Losses in SOFC as a Function of Electrolyte Thickness Plot an ohmic-only polarization curve for a SOFC with (ZrO2 )0.92 (Y2 O3 )0.08 electrolyte at 1000◦ C for a 50-, 100-, and 300-µm-thick electrolyte and an OCV of 0.997 V. That is, ignore kinetic and concentration polarization losses. Assume neat hydrogen and air at 1 atm back pressure is used.

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Figure 5.9

Ionic conductivity of (ZrO2 )0.92 (Y2 O3 )0.08 as function of temperature.

SOLUTION In this case, our fuel cell model reduces to the Nernst potential and ohmic polarization: E cell = E ◦ (T, P) − ηr Plugging in the numbers, where σ i is determined from Eq. (5.22) at 1000◦ C, yields E(T, P) = 0.997 − i A

l l = 0.997 − i σi A 0.121 S/cm

Plotting this for several different l values representing the electrolyte thicknesses results in the following:

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205

COMMENT: Quick calculation of the ion transference number yields a value of unity, so that deviation from the Nernst potential from internal electrical shorting is not significant. The SOFC designs typically rely on mechanical support from one of the electrode assembly components. Designs are typically anode, cathode, or electrolyte supported, although an inert support structure is also used in some designs. The thicker range shown (300 µm) is representative of an electrolyte-supported design. Because the ohmic resistance is dominating in these high-temperature systems, an electrode-supported design is a common choice in planar SOFC designs. This topic is covered in Chapter 7. 5.1.3 Liquid Electrolytes (AFC, MCFC, PAFC) In liquid electrolytes, like other electrolytes, ionic conductivity ultimately depends on the mobility and charge of the ionic species. In liquid electrolyte solutions, the ionic species is solvated by the strong dipoles of the water molecule which surround the ion (Figure 5.10). Consider a charged particle in a potential vector field of strength dφ i /dx = E. It will experience a motive force F = zj eE, where e is the fundamental unit of charge, 1.602 × 10−19 C, and zj is the charge on the ion. In the steady state, a spherical ion moving with low velocity and high viscosity (Re < 1) in viscous fluid has a frictional retarding force of [16]: F = 6π νr j z j V

(5.24)

where ν, r j , and V represent the electrolyte solution viscosity, ion radius, and ion velocity vector, respectively. The maximum velocity of an ion under the effect of an electric field force is determined by equating the electric field and frictional forces: z je

z j e(dφ/d xi ) dφ = 6π νr j V ⇒ V = d xi 6π νr j

(5.25)

In addition to the relationship shown in Eq. (5.11), the ionic mobility uj of an ion in an electrolyte in solution is really a measure of the maximum velocity of the ion for a given potential field: uj =

V |dφ/d xi |

(5.26)

A high mobility physically represents a high ion velocity for a given potential field and is a function of ionic radii, solution viscosity, and ion charge number through Eq. (5.25).

H

H

O-

O-

H H

H

+ O- H O-

H

reff

H

O-

O-

H

H

H

H H

Figure 5.10 Illustration of effective ionic radius of solvated ion.

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Transport in Fuel Cell Systems Table 5.3 Some Typical Electrolyte Conductivities Under Operation for Various Liquid Electrolyte Fuel Cells Type of Fuel Cell

Electrolyte

Alkaline (AFC) Phosphoric acid (PAFC) Molten Carbonate (MCFC)

KOH in 30–50% water Concentrated H3 PO4 Li2 CO3 and K2 CO3

Temperature (◦ C)

Ionic Conductivity σ (S/cm)

60–80 200 650

∼0.4 ∼0.6 ∼0.3

Source: From [16].

The ionic conductivity in a liquid electrolyte is a function of the following: 1. Ion Concentration Theoretically, the more charge carriers that are available, the more charge that can be carried. If the electrolyte is highly diluted with water, conductivity will obviously decrease. Instead of a monotonic increase for increasing ionic species concentration, however, an optimal ion concentration corresponding to maximum electrolyte conductivity is observed. This relationship is due to ion–ion interaction at high concentrations. 2. Ionic Mobility From Eqs. (5.11) and (5.26), ionic mobility is related to electrolyte viscosity, atomic radii, and ion charge number. 3. Temperature This affects the ionic mobility through the solution viscosity. 4. Atomic Radii This theoretically is the radius of the ion but also includes the effective ionic radius, including solvating water, which clusters around the ion (see Figure 5.10). 5. Ion Charge According to Eq. (5.15), the higher the charge, the higher the conductivity. Unfortunately, the higher charges also result in increased water solvation and an increased effective radius. As a result, the mobility is decreased, and a clear trend between differently charged ions cannot be simply derived. As a result of the competing trends in conductivity, theoretical values often differ from those experimentally measured. Some typical electrolyte ionic conductivity values are given in Table 5.3. It should be noted that the values in Table 5.3 are under ideal conditions, and actual values in fuel cells may not exactly match. Example 5.4 Conductivity of a Dilute Electrolyte Solution Consider a solution of 0.05 M aqueous solution of A2 B, that completely dissolves into A+ and B2− ions. The mobility of A is 5 × 10−4 (cm2 /Vs), and the mobility of B is 3 × 10−3 (cm2 /Vs). Determine the approximate ionic conductivity of the solution assuming no ion–ion interactions. SOLUTION Since the 0.05 M solution completely dissociates, the result will be a final electrolyte solution with 0.1 M A+ and 0.05 M B2− ions. Both ions will contribute to the charge transfer, thus the conductivity is the sum of the individual contributions. From Eq. (5.14): σi = F|z j |u j C j

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Thus
2
  mol C   eq  −4 cm σA = 96,485 CA  5 × 10 1 eq mol Vs cm3


and
2
  mol C   eq  −3 cm CB σB = 96,485 2  3 × 10 eq mol Vs cm3


where the molar concentrations of the ions are found from simple unit conversions:


 
mol mol 1 L −4 mol = 0.1 = 1 × 10 CA cm3 L 1000 cm3 cm3 and


CB

mol cm3




= 0.05

mol L



1 1000




L cm3



= 5 × 10−5




mol cm3



Therefore,


cm2 σA = 96,485(5 × 10 ) (1 × 10 ) = 0.00482 Vs −4

−4



and σB = 96,485(2.3 × 10−3 ) (5 × 10−5 ) = 0.0289




cm2 Vs



And the total ionic conductivity is therefore the sum of the two:
2 cm σi = σA + σB = 0.0338 Vs COMMENTS: The reader should verify the unit conversion in this example, as it is not straight forward. As discussed, temperature, concentration, and other factors can drastically affect the ionic mobility of a species. For example, we would expect the solution conductivity to increase with temperature by decreasing solution viscosity, and increase with ionic concentration. The concentration effect will reach a peak value at relatively low concentrations however, where ion–ion interactions begin to become important and reduce concentrated solution conductivity. Example 5.5 Ionic Conductivity of MCFC Electrolyte Shown below is a plot and table with published performance data comparing the relative performance of MCFCs at 1 atm pressure (adapted from [17]). Perform the following analysis: 1. Determine an order-of-magnitude estimation for ionic conductivity per electrolyte thickness in the electrolyte in 1976, 1984, and 1999 based on the plot below. 2. Why do you think the ohmic slope was better in 1984 but overall performance was worse than in 1992 and 1999?

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3. How could you explain the trends in OCV over the years?

1976

1984

1999

Current

Voltage

Current

Voltage

Current

Voltage

7 18 36 56

864 781 672 562

47 68 98 140 207 249 293

867 842 820 793 761 743 724

21.4 37.52 56.16 69.7 101 120.5 176.4 194.9

1042 1013 980 958 911 880 809 796

Note that there has been tremendous improvement in the MCFC performance through the years, and not all can be attributed to ohmic loss improvements, as we will assume in this example for simplicity. However, since this is a high temperature system, polarization is typically dominated by ohmic losses. SOLUTION 1. From the given data, we can determine the slope of the approximately linear curves, which we can use to estimate the order of the electrolyte conductivity per unit thickness of electrolyte. From Ohm’s law dV = RA di

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Electron Transport

209

where A is the geometric active area of the cell. This combination of RA is known as the area specific resistance (ASR) and is sometimes a figure of merit specified for fuel cell ohmic losses to provide a scaling factor between differently sized cells. To determine the conductivity per unit thickness of electrolyte, we do not need to know the A of the fuel cells, however. From the definition of conductivity    1  1 σi   = = l RA  d V /di  The absolute value is needed because the slope is negative. From the data shown, a simple linearized curve-fit can be used to determine the slopes.3 Year

dV/di (V · cm2 /A)

σ i /l (Ω/cm2 )

1976 1984 1999

1.81 0.56 1.48

1.81 0.56 1.48

2. The overall ohmic slope was better in 1984, but overall performance was worse because the initial OCV was lower. Therefore, the benefit of the reduced ohmic polarization was not realized until very high current densities where the efficiency is already undesirably low. One possible explanation for this trend would be the use of a thinner electrolyte bath. The thinner electrolyte would result in reduced ohmic losses but increased crossover and hence reduced OCV. 3. The OCV has steadily increased over the years, indicating that crossover of reactants through the electrolyte and electrical shorts has been significantly improved. COMMENTS: This is an example of how one can use simple polarization data to estimate certain parameter values and compare different cell designs without much information. In this sense, you can diagnose fuel cell systems by a comparison of polarization data. One must be very careful, however, not to overanalyze. Due to the complexity and interrelation between many variables, most of the time, many factors are important. In high-temperature systems, though, the situation is a little more simplified since ohmic losses tend to dominate and mostly linear polarization curves result.

5.2 ELECTRON TRANSPORT Electron transport in fuel cells is mostly ignored in analysis, because, relative to ionic transport, electronic resistance contributes little to the overall fuel cell polarization. Certain cases exist where this may not be true, including 1. a poorly assembled cell or 2. an aged cell with some oxidation on current collector contacts. 3 This

can be done by hand or with a variety of computer programs. Being able to curve-fit data is an important technique. If you are unfamiliar with this, see your instructor.

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Figure 5.11 Through plane electrical resistance as function of compression pressure for common carbon fiber paper used as gas diffusion layer in PEFCs. The gas diffusion layers typically have some fraction of PTFE added to promote liquid water removal, which increases electrical bulk and contact resistance. (Reproduced from Ref. [18].)

In general, the electrical contact resistance between the current collector and the diffusion media (PEFC and AFC) or catalyst layer is the largest electrical conductivity loss. In PEFCs, a common through-plane resistivity is around 0.07  · cm, with a contact resistance of 0.002  · cm2 that depends on compression pressure from the lands and Teflon content in the diffusion media, as shown in Figure 5.11. Electrical conductivity is much more facile than ionic conductivity, with typical metal bulk conductivity on the order of σe ≈ 104 − 106 (S/cm) This compares to a typical ionic conductivity of 0.1–1 S/cm for a polymer electrolyte and 0.1–1 S/cm for a ceramic electrolyte and liquid electrolyte. For a 1-mm-thick metal, the voltage loss from 1 A/cm2 current would be very low:
 il m 10,000 cm2 m 1×1 V = i A R = = 1 µV = σi 105 1000 mm m2 100 cm Because of the low bulk conductivity losses, in practical low-temperature fuel cell applications, a passivation oxide layer on the metal can dominate the bulk electron transfer losses. Metal fuel cell bipolar plates are highly robust and can be less than 0.5 mm in total thickness. Because the current collectors and flow fields are often used for mechanical support, they must have higher electrical conductivity to assure low losses. Remember, each fuel cell has only 1 V to work with, so even millivolts are important.

5.3 5.3.1

GAS-PHASE MASS TRANSPORT General Diffusion Similarly to mass diffusion in electrolytes, gas-phase mass diffusion is driven by concentration gradients. If a spray of perfume is released at the front of a classroom, the students

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Gas-Phase Mass Transport

211

at the front of the room will smell the perfume first. Progressively, students at locations farther back in the room will be able to smell the perfume. In time, the perfume will disperse evenly throughout the room. The process by which random molecular motion acts to mix and eliminate concentration gradients is called diffusion. The fundamental principle behind bulk diffusion is that of intermolecular collisions, as illustrated in Figure 5.1. Imagine a room full of moving basketballs representing molecules, initially with red basketballs at one end of the room and white basketballs at the other end. As the molecules move, they will occasionally collide with one another. The collisions change the trajectory of the basketballs, eventually resulting in a completely homogenous mix of white and red. The average speed of red basketballs from one end to the other end of the court is representative of the diffusion coefficient for the red balls into white balls. The average diffusion coefficient of a given species is a function of the following: 1. The other species present. The other molecules will collide with the diffusing species and affect the net rate of motion. 2. The number of molecules, which corresponds to pressure. The greater the number of molecules, the greater the number of collisions, which reduces the average diffusion rate. 3. The velocity of the molecules, which is proportional to temperature. 4. The size and mass of the molecules (e.g., molecular collision diameter and molecular weight). We shall see that the diffusion coefficient for bulk diffusion is indeed a function of pressure, temperature, molecular size, and weight. Diffusion is a spontaneous process that is a result of the second law of thermodynamics. The second law of thermodynamics requires that thermodynamic processes proceed in a way that maximizes entropy. This ultimately requires uniform mixing of everything in the universe. When there is nonuniform mixing, diffusion occurs to eliminate concentration gradients and can be written as n˙ j,i = −D j,i A

∂C j ∂ xi

(5.27)

which is identical to the ion diffusion rate equation (5.2) except that it is expressed as a total rate, by multiplying the flux by the corss-sectional area, A. In general, this is known as Fick’s law of diffusion, where Dj,i is the diffusion coefficient of species j with units of cubic meters per second, A is the area through which diffusion occurs, Cj is the molar concentration of j, xi is the direction of transport (x, y, or z direction), and nj,i is the molar rate of transport of j in the i direction. In principle, the diffusion coefficient can be a function of concentration, temperature, pressure, other species, and other molecular interactions. For one-dimensional mass flux, Fick’s law of diffusion can be written as n˙ j = −D j A

dC j dx

(5.28)

Diffusion coefficients tend to be around 0.1 cm2 /s for gases and 10−5 cm2 /s for liquids. Solid-state diffusion coefficients are strong functions of temperature and are generally less than 10−10 cm2 /s but can vary by as much as 15 orders of magnitude. Diffusion of gases into solid polymers is generally around 10−8 cm2 /s. Some typical values for

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Transport in Fuel Cell Systems Table 5.4 Some Experimental Gas-Phase Diffusion Coefficients at 1 atm Gasl Pair

Temperature (K)

D (cm2 /s)

Air–O2 Air–H2 O Air–He O2 –H2 O N2 –O2 O2 –He Air–H2 H2 –H2 O H2 –He H2 –CO2 CO–H2

273 298 282 308 293 317 282 307 317 298 296

0.176 0.260 0.658 0.282 0.220 0.822 0.710 0.915 1.706 0.646 0.743

Source: From [19].

gas-phase, liquid-phase, and solid-phase diffusion coefficients from [19] are given in Tables 5.4–5.6, respectively. The diffusion coefficient in a mixture is obviously affected by the other species present, and to account for this a binary diffusion coefficient D12 is specifically related to the diffusivity of species 1 into 2 can be used. Since diffusion of species 1 into 2 is identical to species 2 into 1, D12 = D21 . In cases where the density is low and diffusion flux is primarily a result of self-interaction, the species self-diffusion coefficient (Djj = D) is used, and the effect of interaction with other species is not included. Later in this chapter methods for calculation of diffusion coefficients are given. Transient diffusion problems can be solved with Fick’s second law. If the diffusion coefficient is assumed to be independent of concentration: ∂ 2C j ∂C j = Dj ∂t ∂ xi2

(5.29)

where Dj represents the proper diffusion coefficient of j in its surrounding environment. Table 5.5 Diffusion Coefficients in Water at 298 K and Infinite Dilution Gas into Water

Chemical Formula

D (cm2 /s)

Air Carbon monoxide Carbon dioxide Hydrogen Methane Oxygen Methanol Ethanol Formic acid 1-Propanol

(N2 )0.79 (O2 )0.2l CO CO2 H2 CH4 O2 CH3 OH C2 H6 O CH2 O2 CH3 CH2 CH2 OH

2.00 × 10−5 2.03 × 10−5 1.92 × 10−5 4.50 × 10−5 1.49 × 10−5 2.10 × 10−5 0.84 × 10−5 0.84 × 10−5 1.50 × 10−5 0.87 × 10−5

Source: From [19].

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Table 5.6 Some Representative Solid-Phase Diffusion Coefficients System

Temperature (K)

D (cm2 /s)

293 2000 358 323 293

4.0 × 10−10 95 × 10−11 1.16 × 10−8 1.2 × 10−9 1.3 × 10−30

Hydrogen in SiO2 Cerium in tungsten Hydrogen in nickel Sliver in aluminum Aluminum in copper Source: From [19].

A useful result can be found from this equation that allows us to determine the diffusion penetration distance with time [19]. We can calculate the characteristic time scale of diffusion τ d , which is the time for significant diffusion to reach a given distance δ: τd =

δ2 D

(5.30)

For example, in 1 h, oxygen initially released into water vapor at 308 K (Table 5.1) will travel a penetration distance of



τd D = δ = (3600 s)(0.282 cm2 /s) = 31.86 cm Example 5.6 Characteristic Times for Gas-, Liquid-, and Solid-State Diffusion Estimate typical characteristic times for a gas into gas, a gas into a liquid, a gas into a solid, and a gas into a polymer to diffuse a distance of 1 mm. SOLUTION We assume a typical diffusion coefficient of 0.1 cm2 /s for gases, 10−5 cm2 /s for liquids, 10−8 cm2 /s for polymers, and 10−10 cm2 /s for solids. Solving Eq. (5.30) τd =

(0.1 cm)2 δ2 = D D

Mode of Diffusion

τd for 1 mm Diffusion

Gas phase Liquid phase Gas in polymer Solid state

0.1 s 16.7 min 278 days 76.1 years

COMMENTS: The second law of thermodynamics provides a driving force for everything to become homogeneously mixed in time, so that any material differences (and in a larger sense, every gradient) have some natural driving for mixing. The vast difference between gas- and liquid-phase transport times is an important factor in the stability and control of fuel cells.

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Formula

T c (K)

Pc (atm)

Water Hydrogen Oxygen Nitrogen Air Carbon dioxide Carbon monoxide Methanol

H2 O H2 O2 N2 Mix CO2 CO CH3 OH

647.3 33.2 154 126 133 304 133 513

218.0 12.8 49.8 33.5 37.2 72.9 34.5 78.5

Source: From [20].

Calculation of Binary Gas-Phase Diffusion Coefficients There are many different methods to estimate gas-phase diffusion transport parameters. Based solely on molecular dynamic theory, we can derive Dj ∝

T 3/2 P · MW1/2 σ 2

(5.31)

This is a simple expression of self-diffusion of species j into a mixture of j, independent of other species, where σ is the collision diameter of the molecule.4 In practice, these qualitative dependencies are generally observed, with some deviation, especially for polar molecules. Many other theories of different levels of complexity and accuracy have been developed but are not discussed here for brevity. For fuel cells with gas-phase reactants, an effective estimation of binary (two-species) diffusion coefficients can be taken from [21], developed from kinetic theory and the law of corresponding states [22]:
2 b
1/2
cm 1 a T 1 (Pc1 Pc2 )1/3 (Tc1 Tc2 )5/12 = + (5.32) D12 √ s P MW1 MW2 Tc1 Tc2 where D12 represents diffusivity of species 1 into species 2, temperature T is in Kelvin and pressure P is in atmospheres, and Tc and Pc refer to the thermodynamic critical temperature and pressure, respectively (some are listed in Table 5.7). For a nonpolar gas pair, a and b are 2.745 × 10−4 and 1.823, respectively. For a nonpolar gas–H2 O pair, a and b are 3.640 × 10−4 and 2.334, respectively. For commonly used gases, this simple equation can be used, since everything but temperature and pressure are constants. For example, for oxygen in water vapor, we can show that
2 cm 4.19836 × 10−7 = (T )2.334 (5.33) DH2 O–O2 s P where pressure P is in atmospheres and temperature T is in Kelvin. This theory matches trends predicted by molecular collision theory as well as experimental data fairly well and 4 The reader is referred to advanced texts on transport theory, including Diffusion, by E. L. Cussler, Cambridge University Press, 1997, and Transport Phenomena, 2nd ed., by R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Wiley, 2002.

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Table 5.8 Diffusion Volumes for Eq. (5.34) Gas

Formula

Water vapor Hydrogen Oxygen Nitrogen Air Carbon dioxide Carbon monoxide

H2 O H2 O2 N2 Mix CO2 CO



Vi j

12.7 7.07 16.6 17.9 20.1 26.9 18.9

Source: From [19].

includes the capability to more accurately model polar interacting gases, such as H2 O. It should be noted that there is additional error for hydrogen and helium because these gases do not exactly follow the law of corresponding states, as discussed in Chapter 3. Because the hydrogen is usually not the source of diffusion limitations in a fuel cell, however, the additional error is generally tolerable in light of the convenience of the model. If greater accuracy for hydrogen is required, another method developed using molecular volumes can be used [23]: D12 (T, P) = 10−3 ×

1/MW1 + 1/MW2 T 1.75
2 P   (Vi1 )1/3 + (Vi2 )1/3 i

(5.34)

i

where T and P are in Kelvin and atmospheres, respectively, and some of the molecular volumes V are given in Table 5.8. This method can also be used for other gases besides hydrogen if desired. Another way to quickly obtain approximate data is to assume the functional dependence of pressure and temperature in Eq. (5.31) and extrapolate from known experimental data such as shown in Table 5.4. That is,


T D12 (T, P) = D12,known (Tref , Pref ) Tref

3/2


Pref P

 (5.35)

This will provide fairly accurate results as well, especially for nonpolar molecules. In summary, there are several approaches of varying complexity and precision available to estimate the gas-phase diffusivity. The choice taken depends on the level of precision required. Direct experimental data for all modes of transport are always preferred over a generalized correlation. Multicomponent Diffusion Approaches In most cases, more than two species will be mixed, and calculation of the diffusion rate of a given species into a mixture will be required. The approach for these calculations is as follows: 1. Mixture Property Approach If there are more than two gases involved, such as in a cathode with nitrogen, oxygen, and water, a mole-fraction-based averaging approach can be taken as an estimation. In fact, the critical properties of air are

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already tabulated this way (prove it to yourself by making the calculation), although it is really a mixture property of nitrogen, oxygen, and other minor species. For example, to calculate the diffusivity of oxygen into humidified air: Ĺ Determine the mole fractions of the constituents using the saturation pressure and psychrometric analysis tools of Chapter 3. Ĺ Evaluate the diffusion coefficient based on one of the many methods discussed. Ĺ Evaluate the mixture diffusivity using molar averaging. 2. Ignore Inert Species Approach In this approach, we simply ignore the contributions of the inert species. In the cathode, that means we treat the gas as a binary mixture of oxygen diffusing into water vapor. This is frequently employed in the literature for simplicity. 3. Stefan–Maxwell Approach A more rigorous approach to multispecies diffusion effects is known as the Stefan–Maxwell diffusion model and should be used for higher order models seeking the greatest accuracy. The Stefan–Maxwell equation for multicomponent diffusion flux in the x direction is shown as 1 yi n j − y j n i dyi = dx C j =i Di j

(5.36)

where C is the total molar concentration of the gas mixture and the yi ’s are the mole fractions, which can be determined by the pressure and temperature based on the ideal gas law, C=

P Ru T

(5.37)

The n terms are the molar flux of the components in the x direction. The effective binary diffusion coefficient of the various gas species combinations, Di j , is calculated under specified temperature and pressure according to one of the methods already described. As an example, consider a mixture of oxygen, water vapor, and nitrogen. From Eq. (5.36), we get following equations for the gradients for oxygen, nitrogen, and water vapor mole fractions in the cathode: Ru T dyO2 = dx P

yO2 n H2 O − yH2 O n O2 yO n N − yN2 n O2 + 2 2 DO2 −H2 O DO2 −N2



 yN2 n H2 O − yH2 O n N2 yN n O − yN2 n O2 + 2 2 DN2 −H2 O DN2 −O2
 yH O n O2 − yO2 n H2 O Ru T yH2 O n N2 − yN2 n H2 O + 2 = P DH2 O−N2 DH2 O−O2

dyN2 Ru T = dx P dyH2 O dx





(5.38) (5.39) (5.40)

Example 5.7 Estimation of Diffusivity of Hydrogen and Oxygen in Water Vapor Estimate the diffusivity of hydrogen in water vapor and oxygen in water vapor at 1 atm and 307 K and compare with experimental data in Table 5.4.

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SOLUTION From Eq. (5.32), for the water–nonpolar gas pair, a and b are 3.640 × 10−4 and 2.334, respectively:
D12

cm2 s



a P

=


√

T Tc1 Tc2

b


(Pc1 Pc2 )1/3 (Tc1 Tc2 )5/12

1 1 + MW1 MW2

1/2

Plugging in the numbers yields
DH2 O−H2

cm2 s



3.64 × 10−4 = 1


√

2.334

307 647.4 × 33.3




× (217.5 × 12.8)1/3 (647.4 × 33.3)5/12

1 1 + 18 2

1/2 = 1.36 cm2 /s

Due to hydrogen self-interaction, this value is substantially different (49% higher) from the experimentally determined value of 0.915 cm2 /s. We expect some error for hydrogen, though, as discussed. For the oxygen, we have
DH2 O−O2

cm2 s



3.64 × 10−4 = 1




307

2.334

√ 647.4 × 154.4

× (217.5 × 49.7)1/3 (647.4 × 154.4)5/12




1 1 + 18 32

1/2

= 0.268 cm2 /s which is much closer to the 0.282 cm2 /s found from experimental data in Table 5.4. If we desire greater accuracy for hydrogen, we can use Eq. (5.34):     1/MW1 + 1/MW2   
2      (Vi1 )1/3 + (Vi2 )1/3 i i   1.75 1/2 + 1/18 307 −3 2 = 10 ×  2 = 0.69 cm /s 1/3 1/3 1 12.7 + 7.07

DH2 O−H2 (T, P) = 10−3 ×

T 1.75 P

This estimation is closer but still has significant (24%) error, in this case underestimating the measured value. COMMENTS: As discussed, the error in using hydrogen is usually tolerable in light of the fact that it is not typically hydrogen that limits reaction. The molecular volume approach also can be used for oxygen and other fuel cell species with high accuracy, although the need for the tabulated molecular diffusion volumes is an inconvenience and therefore the approaches shown in Eqs. (5.34) and (5.35) are generally preferred. Also note for later use that the diffusivity of water vapor into hydrogen is 3–4 times greater than that of water vapor into oxygen (and air). This fact is important in PEFCs, which will be discussed in Chapter 6.

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Figure 5.12

5.3.2

Illustration of porous media with (a) low and (b) high tortuosity.

Gas-Phase Flow in Porous Media For gas-phase flow in porous media, such as with the electrodes or gas diffusion media of a PEFC or AFC, the porous nature inhibits the diffusion rate through the media. The inhibition must be related to two factors: 1. Porosity At zero porosity (i.e., a complete solid), the effective gas-phase diffusivity must be zero. At a porosity of 1 (i.e., an open volume with no solid), the effective diffusivity must equal the bulk value. 2. Tortuosity Tortuosity is a measure of the effective average path length though the porous media compared to the linear path length across the media in the direction of transport. The more tortuous the path, the longer the effective path length through the media, and the greater reduction in the effective diffusivity, as illustrated in Figure 5.12. The effective diffusivity for gas-phase flow in porous media can be written as φ (5.41) τ where Deff is the effective bulk gas-phase diffusivity in the porous media φ is the porosity (void volume fraction), D is the diffusivity in gas, and τ is the tortuosity. Since tortuosity is a difficult parameter to estimate except through direct experiment, a Bruggeman correlation is often used for fuel cell studies. This relationship assumes τ is proportional to φ −0.5 , resulting in the simpler expression Deff = D

Deff = Dφ 1.5

(5.42)

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Physically, the porosity correction is to adjust for the longer effective path length through the porous media. Using another approach, Salem and Chilingarian estimated tortuosity to be related to porosity for high-porosity material (φ = 0.62–0.88) [24], which is appropriate for fuel cell media: τ = −2.1472 + 5.2438φ

(5.43)

This relationship yields a value of τ ∼ 1.5φ for a typical PEFC diffusion layer (φ = 0.8), or Deff =

D 1.5

(5.44)

Comparing Eq. (5.44) to (5.42), there is not much difference between the result of using either approximation at high porosities typical of fuel cell media, especially given the inherent uncertainty of many other parameters involved. Gas-Phase Limiting Current Density and Diffusion Resistance In Chapter 4, we derived an expression for concentration polarization based on the concept of a mass-transportlimited reaction rate at a given electrode. Now, we can derive an analytical expression for this value, assuming one-dimensional transport to the catalyst surface. First, we equate the rate of reactant consumption to the diffusive and adjective transport to the reaction surface: dC j il A = −D j A + C j Av x nF    d x     Consumption

(5.45)

Advective transport

Diffusion transport

where il is the mass transfer limiting current density. In some fuel cell designs, flow is intentionally forced to the surface by convection, which is the reason for the inclusion of the advective transport in Eq. (5.45). Additionally, the suction of reactant to the surface will naturally cause some bulk motion and convection near the electrode. However, this blowing/suction effect is typically small relative to the diffusion. The diffusion rate is limited by flow through the porous media diffusion layer (PEFC and AFC) and electrode. If we assume one-dimensional flux to the electrode surface in the x direction with no bulk flow velocity (see Figure 5.13), we can write this as Cs = 0 at i l il = − nFDeff

C

− Cs

= − nFDeff

C

= − nFDeff

yi P/ Ru T

(5.46)

where Cs , the surface concentration, is reduced to zero at the limiting condition and C∞ is the concentration of the reactant at the boundary with the flow channel and is calculated with the ideal gas law. Here, δ is the distance to the electrode surface from the flow channel boundary. For high-temperature fuel cells, the diffusivity is usually high enough that the diffusion limiting current is not a factor. For the PEFC and AFC, the diffusion coefficient through the diffusion media is typically modified by the Bruggeman relationship to account

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Figure 5.13

Schematic of gas-phase limiting current density at electrode.

for the porosity: il = −nFDeff

C∞ yi P/Ru T = −nFDφ 1.5 δ δ

(5.47)

This approach can easily be extended from just the diffusion media to include the catalyst layer as well. If we assume that the average reaction location is about midway through the catalyst layer of thickness γ , then we can write Cs = 0 il = − nFDeff,DM

C

− CDM+

= − nFDeff,CL

CDM+ − Cs 2

(5.48)

where CDM+ is the concentration of the reacting species at the diffusion media and catalyst layer interface. Solving for CDM+ and plugging back in, we can show that 
nFDeff,DM yi P il γ C∞ − il γ /(2nFDeff,CL ) = − il = −nFDeff,DM δ δ Ru T 2nFDeff,CL (5.49) If the porosities in the catalyst layer and diffusion media are the same so that the effective diffusivities in the diffusion media and catalyst layer are identical, we can show that il =

nFDeff (yi P/Ru T ) δ + γ /2

(5.50)

which is a result we could have expected. If the porosities are not the same (as is often the case), then Eq. (5.48) can be solved for the limiting current as il =

1.5 nFDφDM (yi P/Ru T ) nFDeff,DM (yi P/Ru T ) = 1.5 1.5 δ + γ Deff,DM /(2Deff,CL ) δ + (γ /2)(φDM /φCL )

(5.51)

Example 5.8 Calculation of Gas-Phase Transport Limited Current Density through Diffusion Media Calculate the oxygen and hydrogen gas-phase transport limiting current density in a hydrogen PEFC for the anode and cathode sides at 80◦ C, 2 atm pressure operation with fully humidified gas streams and high stoichiometry. Assume the anode

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and cathode diffusion layers are 300 µm thick with 70% porosity. Ignore the catalyst layer restriction in this problem. SOLUTION We know the solution can be found with application of Eq. (5.47). However, this problem also has several intermediate steps which integrate the previous chapters nicely: Step 1: Determine the mole fractions of reactants using mixture properties. From Chapter 3, we know that RH =

yv P Pv RH = ⇒ yv = Psat (T ) Psat (T ) Psat (T ) P

where Psat (T ) = −2846.4 + 411.24T (◦ C) − 10.554T (◦ C)2 + 0.16636T (◦ C)3 and

yi = 1

At 80◦ C, Psat ∼ = 31,287 Pa, and yv =

1 × 31,287 = 0.154 202,650

on both the anode and cathode. On the anode yH2 = 1 − 0.154 = 0.846 On the cathode we have two equations and two unknowns: 0.21 yO2 = yN2 0.79

and

yO2 + yN2 + 0.154 = 1

Solving, we find that yO2 = 0.178, yN2 = 0.668. Step 2: Determine the diffusivities of the reactants. For the anode, this time we will use the diffusion volume approach. For the cathode, from Eq. (5.34)     1/MW1 + 1/MW2   
2      (Vi1 )1/3 + (Vi2 )1/3 i i   1.75 353 1/2 + 1/18 −3 2 = 10 ×  2 = 0.44 cm /s 2 12.71/3 + 7.071/3

DH2 O−H2 (T, P) = 10−3 ×

T 1.75 P

For the cathode, from Eq. (5.33)
2 cm 4.19836 × 10−7 = DH2 O−O2 (T )2.334 = 0.186 cm2 /s s P (atm)

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Step 3: Determine the effective diffusivities of the reactants through the porous media. From the Bruggeman relationship [we could also use Eq. (5.44) with little change], Deff = Dφ 1.5 For the anode we have DH2 O−H2 ,eff = 0.44 × 0.71.5 = 0.258 cm2 /s which is lower than the open channel case, as expected. The porous media should reduce the diffusivity. For the cathode: DH2 O−O2 ,eff = 0.186 × 0.71.5 = 0.109 cm2 /s Step 4: Evaluate Eq. (5.47) for the anode and cathode: il = −nFDeff

C∞ yi P/Ru T = −nFDeff δ δ

For the cathode il = −(4 eq/mol)(96,485 C/eq)(0.109 cm2 /s) (0.178 mol O2 /mol mix) (202,650 N/m2 )/(8.314 N · m/mol · K)(353 K) × (300 × 10−4 cm)
3 m 1 = 17.23 A/cm2 × 1 × 106 cm3 For the anode il = −(2 eq/mol)(96,485 C/eq)(0.258 cm2 /s) (0.846 mol H2 /mol mix)(202,650 N/m2 )/(8.314 N · m/mol · K)(353 K) × 300 × 10−4 cm
3 m 1 = 96.94 A/cm2 × 1 × 106 cm3 The higher limiting current density on the anode compared to the cathode is typical and a result of the relatively high diffusivity of hydrogen. COMMENTS: In practical PEFCs, the limiting current density observed is much less, around 2–4 A/cm2 . The discrepancy is a result of factors not accounted for in this basic gas-phase approach. Specifically, we have not included the diffusion resistances of liquid water from flooding and the effect of an ionomer film on the catalyst. The assumption of high stoichiometry is needed because at lower stoiciometry the consumption of reactant means that the limiting current density near the inlet is different from the outlet because of consumption of the reactant along the flow path. If we would have used the expression including the catalyst layer resistance in Eq. (5.51), we would expect a slightly lower limiting current density.

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Figure 5.14 Diffusion in large channel. The molecular interactions with the channel wall are negligible compared to the collisions with other molecules.

5.3.3 Knudsen Diffusion Compared to the molecules themselves, the channels and pores through which the molecules diffuse are typically large, and the main interaction for a particular molecule is collision with other molecules, the driving force for bulk diffusion. In some cases for flow in very small pores and channels, however, the molecular collisions with the solid walls of the channel become a significant component of the overall number of collisions the molecule experiences, and the effective diffusion will deviate from that predicted with Fickian diffusion theory. Consider “normal” diffusion in a cylindrical pore (Figure 5.14). The molecular interactions with the channel wall are negligible compared to the collisions with other molecules. For diffusion through very small pores (Figure 5.15), however, Knudsen diffusion becomes dominant at small pore sizes where wall interactions become significant. Physically, the wall is acting as another interacting molecular species adding a “wall viscosity” to the motion of the species, which acts to retard motion. The key parameter in Knudsen diffusion is the average path length of the molecules between collisions. If the path length becomes similar to the same length as the pore diameter, then wall interaction (Knudsen diffusion) will be important. For liquids, the density is so high that the path length is very small and Knudsen diffusion is unimportant. For gases, however, the mean free path length, l, can be estimated based on molecular dynamics [22]: kB T l=√ 2π σii2 P

(5.52)

The relationship is linear in temperature and inversely proportional to pressure. Here, σ ii is the collision diameter of the species, some of which are tabulated in Table 5.9, P is the pressure in Pascals, T is the temperature in Kelvin, and kB is Boltzmann’s constant

Figure 5.15 Flow in a very small channel. The molecular interactions with the channel wall are no longer negligible compared to the collisions with other molecules.

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Transport in Fuel Cell Systems Table 5.9 Collision Diameters σ ii for Various Fuel Cell Species From Species

Formula

˚ σ ii (A)

Carbon dioxide Carbon monoxide Hydrogen Oxygen Nitrogen Hydrogen peroxide Hydrogen sulfide Methanol Water Dimethyl ether Air

CO2 CO H2 O2 N2 H2 O2 H2 S CH3 OH H2 O CH3 OCH3 Mix

3.941 3.690 2.827 3.467 3.798 4.196 3.623 3.626 2.641 4.307 3.711

Source: From [19].

(1.3807 × 10−23 J/K). For example, for oxygen at 1 atm pressure and 1000 ◦ C,   1.3807 × 10−23 N · m/K (1273 K) l=√  = 0.325 µm 2 2π 3.467 × 10−10 m (101,325 N/m2 ) For hydrogen, we can solve for a path length of 0.489 µm under the same conditions. In order to determine if Knudsen diffusion is significant, the Knudsen number (Kn) must be calculated according to the following criteria: Kn =

kB T l =√ d 2π σii2 Pd

(5.53)

Ĺ When Kn > 10, Knudsen flow dominates. Ĺ When Kn < 0.01, bulk diffusion flow dominates. Ĺ For 0.01 < Kn < 10, both Knudsen and bulk diffusion are important and a combination flow exists. For Knudsen flow, the effective diffusion coefficient can be determined from the kinetic theory of rigid spheres [19]:
DKn

cm2 s

 =

  d 2k B T 1/2 3 mi

(5.54)

where mi is the molecular mass of species i. Alternate theory yields a larger value [15]: √
2 cm 4850d T = DKn (5.55) s MWi where MWi is the molecular weight of species i. The magnitude of Knudsen diffusion is a direct function of pore size. It is around 3 × 10−3 cm2 /s for a 50-nm pore with hydrogen diffusion at 353 K. As the molecular weight increases, Knudsen diffusivity decreases, and as pore diameter increases, diffusivity increases (less collisions to interfere with motion), to

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the limit of transition to bulk diffusion. Also notice there is no pressure or multicomponent factor in Knudsen diffusion. This is because in the Knudsen limit intermolecular collisions are rare. Also notice bulk diffusion varies with T 1.5 , where Knudsen diffusivity varies with T 0.5 . Knudsen diffusion flux is modeled with the Fickian equation, with a modified Knudsen diffusion coefficient replacing the binary diffusion coefficient: n˙ j = −DKn A

dC j dx

(5.56)

Also note that the model assumes a straight pore path. As in bulk media, any tortuosity will increase the real path length, and this must be added to the result as in Eq. (5.41). In the context of the length scales involved with Knudsen diffusion, however, it is unlikely significant error will result without the use of a tortuosity correction. Example 5.9 Knudsen Flow Estimate the pore diameters where Knudsen flow will be important as a function of temperature from 273 to 1000◦ C for oxygen and hydrogen at 1 atm. SOLUTION

We can easily solve for the mean molecular path length: kB T l=√ 2π σii2 P

From this we can plot the regions where the ratio of l/d falls within the three flow regimes.

COMMENTS: The range of pore diameters where Knudsen diffusion dominates is below ∼0.05 µm. Not many media in fuel cells have pore diameters less than 0.05 µm, so that Knudsen diffusion does not likely dominate anywhere, besides possibly in very small pore catalyst layers. However, for diameters less than around 10 µm, there should be some mixed

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bulk/Knudsen diffusion effect. For simple analysis, transition region flow can be modeled in several ways: (1) as parallel flux of bulk and Knudsen flow if the media has a bimodal (bulk- and Knudsen-dominated) pore distribution, as occurs in some PEFC diffusion media; (2) as an effective diffusion resistance with a decrease in the bulk diffusivity to account for the Knudsen effect; or (3) by using more advanced mathematical model multicomponent gas mixtures specifically designed to predict flow behavior in the transitional flow regime, as in ref. [25].

5.3.4

Liquid-Phase Diffusion As shown in Table 5.4, diffusion coefficients of gases in liquids tend to fall in the 10−5 -cm2 /s range. In fuel cells, diffusion of gases in liquids occurs between the gas phase and a liquid electrolyte (although there can be additional interactions with the electrolyte besides pure diffusion) and in low-temperature PEFCs under slightly flooded conditions or with a liquid fuel solution feed such as a DMFC. Since diffusion in liquids is so slow relative to gases, it can be limiting in these situations. The Stokes–Einstein equation is commonly used to estimate liquid diffusion coefficients: D=

kB T 6π µRo

(5.57)

where kB is the Boltzmann constant (1.3807×10−23 J/K), µ is the solvent viscosity, and Ro is the solute radius, some of which are tabulated in Table 5.10. The accuracy of diffusion correlations for liquid is less than that for gases but is typically within 20% in most applications. Other empirical correlations exist and can be used if higher accuracy is desired. (See, e.g., [19].) To determine the viscosity of the solvent, we can use Eq. (5.13). Example 5.10 Liquid Layer Penetration Time Estimate the time required for oxygen to penetrate and diffuse across a 10-µm liquid film on a catalyst in a partially flooded PEFC at 80◦ C.

Table 5.10 Estimated Solvent Radius Gas

Formula

˚ Ro (A)

Hydrogen Oxygen Nitrogen Air Carbon dioxide Carbon monoxide Hydrogen peroxide Ethanol Methanol

H2 O2 N2 Mix CO2 CO H2 O2 C2 H5 OH CH3 OH

1.414 1.734 1.899 1.856 1.971 1.845 2.098 2.265 1.813

Source: Adapted from data in [19].

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SOLUTION The diffusivity of oxygen in water can be estimated from Eq. (5.57):
2 cm kB T (1.3807 × 10−23 J/K)(353 K) D = (10,000 cm2 /m2 ) = s 6π µRo 6π µ(1.734 × 10−10 m) The viscosity of water can be estimated from a rearrangement of Eq. (5.13) 
2 
 To To + µo +c µ = exp a + b T T  
 
273.16 2 273.16 + 6.74 = exp −1.94 − 4.80 (1.792 × 10−3 kg/ms) 353 353 = (1.155 × 10−3 kg/ms) Now we can evaluate the diffusion coefficient:
2 cm kB T (1.3807 × 10−23 J/K)(353 K) D = = s 6π µRo 6π (1.155 × 10−3 kg/ms)(1.734 × 10−10 m) × (10,000 cm2 /m2 ) = 1.29 × 10−5 cm2 /s and the characteristic time to penetrate this water layer is estimated from Eq. (5.30), 2  1 × 10−4 cm δ2 τd = = = 7.75 s D 1.29 × 10−5 cm2 /s COMMENTS: Note there is no pressure dependence for diffusion through the liquid. However, there is a pressure dependence on the concentration of oxygen in the liquid, as discussed later in this chapter. 5.3.5 Diffusion through a Polymer Electrolyte As we have discussed, the diffusion into the polymer electrolyte is an important consideration for PEFCs for two conflicting reasons: 1. The catalyst is typically covered in a thin electrolyte layer, so that high diffusivity of reactants in the electrolyte is desired. 2. Reactant crossover through the electrolyte reduces OCV and efficiency, so that low diffusivity of reactants in the electrolyte is desired. Based on the competing needs of these factors, an electrolyte with some diffusivity of reactants is needed. For the PEFC, the diffusivity has been correlated from experimental data for 1100-EW Nafion, the most well-studied polymer electrolyte. Other electrolyte polymers should have similar trends, but actual values change with EW values. In general, low-EW polymers that absorb more water will have higher gas-phase species diffusion coefficients than higher EW electrolytes. Transport properties in the polyflourosulfonic acid (PFSA) based membranes such as Nafion are generally dependent on the water sorption in the membrane. For dry membranes, ionic conductivity and water mobility are very low. As water sorption is increased, the membrane swells, and particularly at over 60% RH,

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the water uptake increases dramatically, and transport properties approach that of a dilute electrolyte solution. The diffusivity of water vapor into PEFC electrolyte Nafion is a function of the material’s water uptake, since the vapor must diffuse through the entire media. There is significant discrepancy between various authors on the measured values of the water diffusivity coefficient, since it is a difficult parameter to accurately measure, and the membrane itself swells with water uptake. The diffusion coefficient of water in 1100-EW Nafion PFSA polymer with λ > 4 has been correlated as [12]:
2  
cm 1 1 = 10−6 exp 2416 (2.563 − 0.33λ + 0.0264λ2 − 0.000671λ3 ) − Dw s 303 T (5.58) where λ is given in Eq. (5.18). The diffusion coefficient of water in Nafion has been studied by many authors, and a surprising degree of difference between results exists, Eq. (5.58) is commonly used in modely however, and is considered a reasonable correlation. Oxygen diffusivity into 1100-EW Nafion has been given empirically as [26]:
2  
cm 1 1 −6 = 2.88 × 10 exp 2933 − (5.59) DO2 −Nafion s 313 T For 1200-EW polymer [27]:
DO2 −Nafion

cm2 s



−3

= 3.1 × 10


2768 exp − T

(5.60)

Both approaches yield the same order of magnitude in results. Hydrogen diffusivity into Nafion 1100-EW as a function of temperature (in Kelvin) for a fully moist Nafion 1100-EW polymer has been correlated as [28]
2 
cm −2602 −3 = 4.1 × 10 exp (5.61) DH2 −Nafion s T It should be cautioned that the availability of precise transport coefficients is incomplete in the literature. There are significant differences between research results for much of these data, and complete details under a full range of temperature and humidity, and for all materials are not yet available. Nevertheless, the values presented here serve as a reasonable approximation to the diffusion coefficients for calculation purposes. 5.3.6

Interfacial Flow between Phases and Film Resistance From Example 5.7, we see that the pure gas-phase resistance is typically not the limiting resistance to mass transport to the catalyst. The diffusion resistance model can be expanded to make it more complete by adding in additional resistances, such as diffusion into the electrolyte covering the catalyst or through a film of liquid water flooding the catalyst. However, these film effects are localized around only a fraction of the catalysts, and by including an effective film resistance, we are showing only qualitative aggregate effects. However, in many instances in fuel cells, especially PEFCs, mass flux across different

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yO2, gas side

yO2, liquid side Figure 5.16 Schematic mass transfer across a gas/liquid-phase boundary. There is a sharp drop in molar concentration from the gas phase to the liquid phase that is a strong function of temperature.

phases occurs. For example, reactant flux typically must penetrate a thin layer of electrolyte, and possibly water, to reach the catalyst. In Example 5.7, we solved for the gas-phase transport limited current density and found that, even when restricted by porous media, the predicted mass transport limiting current density is much greater than actually observed for PEFC systems. In this section, the film resistance caused by mass transport across a phase boundary is examined. Unlike a no-slip condition in fluid mechanics or a no-temperaturejump condition in heat transfer, there can be a significant concentration discontinuity across a phase interface. Mass Flux across Phase Boundary: Henry’s Law When there is species transport across a phase boundary (e.g., gas into a liquid), there is a discontinuous change in the molar concentration of the species across the phase interface, as shown in Figure 5.16. The concentration discontinuity across the phase boundary between a liquid and gas on across a membrane to gas interface is typically modeled with Henry’s law: yi,liquid/membrane side =

yi,gas side Pgas side H (T )

(5.62)

where H is Henry’s constant, known to be a function of temperature. Assuming a dilute solution, the liquid-phase mole fraction can be converted into concentration by the following:

 moli moli = yi,liquid/membrane side Ci,liquid/membrane side cm3 mol mix   ρliquid kg/cm3 × (5.63) MWliquid (kg mix/mol mix) Sometimes the conversion to solid- or liquid-side concentration is already made part of Henry’s constant and termed the solubility. In this text, we will use this convention. That is, we will define Henry’s law as
 yi,gas side Pgas side mol = (5.64) Ci,liquid/membrane side 3 cm H (T ) Henry’s constant for a variety of common gas-phase species into liquid water is tabulated in Table 5.11.

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Transport in Fuel Cell Systems Table 5.11 Henry’s Law Constants (atm · cm3 /mol) as a Function of Temperature for Gases into Water Species

290 K

300 K

310 K

320 K

330 K

340 K

CO2 O2 H2 CO Air N2

66 2079 3666 2791 3393 4159

94 2462 3940 3283 4049 4870

119 2845 4104 3666 4596 5527

149 3119 4159 4049 5034 6019

176 3338 4213 4378 5417 6457

— 3557 4159 4596 5691 6785

Source: Data adapted from [29].

Notice that the oxygen constant increases with temperature, which means the oxygen concentration in the liquid decreases with temperature. This is why the water temperature in a fishbowl is so critical. If the water temperature is too high, too little oxygen concentration is available for the fish and they will suffocate. The oxygen into water can be curve-fit using the data from Table 5.11 as

 atm · cm3 −1048 = exp + 11.29 (5.65) HO2 −water mol T For PEFC electrolyte the oxygen and hydrogen flux is very important in the membrane. Henry’s constant (in slightly different units, so that the solid-phase concentration and not the mole fraction is known) has been correlated [30]:
HO2 −Nafion

atm · cm3 mol






−666.0 = exp + 14.1 T

 (5.66)

For hydrogen into Nafion, Henry’s constant is relatively constant in temperature, as measured for Nafion 120 polymer at 25◦ C [30]: HH2 −Nafion (atm · cm3 /mol) = 4.5 × 104

(5.67)

Once the reactant is across the phase boundary, it diffuses in the new phase toward the catalyst. Example 5.11 Crossover through Solid Electrolyte Calculate the molar flow rate of hydrogen crossover into and through a 51-µm-thick Nafion electrolyte. The anode is operating at 353 K and 1 atm pressure with a mole fraction of 0.6 hydrogen. Determine the mass transfer limiting hydrogen crossover current density from this value. SOLUTION

First you can solve for the concentration at the anode side in the Nafion:


CH2 /membrane side

mol cm3

 =

yi,gas side Pgas side 0.6 × 1 = H (T ) 4.5 × 104

= 1.33 × 10−5 mol/cm3




mol cm3



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Now this concentration must diffuse toward the cathode, which, presumably, has zero concentration of hydrogen. From Fick’s law and Eq. (5.61) at 353 K
 
mol 1.33 × 10−5 ∂C −2602 = 4.1 × 10−3 exp · n˙ H2 = −DH2 −Nafion ∂x T 51 × 10−4 cm2 · s = 6.74 × 109 mol/cm2 · s As discussed in Chapter 4, fuel crossover is typically measured as an effective crossover current density. The mass transfer limiting hydrogen crossover current density is the maximum current density that could be achieved if all of the hydrogen crossover were used as fuel. This corresponds to a limiting current density of n˙ H2 =

iA = 6.74 × 109 mol/s ⇒ (6.74 × 109 )n F = i limiting = 1.31 mA/cm2 nF

COMMENTS: Typical PEFCs have a range of about 1–10 mA/cm2 hydrogen crossover. Also, there is some additional resistance from the ionomer in the catalyst layers which was not accounted for here. We could account for this by assuming an equivalent ionomer thickness in the catalyst layer based on the ionomer content. Example 5.12 Mass Transfer Limiting Current Density with Film Resistances for PEFC In Example 5.8, we solved for the mass transport limiting current density of an electrode based on the resistance to gas-phase transport only. In the PEFC and some other fuel cells, a thin layer of liquid or ionomer may cover portions of the catalyst surface, resulting in an additional film resistance. Symbolically show this situation to form a more precise model of mass transfer limited current density at an electrode. Ignore convective effects and Knudsen diffusion in this problem. SOLUTION The film resistance acts in series with the resistance in the diffusion media and catalyst layer. We can start by showing the resistance flow through the diffusion media, into the catalyst layer in the gas phase, and into an ionomer and liquid films: C∞ − CDM+ C + − CDM− = −nFDeff,CL DM δDM δCL CH2 O+ − CH2 O− CNF+ − Cs = −nFDR,water = −nFD R,NF δw δNF

il = −nFDeff,DM

which represents four equations and eight unknowns: C∞ , CDM+ , CDM− , CH2 O+ , CH2 O− , CNF+ , Cs , and il . One of the remaining necessary four equations comes from the ideal gas law: C∞ =

yi P Ru T

Another unknown is eliminated under limiting conditions as Cs goes to zero at i = il . Another two come from Henry’s law, to step across the gas–liquid phase boundary and the gas–Nafion phase boundary:
 yi,gas side Pgas side mol = Ci,liquid/membrane side cm3 H (T )

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or
CH2 O−

mol cm3






yH O+ P = 2 HW (T )

and

CNF+

mol cm3

 =

yH2 O+ P HNF (T )

A final equation can be determined by substitution of one of the diffusion equations into another to substitute for an unknown. Any can be chosen. For example, −nFD R,water

CH2 O+ − CH2 O− CNF+ − Cs = −nFD R,NF δw δNF  D R,water δNF  CH2 O+ − CH2 O− = CNF+ ⇒ D R,NF δw

The resulting calculations are very tedious by hand but yield substantially reduced limiting current density values that are closer to those actually experienced. Reactant Flow

c

c

Flow Channel

8

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n˙ = −D

∂C ∂x

Diffusion Media (DM)

δDM

Catalyst Layer

δCL

? Electrolyte

CCL CH2O+ CH2OCNF CS= 0

δW δNF

Water Layer Ionomer Layer Catalyst

COMMENTS: We could also have added the catalyst layer diffusion resistance. This model, while serving as a useful qualitative tool, is not precise, simply because we have no idea of the thickness of any layer of liquid water of ionomer locally in the electrode structures. Also, some local flooding simply turns off the current in this location by these effects, but this only means areas which are flooding have reduced performance. Other areas in the fuel cell may not be flooded, so that the net effect of the flooding is actually to reduce the electrochemically active surface area, which is an approach taken by modely including flooding, discussed later in this chapter.

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Table 5.12 Summary of Orders of Magnitude of Diffusion Coefficients for Various Modes of Transport Mode of Diffusion

Order (cm2 /s)

Bulk gas in gas Dissolved gas in liquid Gas into liquid Knudsen O2 /H2 in Nafion Surface diffusion

O(0.1) O(10−5 ) O(10−4 ) O(10−3 –0) f (pore size) O(10−6 ) at 353 K O(10−5 –10−7 )

5.3.7 Surface Diffusion At the catalyst–electrolyte surface we have gas-phase diffusion, and there can also be additional surface diffusion. In surface diffusion, gas molecules physically or chemically absorb onto a solid surface. If it is physical absorption, the species are highly mobile. If it is chemisorption and the molecule is more strongly bonded to the specific site, species are not directly mobile but can move via a hopping mechanism. Surface diffusion rates can be measured by direct measurement of the flux of a nonreacting gas across the material surface. The difference between the measured diffusion and predicted Knudsen diffusion is calculated to be the surface diffusion component. Values of the surface diffusion coefficient (Ds ) are ∼10−5 cm2 /s in solids and liquids, but these vary widely since surface interaction is involved. Also, Ds is a strong function of temperature and surface concentration. Surface diffusion adds to the overall diffusion but is typically less than one-half of the Knudsen component and so has been mostly neglected in fuel cell analysis. 5.3.8 Diffusion Summary To help summarize the concepts covered on diffusion transport, Table 5.12 is provided. Tortuosity and porosity further modify the gas–gas diffusivities if flow is through a porous media. Pressure, temperature, and other parametric dependencies vary between the modes.

5.4 SINGLE-PHASE FLOW IN CHANNELS It is the goal of reactant flow manifold and channel design in PEFCs to provide excellent access to the catalyst while suffering the lowest possible pressure drop. Since parasitic blowers or fans typically must power air and possibly fuel through the fuel cell, the pressure loss is directly related to the power output of the fuel cell. For some higher pressure systems, the power consumed by pumps and blowers can reach 30% of the power generated by the fuel cell. 5.4.1 Pressure Drop One of the most important aspects of fuel cell design is the reactant flow through the manifolds and flow field, because parasitic losses from driving the flow through the cell can

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Transport in Fuel Cell Systems ∆P Frictional pressure drop Consumption flow to catalyst layer

Droplet

Product flow uptake

Slug blockage

Flow channel

Diffusion media Catalyst layer Electrolyte

Figure 5.17

Schematic of pressure drop and mass exchange in the flow channel of fuel cell.

be the dominant. The pressure change in flow channels is a result of several phenomena, as illustrated in Figure 5.17: 1. Frictional Losses This is the most easily recognized source of pressure loss in the flow channel. In all channels, the viscous losses retard the flow so that a pressure drop per length of the channel is required to maintain a given flow rate. In the limit of high stoichiometry, this loss dominates pressure drop. 2. Consumption of Reactant The consumption of reactant reduces the pressure in the fuel cell flow channel. In the limit, with neat hydrogen and a high fuel utilization, the flow at the exit can be near a vacuum state. 3. Production of Species Product species are added to the flow in the channel. Water vapor generated by reaction will enter the vapor state until the saturation limit. 4. Two-Phase Flow or Blockages In low-temperature PEFCs, liquid water droplets can accumulate in a sporadic and nonuniform fashion and block flow channels, increasing pressure drop. In all fuel cells, partial channel blockage from materials in the flow channel (e.g., in PEFCs, the gas diffusion media can sometimes sag into the channel) will result in increased pressure drop. Frictional Losses The basic dimensionless parameter representing the ratio of momentum to vicious losses is the Reynolds number Re:5 Re =

ρV dh µ

(5.68)

where V is the velocity, ρ is the fluid density, µ is the fluid viscosity, and dh is the hydraulic diameter, defined as dh =

4A x Pw

(5.69)

where Ax is the cross-sectional area of flow and Pw is the length of the perimeter wet by flow. For round channels, this reduces to simply the channel diameter, where for rectangular 5 In

this text, it is assumed the reader has a basic background in fluid mechanics. The reader is referred to undergraduate texts in fluid mechanics, such as F. M. White, Fluid Mechanics, 5th ed., McGraw Hill, New York, 2003.

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Single-Phase Flow in Channels

235

(a)

(b) Figure 5.18

Illustration of individual particle flow trajectories in (a) laminar and (b) turbulent flow.

channels [2] of width w and height h dh =

2w h 4w h = 2w + 2h w +h

(5.70)

For Re < 3000 in an internal channel, the flow is typically laminar, a condition characterized by uniform streamlines and locally steady flow. For an internal channel with Re > 3000, the flow transitions to turbulent flow, characterized by local velocity profile fluctuations and enhanced mixing, as illustrated in Figure 5.18. The flow in a vast majority of fuel cells is highly laminar, which greatly simplifies many important calculations. Physically, the cause of the pressure drop for internal flow is the viscous interaction with the wall, where there is a no-slip condition (V wall = V fluid ). The one-dimensional shear force at the wall for a Newtonian fluid is proportional to the fluid strain and is related to fluid viscosity: Fwall = τ A = Aµ

du dy

(5.71)

where A is the surface area of contact between the fluid and the wall and du/dy is the slope of the change in velocity with distance from the wall. To overcome the shear restraining force imposed by the channel walls and the viscous nature of the fluid, the flow will experience a pressure drop along the channel. In open-field flow, such as in the atmosphere, there are no restraining walls or objects that impose the no-slip condition. When flow from an open channel or flow manifold enters a channel, the flow field develops along an entry length. The internal flow profile for developing flow is shown in Figure 5.19. At first, the flow entering the confined channel is undeveloped, and the flow profile still varies along the axial direction. Because of the no-slip condition, the particles at the wall must have the same velocity as the wall, which sets up a very steep du/dy profile within the developing boundary layer. Hence, in this developing entrance region, the pressure drop per unit length is higher than in the developed section of the channel. Further on down the channel, the boundary layers grow and eventually converge until the flow profile no longer changes in the axial direction. The distance from the entrance of the channel to the point where the internal flow profile becomes independent of the axial location is termed the entrance length (Le ) and is characterized by a higher

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V∞ from manifold

du

dy at wall is very steep

?

∆P

x

0

x

le

Figure 5.19 Developing flow profile in a channel. The shear forces that accumulate along the wall result in a pressure drop along the channel that must be provided for by the reactant flow system.

pressure drop and mixing per unit length compared to the fully developed portion of the channel. The entrance length for laminar internal flow can be estimated from Le ≈ 0.06 Re dh

(5.72)

With a critical Reynolds number for transition to turbulence around 3000,6 the maximum length of developing flow is about 180 diameters. A typical fuel cell flow channel hydraulic diameter is around 1 mm, which means the flow will be developing (and experiencing greater pressure loss and enhanced mixing) for up to 18 cm of the flow channel length. When the flow experiences a sudden turn, or switchback, recirculation zones and additional development length after the turn occur. As a result of entrance and flow field effects, the actual frictional pressure drop in a fuel cell flow channel is typically greater than predicted by fully developed flow theory. For turbulent flow, the following relationship for entrance length is used: Le ≈ 4.4 Re1/6 dh

(5.73)

The entrance length for turbulent flow can be technically infinite if Re is infinite but is typically less than that for laminar flow because of the enhanced mixing. Additionally, 6 Many

authors refer to the critical Reynolds number (Recrit ) as 2300. The transition from laminar to turbulent profiles can actually occur over a relatively broad range and is a function of the channel geometry and surface roughness. In this text, Recrit = 3000 is used as a general guideline.

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Single-Phase Flow in Channels

du

237

dy

(a)

du

dy

(b) Figure 5.20 Laminar and turbulent profile boundaries: (a) fully developed laminar profile; (b) fully developed turbulent profile. Notice the turbulent du/dy profile is much steeper, leading to a higher pressure drop per unit length via Eq. (5.71).

the initial and fully developed flow profiles are more similar (see Figure 5.20). For a very turbulent Reynolds number of 1,000,000, the entrance length is still only 44 hydraulic diameters. While this may suggest that reduced pressure drop could be obtained in fuel cells if the flow was turbulent, the overall pressure drop (and parasitic losses required to obtain turbulent flow velocity) is far greater for turbulent flow due to the higher du/dy profile at the wall for a turbulent-flow profile. From a force balance on the internal flow surface and conservation of energy, we can derive the following equation relating frictional pressure drop per unit length in a closed channel for fully developed flow: ρV 2 P = f L 2dh

(5.74)

where f is the Darcy friction factor. As discussed, the velocity V is not constant in a fuel cell due to consumption and other factors and is a function of location along the channel. For laminar flow, f can be determined from flow theory [2]: f lam =

64 Re

(5.75)

Therefore, for laminar flow, the pressure drop is proportional to the velocity. For laminar, fully developed flow, the pressure drop can be modeled as Hagen–Pouiseville flow: P µV = 32 2 L dh

(laminar flow)

(5.76)

where V is the velocity and P is the pressure drop through the pore. For turbulent flow, much experimental data have been correlated, and the following equation by Colebrook

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[31] is the most commonly applied: 1 f turb



ε/dh 2.51 + = −2.0 log 1/2 3.7 Re f turb

 (5.77)

This implicit equation for f can be easily solved computationally but is rarely needed in fuel cells since the flow is typically laminar in nature. Here ε is the wall roughness height, which is a function of the surface of the channel walls. For advanced modeling purposes, the addition of minor loss, flow field switchback, and manifolding effects can be approached analytically. In practice, however, the actual pressure drop in an cell or stack is very difficult to predict with high precision due to the effects of entry length, local turbulence, additional minor losses from switchback, consumption, uptake and other effects. Additionally, in PEFCs and AFCs with a porous diffusion media, there can be unintentional convective flow under the channels, which reduces overall pressure drop, as discussed in Chapter 6. Therefore, a good starting point is to assume the frictional pressure drop dominates (which has been found to be true in certain PEFCs [32]) and calculate an expected loss from Eq. (5.76). For a particular fuel cell, the pressure drop can be correlated as a function of entrance velocity, since this is relatively easy experimental data to obtain. An example is shown in Figure 5.21 where the general linearity indicates pressure drop is dominated by laminar frictional losses. For the particular stack in Figure 5.21 (and in fact many stacks), the pressure drop can be correlated as a polynomial function of velocity, which globally accounts for the laminar (V dependence) and turbulent/minor loss dependency (∼V 2 dependence): P = aV + bV 2

(5.78)

where a and b are empirically derived constants for a particular fuel cell and are by no means uniform for different cell, manifold, stack designs, or operating conditions. Consumption of Reactant Due to consumption, the uptake of product or moisture, the molar flow rate (and velocity) of the reactant mixture in the channel is not a constant and

Figure 5.21 Measured and correlated pressure drop in a Ballard fuel cell as a function of velocity. (From Ref. [32] with permission.)

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Multiphase Mass Transport in Channels and Porous Media

239

varies with location along the channel length. At the inlet, we can show that n˙ mix (inlet) = Q A =

λ I yi n F

(5.79)

where Q is the volume flow rate, yi is the mole fraction of the reacting species, and I is the current. For a constant current across the electrode surface, we can show that along the flow path the initial reactant gas is reduced by consumption:
 λ I x (5.80) n˙ mix (x) = − n F yi L where x is the length along the channel and L is the total length of the channel. Consumption or uptake of species into the flow results in a changing flow velocity, but the pressure is always highest at the input and decreases along the flow channel. Along the channel, with a net uptake of mass considered (e.g., water vapor uptake), conservation of mass yields
 iA λ x + n˙ uptake (x) n˙ mix (x) = − (5.81) n F yi L where n˙ uptake water vapor and other gas-phase species production combined and the current density is assumed to be uniform across the fuel cell surface. At the exit of the fuel cell under the same assumptions, we can show that
 λ iA iA iA λ ˙n mix,out = n˙ mix,in − n˙ consumed + n˙ uptake = − 1 + n˙ uptake − = yi n F nF n F yi (5.82) The fuel cell polarization model developed in Chapter 4 can be extended to multiple dimensions, and the current density distribution can also be modeled based on concepts in this book. In the limit of high stoichiometry, Eq. (5.81) becomes invariant in x, and the reactant concentration is constant in the flow channel. At low stoichiometry, however, the reactant concentration decreases throughout the channel length and can result in greatly decreased current density at the exit locations [33]. In general, almost nothing in a fuel cell is actually homogeneous. The current, temperature, and species vary throughout the fuel cell in all directions for almost every fuel cell design. In many cases, the variation in many parameters such as temperature can be used to an advantage and is a critical component in design optimization.

5.5 MULTIPHASE MASS TRANSPORT IN CHANNELS AND POROUS MEDIA7 5.5.1 Multiphase Flow in Gas Channels Mixed liquid/gas-phase flow can occur in direct alcohol and hydrogen polymer electrolyte fuel cells. For the hydrogen fuel cell, liquid water can build up in either the anode or 7 This

section may be omitted without loss of continuity providing detailed analysis of PEFC flooding covered in Chapter 6 is also omitted.

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Flow direction 10

Superficial water velocity, VSL (ft/s)

c05

Annular mist (water dispersed)

1.0

Bubble (Air dispersed)

Froth (Both phases dispersed)

Slug 4 (Air dispersed)

0.1

0.1

10

1.0

100

Superficial gas velocity, VSG (ft/s) Figure 5.22 Various flow regimes: (a) bubble flow; (b) slug; (c) froth; (d) annular mist. (Adapted from Ref. [34].)

cathode flow channels and porous media, depending on operating conditions. In general, multiphase mixtures can be characterized by several different flow regimes, based on the characteristics of the two-phase flow, as illustrated in Figure 5.22. The flow regime transition regions are not discrete, and the discernment between different flow regimes is somewhat subjective. Additional subregimes beyond those shown have also been defined for different situations. The phases are classified according to the superficial gas and liquid velocity. The superficial gas-phase velocity can be written as VSG =

QG Achannel

(5.83)

where QG is the volume flow rate of gas in the channel and Achannel is the cross-sectional area of the channel. Thus, the superficial gas-phase velocity represents the velocity the gas phase would have if it occupied the channel as a single phase. The superficial liquid velocity is defined similarly: VSL =

QL Achannel

(5.84)

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Multiphase Mass Transport in Channels and Porous Media

241

Flow velocity

Diffusion media Figure 5.23

Image of liquid droplet in flow channel under shear.

At low superficial gas velocities, flow is in the bubble regime, because of the low volume of the gas phase. This regime is appropriate for liquid reactant solutions with gas-phase products of reaction, as occurs in the DMFC anode covered in Chapter 6. As the gasphase velocity increases, the viscous drag on the liquid phase increases, and a transition is made into a slug regime, which is represented by coalesced droplets of liquid that are charaterised by nonuniform, irregular motions. The droplet in Figure 5.23 is shown under drag in a flow channel in the slug flow regime [35]. Beyond the slug regime, as the liquid droplets become more sparse and the gas-phase velocity increases, the flow transitions into a froth regime, characterized by high turbulence and a general pattern of liquid slugs and mist flow. As the gas-phase flow rate is further increased, the high drag on the droplets in the flow channel create an annular mist flow, where some liquid will form as a coalesced film on channel walls and as a fine mist of droplets in the gas flow stream. A neutron image of a 50-cm2 fuel cell flow field that shows some annular and slug behavior is shown in Figure 5.24. The channel wall shape and surface properties also have an important effect. Annular films will not tend to form on hydrophobic surfaces or along surfaces with sharp angles, such as the triangular shape. A photograph of liquid water droplets along the surface of a triangular and rounded channel is shown in Figure 5.25. In operation, the presence of an annular film is difficult to remove but results in a more evenly balanced pressure distribution by absorbing slugs, thus helping prevent misdistribution of flow in stacks. For slugs in channels, shear force dominates the removal [35]. The shear force is directly related to the channel velocity, so that droplet purge can be accomplished with short bursts of increased channel flow velocity. Because the superficial liquid velocity is so low in most PEFCs, the flow regime most characteristic is the annular mist regime, although at low gas-phase velocity conditions, such as occur in the anode under low power, a slug regime can be normal. The pressure drop in the slug regime can be sporadic, which can have important consequences on the flow distribution in the stack plates or individual channels. Specifically, if the pressure drop in one plate is much higher than others, the flow from the

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Figure 5.24 Neutron Image of flow in PEFC showing some partial slug and annular flow behavior along channel walls [37].

manifold can be redirected to nonflooded fuel cells and result in a starved fuel cell plate and possible voltage reversal if flooding occurs. Because the various flow regimes are quite complex, a generally unified treatment of the flow patterns does not exist, and the background knowledge is taken from experimental studies of oil–air, oil–water, or water–oil flow in much larger pipes than the relatively

Figure 5.25 Image of liquid water inside a fuel cell flow channel with triangular and rounded surfaces. (From Ref. [32] with permission.)

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10

Superficial liquid velocity, VSL, ft/sec

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1.0 Annular Mist

Slug

Bubble

0.1 Froth Phase Mixed

Light Phase Disersed

0.01 0.1

1.0

10

Heavy Phase Dispersed

100

500

Superficial gas velocity, VSG, ft/sec Figure 5.26 Generalized flow regime map for vertical pipes. (Adapted from [34].)

small channels used in most fuel cells. Thus, some ambiguity exists, although microfluidic study is rapidly advancing for geometries more appropriate for fuel cells. Gravity effects do play an important role in the transition between different regimes, and as a result the channel orientation has an effect on the transition. Gravity effects play an important factor in liquid water removal in the manifolds and flow channels, so stock orientation is on important design consideration. A generalized flow regime chart for vertically oriented pipes is shown in Figure 5.26. For horizontal pipes, a generalized flow regime map for air–water mixtures is given in Figure 5.27.

5.5.2 Multiphase Flow in PEFC Porous Media8 Multiphase flow in porous media is a very important topic for low-temperature PEFCs because water produced at the cathode flows through the porous catalyst layers and porous gas diffusion media. Any local blockage of normally open pores restricts reactant flow to the reaction sites, a phenomenon known as flooding. The water balance and flooding in a PEFC is described in detail in Chapter 6. Here, the basic fundamentals that describe two-phase flow in porous media are described to guide and understanding. Unfortunately, the science of multiphase flow though thin-film mixed hydrophobic/ hydrophilic porous media in fuel cells, which includes the catalyst layers and diffusion media is not yet well developed, and much of the present level of understanding is based on 8 This

section may be omitted without loss of continuity providing detailed analysis of PEFC flooding covered in Chapter 6 is also omitted.

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20 Dispersed bubble

10

Superficial water velocity, VSL (ft/s)

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Elongated bubble

Slug

1.0

Stratified

Wave

Annular mist

0.1

0.01 0.1

1.0

10

100

500

Superficial air velocity, VSG (ft/s) Figure 5.27

Generalized flow regime map for horizontal pipes. (Adapted from [34].)

application of porous media theory from civil and petroleum engineering studies of flow of water or oil through packed soil beds. The minute length scales and complex materials in fuel cells present many unique and challenging physicochemical issues. There are a few key differences between the understanding from soil science and petroleum engineering and fuel cell media which make the direct use of semiempirical relationships derived using unconsolidated soil for consolidated porous fuel cell media somewhat dubious: 1. The transport length scale in fuel cell media is much smaller. 2. The thin-film media in fuel cells have a very large surface area–volume ratio, so that interfacial effects not dealt with in bulk flow theory become very important. 3. Very little treatment of vaporization/condensation is available from soil science, which has a major impact on low-temperature fuel cells. 4. Most soil science studies have been conducted with hydrophilic media, whereas the PEFC media typically have a highly heterogeneous surface energy distribution with a net hydrophobic surface condition. 5. Most soil science modeling/work is done in the saturated domain (that is, the pores of the soil are completely filled with fluid). Fuel cell materials are almost always only partially saturated. 6. The models and physics attempt to account for bulk flow, but not for unconnected orphan droplets believed to be common in fuel cell media.

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Flow of the liquid phase in fuel cell porous media is driven by several forces: 1. Capillary Action This is a result of a pressure difference between the phases and dominates for small pores. Capillary forces are responsible for the motion of water into a sponge, wax up a candle wick, and the creep of a table top spill of water under the cover of a book. 2. Gravitational Forces These forces are typically very small compared to the capillary forces for small pores in the fuel cell media and can be neglected in the electrolyte, catalyst larger, and diffusion media but play a key role in flow channels. 3. Convection Forces The importance of this effect depends on the flow field design. 4. Evaporation/Condensation These processes also result in significant liquid removal and motion. 5. Interfacial Effects The interface between different layers of media can have a substantial effect on the accumulation and storage of liquid water in porous media and is an important area of research under development.

5.5.3 Basic Governing Parameters and Relationships of Two-Phase Flow in Fuel Cell Diffusion Media Porosity Porous media (PM) is composed of a solid backbone material and void pores. The volumetric porosity is defined as the ratio of void space to the bulk volume of porous media containing that void space: φ=

void volume total PM volume

(5.85)

The true flow porosity available for multiphase flow represents the interconnected pore volume that can contribute to fluid flow within the porous media and excludes isolated pores. Typically, the true flow porosity is slightly less than the volumetric porosity of the media due to the existence of isolated (orphan) pores. Wettability When two or more fluids occupy a porous medium, one of the fluids is absorbed on the surface more strongly and displaces the other fluid. The fluid absorbed on the surface is called wetting fluid. The displaced fluid is the nonwetting phase. A porous solid will tend to imbibe the wetting phase while displacing the nonwetting phase [37] because the wetting phase will compress the nonwetting phase as it is absorbed. On hydrophobic fuel cell diffusion media surfaces, water will be the nonwetting phase, whereas gas will be the wetting phase. Wettability can also be considered as a measure of the speed with which fluids spread over solid surfaces. The speed of spreading is directly controlled by the interfacial forces at the solid surface. The spreading can be increased by lower surface tension and lower fluid viscosity. For two-phase flow in porous media, the wetting angle influences the capillary pressure and liquid transport considerably hence, an important aspect of PEFC material design is hydrophobic content.

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Saturation In two-phase systems, the volume fraction of total pore volume occupied by a phase is termed the phase saturation. Saturation, s, is a key parameter for multiphase flow, because it represents the available volume through which both phases can still flow. The phase saturation sj is expressed as sj =

volume taken by phase j total pore volume

(5.86)

The of all phases (including water, gas, ice, and other fluids) add to unity, that saturations n s j = 1 where j represents liquid, gas, and ice phases. For unsaturated flow (most is i=1 common in fuel cells), the pore volume is not fully occupied by liquid water and 0 < sl < 1. The greater the liquid saturation, the greater the restriction in gas-phase transport. The restriction of the diffusion due to pore saturation can be represented by the effective saturated porosity: φeff = φ(1 − sl )

(5.87)

This equation can be used to modify the effective diffusion coefficient an catalyst active surface area under flooded conditions. Another important parameter is irreducible liquid saturation, also called the immobile saturation (sirr ), which represents the amount of isolated trapped water in the pores of the PM. That is, even when a high flow rate of gas is introduced into the porous media, some fraction of liquid will remain (unless evaporated) primarily due to discontinuity or isolation with the rest of the pores. The irreducible fraction does not represent the fraction of liquid in the porous media which cannot be removed from the fuel cell media. In fact, removal from drag forces is not possible, but removal from evaporation is. Contact Angle and Surface Tension Contact angle is a critical parameter in two-phase flow defined as the angle between the gas–liquid interface and the solid surface. It is measured at the triple point where all three points intersect. This can be interpreted as a measure of the wetting of the solid surface by a liquid on different surfaces. Contact angles depend on the base material of surface temperature, surface impurities, and surface morphology (roughness). For a static system, solid surface interfacial tensions can be calculated from the measured contact angles by using a mechanical equilibrium relation derived by Young in 1800 [38]. The liquid droplet contact angle on any solid surface can be defined by the mechanical equilibrium of the droplet under the action of three interfacial tensions. The interfacial tension σ ij is defined as the amount of work that must be performed in order to separate a unit area of fluid j from k. The term σ j is the surface tension between substance j and its own vapor phase (Figure 5.28). The work to separate two phases is expressed as W jk = γ j + γk − γ jk

(5.88)

Figure 5.28 represents a droplet of liquid l on top of solid s equilibrated with gas g. A simple force balance on the droplet contact surfaces in the x direction gives the surface tension components of the solid material: cos θ =

γsg − γsl γgl

(5.89)

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g

γ

247

gl

θ γ sl

γ sg

s Figure 5.28 Contact angle on a hydrophilic surface.

where γ gl , γ sl and γ sg represent the liquid–vapor, solid–liquid and solid–vapor surface tensions, respectively. Depending upon the molecular force balance at the contact line, the surface tends to either contract or stretch the liquid droplet like an elastic membrane. The angle θ is known as the contact angle. The adhesion tension is γgl cos θ . If θ < 90◦ , the fluid is termed wetting, and the surface is hydrophilic to the fluid. If θ > 90◦ , the fluid is called nonwetting and the surface is hydrophobic to the fluid. Consider a droplet of rain on the hood a polished automobile. The water will bead and is nonwetting on the hydrophobic surface. On a dirty automobile, the surface is hydrophilic to water, and the water will spread out and form a sheet. A schematic of a water droplet emerging on a hydrophobic and hydrophilic diffusion media surface is given in Figure 5.29. In PEFC porous media, the pore size distribution and surface properties are tailored to achieve the desired two-phase flow characteristics. Typically, highly hydrophobic PTFE is added to the naturally hydrophilic diffusion media structure. The result is a mixed hydrophobic–hydrophilic surface and internal structure. Figure 5.30 shows a microscopic view of a wet diffusion media material. There is clearly a complex structure of mixed surface tension behavior in these media. The interrelation of the measured surface-phase tensions as a function of PTFE content for

Figure 5.29

Liquid droplet shape on hydrophobic and hydrophilic DM.

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Figure 5.30 Microscopic view of wet diffusion media paper surface. Some of the surfaces coated in PTFE in the DM are hydrophobic, while the base carbon fiber is hydrophilic. As a result, the fundamental description of the flow through this medium is extremely difficult [39]. Image courtesy of Prof. Massoud Kaviani.

SIGRACET carbon-fiber-based nonwovens has been correlated [35]: γlv cos θ A = γsv − γsl = 0.0006 × %PTFE − 0.0274 N/m

(5.90)

This linear equation relating γ sl − γ sv and PTFE content can be used to estimate surface tension values over the range of 5–20% PTFE loadings. This equation is determined based on observation of droplets on the surface of the diffusion media; thus the internal structure and behavior are still the subject of investigation. Permeability and Darcy’s Law Permeability refers to the tendency of a porous material to allow fluid to move through its pores. Permeability of a porous medium is one of the controlling factors that affect the rate at which fluids travels through the pores. For instance, porous media with higher permeability facilitate the transport of reactants and products. The intrinsic permeability is a property of the porous media only, not the flowing fluid, and is defined as k = Cd 2

(5.91)

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where k and d are intrinsic permeability and average pore diameter, respectively, and C represents a dimensionless constant describing the configuration of the flow path. Permeability is either directly measured or empirically estimated using Darcy’s law. Darcy’s law states that the flow rate through a porous body is equal to the product of the permeability of the medium and the pressure gradient across the porous body divided by the viscosity of the flowing fluid: Q=

−k A P µ L

(5.92)

This relationship is based on experiments of water flow through a range of sand beds. Here, Q, A, and µ represent the flow rate, cross-sectional area of flow, and viscosity of the fluid. The actual permeability of a given phase is given by k, and P/L is the pressure gradient across the porous medium having a thickness of L. A common unit for permeability is the darcy (1 darcy ∼10−12 m2 ) in petroleum science, whereas it is represented by centimeters squared or meters squared in SI units. When a measured value of absolute permeability is unavailable, the Carman–Kozeny equation can be used to make an estimate of the absolute gas-phase permeability of the medium: kabs =

r 2φ3 18τ (1 − φ)2

(5.93)

Here, r, φ, and τ are the mean radius of the pores and the porosity and tortuosity of the medium, respectively. Relative Permeability In liquid–gas two-phase flow in porous media, the available pore space is shared by the liquid and gas, and thus the effective cross-sectional area available for each fluid is less than the total available pore space. This effect is taken into account by the relative permeability, kr , which is defined as the ratio of the actual permeability for a phase at a given saturation to the total intrinsic permeability of the porous media: kr =

k kabs

(5.94)

Thus, the k in Eq. (5.92) must be modified with kr if there is any saturation. If the porous media are dry, then k = kabs . Direct experimental measurement of relative permeability for different types of soils has been performed in soil science. However, to date, mathematical approaches based on previous experiments are commonly preferred for estimating the relative permeability because of the difficulty in conducting direct experiments. Various researchers have proposed correlations based on experimental data or mathematical derivations to predict the phase relative permeability. Most of the existing relative permeability correlations are based on different physical models, including capillary model, statistical model, empirical model, and network model [40]. Typically, the general shape of the relative permeability curves can be estimated by the following equations [40]: kr,nw = A(snw )n

and

kr,w = B(1 − snw )m

(5.95)

where nw and w represent the wetting and nonwetting fluids, respectively and A, B, n, and m are constants depending upon the structure of the porous media. Figure 5.31 depicts a

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100

0

1.0

kr,w + kr,nw kr,w, kr,nw

c05

0.5

kr,nw

kr,w

0 0

SW0

100 SW (%)

Figure 5.31

Typical relative permeability as function of saturation. (Adapted from [41].)

typical relative permeability curve as a function of saturation. The relative permeability curve for the liquid (nonwetting) phase shows a modest increase at low saturations, because at low saturations only a small portion of the pores is occupied by the liquid water, whereas a large portion of the pores is still available for the gas-phase transport. Hence, there is no significant impact of saturation on the reactant flow. However, at high saturations, the relative permeability exhibits a considerable increase with small increases in saturation, because as the available pores are nearly all filled by the liquid water, gas-phase transport is highly restricted. In PEFC modeling studies, a typical relative permeability expression for nonconsolidated sands is adapted to describe the phase transport in DM due to its simplicity [kr =(snw )3 ]. However, recent work has indicated a slightly different relationship is more appropriate [42]: 2.16 kr −nw = snw

(5.96)

Since this relationship is a function of morphology, a value of ∼2.5 is suggested for the value of n unless other data are available. Four well-established empirical correlations along with the empirical fit by [42] are presented in Table 5.13. Table 5.13 Summary of Relative Permeability Models Relative Permeability Models Wyllie model Corey model Brooks–Corey model Van Genuchten model Kumbur et al. [42] as e

Nonwetting Phase kr,nw kr,nw kr,nw kr,nw kr,nw

= (se,nw )3 = [1 − (se,w )2 ][1 − se,w ]2 = (1 − se,w )2 [1 − (se,w )(2+λ)/λ ] = (1 − se,w )1/3 [1 − (se,w )1/m ]2m = (snw )2.16

Wetting Phase kr,w = (1 − se,nw )3 kr,w = (se,w )4 kr,w = (se,w )(2+3λ)/λ kr,w = (se,w )0.5 [1 − (1 − (se,w )1/m )m ]2 kr,nw = (1 − snw )2.16

represents the effective saturation defined as se = (s − so )/(1 − so ).

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r’, r’’ are radii of curvature Water r’ of water–air r’’ interface Solid Solid

Figure 5.32

Equilibrium at curved interface. (Reproduced from [41].)

5.5.4 Capillary Transport in Fuel Cell Diffusion Media Capillary Pressure Whenever two or more fluids coexist in a system, there exists a pressure difference at the interface between the phases due to the interfacial tensions caused by the imbalance of the molecular forces at the line of contact. The difference between the pressures of any two phases at the interface is referred as the capillary pressure. The capillary pressure between wetting and nonwetting phases is defined as 
2γ 1 1 +

= ∗ (5.97) Pc = Pnw − Pw = γ
r r r Here, r
and r

are the two principal radii of the interface between the solid pore surface and the liquid surface curvature, and r is the mean radius of curvature, and on the same order as the pore size as shown in Figure 5.32. Equation (5.97) is also called the Laplace equation for capillary force. The surface tension of water can be correlated as a function of temperature: γ (N/m) = −1.78 × 10−4 (T ) + 0.1247

(5.98)

where temperature is in Kelvin. Most modeling studies of fuel cells adopt a capillary tube model, in which the porous media is composed of capillary tubes of different radii when the mean radius of the tubes is r ∗ . Using this formulation, the variable contact angle produced by a hydrophobic additive can be included in the model. The capillary force for the tube model can be written as Pc = Pnw − Pw =

2γ cos θ r∗

(5.99)

where the r* is taken as a negative value to assure the signs match between formulations. It should be noted that upon initially saturating a porous medium, for example, by condensation into a PEFC DM, liquid water remains unconnected and unable to transmit pressure and drive liquid flow. As saturation level increases, the isolated droplets become connected between pores, and capillary flow can be initiated. Capillary pressure increases as pore radius decreases, so that the very small pores in a catalyst layer can have very high capillary pressure. It is important to emphasize that, even for very homogeneous porous media, these relationships cannot be applied on a microscopic level to the entire media due to the complex and highly varied pore structure in PEFCs, and attempts at modeling the effects are considered global and meant to capture the qualitative trends using bulk parameters derived that are representative of the bulk media. Therefore, these parameters must be derived experimentally and are highly dependent on material properties, and in fuel cells, interfacial effects are not treated in the

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θ

θ

Wetting fluid

Figure 5.33 bic walls.

θ

Nonwetting fluid

θ

Downward surface tension force

Illustration of capillary action in a column for (a) hydrophilic walls and (b) hydropho-

bulk approach. Nevertheless, we can understand the basic principles involved in capillary flow by considering a single capillary column, as shown in Figure 5.33. If the walls of the capillary tube are hydrophilic to the fluid, a net capillary suction force will draw fluid up the walls of the tube until the gravity force balances the surface tension force. If the walls of the tube are hydrophobic to the fluid, the meniscus will be concave down, and the air will be the wetting fluid. In hydrophobic DM, the liquid pressure (nonwetting phase) is larger than the gas (wetting) phase pressure, whereas in hydrophilic DM, gas-phase pressure is higher than liquid pressure: pc = pnw − pw pc > 0 ⇔ pnw > pw pc < 0 ⇔ pnw < pw

for θ > 90◦ for θ < 90◦

(i.e., hydrophobic) (i.e., hydrophilic)

(5.100)

The resulting pressure imbalance can cause water to flow from locations of high pc to low pc . In fuel cell studies, it is reasonable to assume immiscible flow, meaning we treat the gas phase and liquid phase as nonmixing (even though some amount of gas phase will dissolve into the liquid phase). This allows us to separate the phases into nonwetting and wetting components. In fuel cell DM, once the gas phase is fully saturated with water vapor, assuming evaporation and condensation does not take place in the DM, liquid water flow becomes the only mode of water transport across the DM [5]. Water generation in the catalyst layer, water transport across the membrane, and condensation or evaporation within the DM pores cause nonuniformity in saturation distribution. As hydrophobic DM pores are filled by the liquid water, the liquid-phase pressure increases, eventually driving the liquid water from higher to lower liquid pressure regions. As a result, the liquid water in the DM is driven via capillary action produced by the liquid saturation gradients in DM. In an operating PEFC, the higher saturation generally occurs in the catalyst layer, and it decreases in the vicinity of the channel, implying that capillary transport takes place from high- to low-saturation regions in DM [43, 44], as depicted in Figure 5.34. Example 5.13 Comparison of Capillary and Gravitational Effects Compare the expected capillary pressure force on a 0.1-mm water droplet (ρ = 971 kg/m3 ) in a hydrophobic (θ = 105◦ ) diffusion media pore with the same diameter to the gravitational force on the same droplet at 80◦ C.

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Gas saturation, s g

1

253

0 Catalyst layer

Diffusion media

Reactant flow

Liquid flow

Reactant flow channel

c05

Water Water generation Generation

0

Liquid saturation, s l

Figure 5.34

SOLUTION

1

Capillary-induced liquid transport in a hydrophobic fuel cell DM.

The gravitational body force is simply calculated as

  0.1  mm 3 4 Fg = ρV g = (971 kg/m3 ) π 9.8 m/s2 = 4 × 10−8 N 3 1000 m The capillary pressure is estimated as
pc = pnw − pw = γ

1 1 + r
r



 ≈

2γ 0.062 N/m =2× = 124 N/m2 r 0.1/1000 m

To solve for the resultant force on the droplet, we multiply by the cross-sectional area of the droplet: Fcap = (124 N/m2 )π (0.1/1000m)2 = 3.9 × 10−6 N So the capillary force on the droplet is about two orders of magnitude larger than the gravitational force, meaning we can neglect the gravity force in this circumstance. COMMENTS: Comparison of the gravitational to surface tension forces is commonly done through the Bond number, which is a dimensionless comparison of the gravitational and surface tension forces: Bo =

ρgl 2 γ

(5.101)

Here, l is the representative length scale of the fluid. Gravitational √ and surface tension forces are comparable when Bo = 1, which will occur when l = γ /ρg. For an air–water

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surface at 80◦ C, this length is approximately   γ 0.0626 = = 2.6 mm l= ρg 971 × 9.81 Therefore PEFC diffusion media and catalyst layers will be dominated by surface tension forces, with gravitational forces playing a real role only in the in-plane direction in flow channels and in manifolds where length scales can exceed a few millimeters. However, surface tension effects in the channels are also important, especially in the direction normal to the catalyst layer surface. Leverett Function The most important relationship that must be established for an accurate prediction of the liquid–gas transport in the DM is the relationship between the capillary pressure and the liquid saturation. Capillary pressure depends on a variety of parameters, including temperature through surface tension and the morphology, tortuosity, and pore size of the material but most importantly liquid saturation. Several empirical and semiempirical expressions are available which attempt to describe the behavior of capillary pressure in terms of a porous media and fluid properties. A generic Leverett function from soil science has been commonly employed to describe the capillary transport behavior of the porous media in multiphase models. Since many porous media share similar characteristic behavior, for PEFC gas diffusion layer material, a Leverett-type function has been used to represent this behavior as a first step toward achieving an accurate two-phase transport model. Udell [45] used Leverett’s approach [46] to develop a semiempirical relation correlating capillary pressure and saturation data for clean unconsolidated sands of various permeability and porosity by means of defining a capillary pressure function: Pc = γ cos θ


1/2 φ J (s) k

(5.102)

where k, φ, and θ are the permeability and porosity of the porous media and a representative contact angle, respectively, and J(s) represents the Leverett function for scaling drainage capillary pressure curves:  1.417(1 − sl ) − 2.120(1 − sl )2 + 1.263(1 − sl )3 if θ < 90◦ ⇒ Hydrophilic J (sl ) = 1.417sl − 2.120sl2 + 1.263sl3 if θ > 90◦ ⇒ Hydrophobic (5.103) The Leverett approach incorporates the effects of interfacial tension but uses a simple relation for the average pore radius (k/φ)0.5 , basically ignoring the tortuous nature of porous media [37]. Although this approach serves as a useful starting point, the applicability of a generic Leverett function to the highly anisotropic thin-film DM is unclear and unverified. Specific concerns center around the differences in fuel cell DM and conditions under which the Leverett function was derived. In particular, the definitions of wetting and nonwetting phases used to determine capillary pressure and surface tension angle are taken as a statistical average over the entire medium, obscuring local effects which differ from the whole. Because the droplet/bubble

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sizes are on the same order of magnitude as the DM thickness, a volume-averaged approach may not be appropriate. In addition, most porous PEFC material is impregnated with an anisotropic coating of hydrophobic material (PTFE or other), thus yielding a complex bimodal (hydrophobic and hydrophilic) pore size distribution. With heterogeneous wettability, certain regions of the pore space will have a greater affinity for liquid, while other regions will tend to repel water, so that within the bulk media liquid water will be both the wetting (on untreated DM fiber) and nonwetting (on PTFE) phases. This situation obviously cannot be dealt with using a single function. The chemical nature of the surface and the spatial distribution of the wettability significantly affect the capillary transport characteristics of these thin-film media. Instead of a single function to describe capillary pressure as a function of liquid saturation, it may be more appropriate to construct a model based on two or more functions acting in parallel in the DM that emulate the transport of both phases through the discrete flow paths. Modified Leverett Function Appropriate for Fuel Cell Media The standard Leverett function has been found to be appropriate for qualitative matching of the flow characteristics through the media; however, actual measurements of PEFC diffusion media show different quantitative behavior. Kumbur et al. [47] presented a modified Leverett function appropriate for thin-film fuel cell DM to estimate the capillary pressure as a function of liquid saturation and hydrophobic additive content. This empirical fit was derived from the direct measurement of capillary pressure–saturation for different types of DMs (cloth and paper) with PTFE content ranging from 0 to 20% of weight and a microporous layer. Figure 5.35 depicts the measured capillary pressure (Pc ) versus nonwetting liquid saturation for carbon paper DM tailored with 20% PTFE content. The nature of the capillary pressure–saturation curves exhibits a continuous “S” shape, rather than “J” shape, and yields four inflection points. For saturation leads under 0.5, the capillary pressure in the DM was fit to a modified Leverett function, appropriate for the hydrophobic pores: Pc = γ


1/2 φ M(snw ) k

(5.104)

where  M(snw ) =

2 3 %wt(0.0469 − 0.00152 × %wt − 0.0406snw + 0.143snw ) + 0.0561 ln snw

for

0 < snw < 0.50

where %wt and snw represent the PTFE weight percentage of the DM and nonwetting liquid saturation, respectively. For hydrophilic pores, liquid water must be removed by evaporation or convective forces since inhibition, not drainage, will be spontaneous. A key feature of this empirical function is that the contact angle parameter is implicitly embedded in the adjustable PTFE parameter, which enables successful iteration of the capillary pressure as a function of the hydrophobic content of the DM. Compression and temperature also play an important role in the capillary pressure saturation relationship. For more information, the reader should consult ref. [47].

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Figure 5.35 Measured capillary pressure (Pc ) and predicted Pc by Leverett function versus saturation for carbon paper DM tailored with 20% PTFE content [48].

Example 5.14 Determination of Capillary Pressure Using Leverett Approach Capillary pressure can be represented by Leverett approach for hydrophobic DM pores. Determine the capillary pressure as a function of the given DM properties at a liquid saturation of 0.4 and briefly explain: (a) What is the expected change in capillary pressure when contact angle is changed from 110◦ to 150◦ ? Explain why the given change occurs. (b) Determine the change in capillary pressure for an increase in porosity to 0.9. (c) Determine the qualitative trend expected if the temperature is increased.
1/2 φ PC = γ cos θ J (sl ) k J (sl ) = 1.417(sl ) − 2.120(sl )2 + 1.263(sl )3

Properties Contact Angle (deg) Porosity, φ Permeability, k (m2 ) Surface tension (N/m)

110 0.7 10−12 0.062

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SOLUTION
PC = (0.062 N/m) |cos 110|

0.7

1/2

10−12 m2

J (0.4)

J (0.4) = 1.417(0.4) − 2.120(0.4)2 + 1.263(0.4)3 = 0.308 PC = 5.4 kPa (a) If the contact angle is changed from 110◦ to 150◦ , then the new capillary pressure becomes   ◦  cos 110  PC |θ=110   = ◦  cos 150  PC |θ=150

◦

◦

PC |θ=150 = 2.53 PC |θ=110 = 13.8 kPa

As the DM becomes more hydrophobic, the representative contact angle increases. The increase in contact angle leads to an increase in capillary pressure due to the increase in hydrophobicity. Therefore, rendering the DM more hydrophobic enhances the liquid water drainage from the DM by increasing the driving force for water motion. (b) If the porosity is increased from 0.7 to 0.9:   0.7 0.5 PC |φ=0.7 = 0.9 PC |φ=0.9

PC |φ=0.9 = 4.76 kPa

The capillary pressure is reduced through increased porosity. In the extreme of 100% porosity, the capillary pressure is the lowest, which is one factor that drives flow to the channel from the hydrophobic pores of the DM. (c) Surface tension is a function of temperature and is given as γ (N/m) = −1.78 × 10−4 (T ) + 0.1247 Therefore, if the temperature is increased, surface tension will decrease, thereby yielding lower capillary pressure at given conditions. COMMENTS: The values for capillary pressure solved for here are on the order of 0.1 atm. This is the driving force for liquid motion. The areas with high capillary pressure drive the liquid to areas of low capillary pressure, which are areas of higher pore size, or low hydrophobicity such as the flow channels or hydrophilic pores. Example 5.15 Effect of Microporous Layer Often, to enhance water transport, a special highly hydrophobic coating between the DM and catalyst layer will be used, called the microporous layer (MPL). This layer has an average pore size somewhere between that of the catalyst layer and the macro-DM. Consider a bilayered DM coated with an MPL. In equilibrium, there will be a liquid saturation jump at the interface between the MPL and the DM, because of the discontinuity in pore sizes. That is, in order to have a liquid phase pressure balance at the MPL–DM interface, as required for equilibrium, the saturation in the MPL will be lower, since the pore size is lower, increasing the capillary pressure. Assume

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that at the interface, the DM has a local saturation value of sint . What will be the boundary condition to calculate the saturation jump at the interface and write down the necessary equation? Use the Leverett approach in this example:
1/2 φ J (sl ) PC = γ cos θ k SOLUTION Liquid pressure across the interface of the DM and MPL should be continuous in equilibrium. However, the different material properties of these two layers cause a discontinuity in the liquid saturation across the interface, even though the capillary pressure at the interface is equal.

Imposing the pressure balance at the interface yields PCDM |DM−MPL Interface = PCMPL |DM–MPL Interface where
1/2 φ J (sl ) k
  MPL  φDM 1/2  DM  = cos θDM J sint J sint kDM PC = γ cos θ


cos θMPL

φMPL kMPL

1/2

COMMENTS: One can solve the saturation jump using this equation at given conditions. The magnitude of the discontinuity or the jump in the saturation strongly depends on the

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259

material properties of these two layers and the amount of liquid water flux at the interface. In general, the medium that is more hydrophobic and has smaller pore sizes has a reduced saturation, and flow is driven to areas of high pore size or increased wettability. In this case, with an MPL, the DM will have a much higher saturation than the MPL since the pore size is smaller and the structure is more hydrophobic in the MPL. Example 5.16 Local Saturation in Diffusion Media of PEFC Consider net hydrophobic fuel cell DM. The fuel cell is operating at 80◦ C, supplying 1 A/cm2 , and water generated (Nw = iA/2F) is in the liquid phase. Assume that the only water flux coming into the DM is the generated water from the catalyst layer. According to the given DM properties and necessary correlations below, find the local position (distance from the catalyst layer) in the DM where the liquid saturation values are 0.2, 0.3, and 0.4: −k ∇ PC (Darcy law) µ
1/2 φ PC = γ cos θ J (sl ) k ul =

kr = sl3

(relative permeability)

Note that the liquid water flowing inside the DM is assumed to be Newtonian and incompressible, and the flow in the pores of the DM is presumed to be one dimensional, steady, and laminar. Inside the DM, the gas-phase pressure is assumed to be constant (Pg ≈ const).

Properties Thickness (µm) Contact angle (degs) Porosity, φ Permeability, k(m2 ) Surface tension at 80◦ C (N/m)

300 150 0.7 10−12 0.062

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SOLUTION Based on Darcy’s law, the governing liquid transport equation in the porous DM is expressed as ul =

−kl ∇ PC µ

where

kl = kr k

Here, kl , kr , and k are the liquid permeability, relative permeability, and absolute permeability of the porous media. The capillary pressure in a hydrophobic diffusion media is represented as PC = Pl − Pg ∇ PC ≈ ∇ Pl

(Pg ≈ const)

Using the Leverett function, PC = γ cos θ


1/2 φ J (sl ) k

where for hydrophobic media J (sl ) = 1.417(sl ) − 2.120(sl )2 + 1.263(sl )3 Therefore, the capillary pressure gradient will become 
 φ d J dsl ∇ PC ≈ ∇ Pl = γ cos θ k dsl d x At steady state, the mass flux of liquid water going into the cathode DM is equal to the amount of water generated in the catalyst layer due to the electrochemical reaction. Using the mass balance on the control volume, the continuity equation for the liquid water inside the DM is ρl u l =

i MWH2 O 2F

where MWH2 O is the molecular weight of the water and ul is given. Note that this also assumes zero net transport through the electrolyte. Rearranging, the final form of the governing equation becomes d J dsl i · MWH2 O · µl = −kr √ dsl d x 2Fγ cos θρ kφ where kr = sl3 and x0 0

i · MWH2 O · µl − √ dx = 2Fγ cos θρ kφ

s

  1.417sl3 − 4.24sl4 + 3.78sl5 dsl

0

x0 = −

0.35sl4 − 0.85sl5 + 0.63sl6 i·MWH2 O ·µ √l 2Fγ cos θρ kφ

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Inserting the values of the given properties along with the desired the local saturation values, the corresponding locations will be For s = 0.30 For s = 0.25 For s = 0.20 COMMENT:

x0 = 300 µm x0 = 200 µm x0 = 90 µm

This type of model is well suited for computational anaylsis.

5.5.5 Imbibition and Drainage Process The process for wetting fluid replacing nonwetting fluid in a porous media is called imbibition. The opposite process is called drainage. A key relationship in capillary flow is that relating the liquid saturation to the capillary pressure, which drives the motion of flow. Figure 5.36 shows a typical relationship Pc = Pc (sw ) during imbibition and drainage for a porous medium. As shown snw,0 is the residual saturation of the nonwetting fluid and therefore limits the maximum saturation achievable with imbibition (condensation in the pores can still fill this residual fraction unless these pores are totally orphaned). Point A on Figure 5.36 shows the bubbling (or breakthrough) pressure Pb , which is the minimum pressure needed to initiate displacement of wetting fluid by nonwetting fluid. The hysteresis in porous media observed between imbibition and drainage is a result of several effects, including the so-called ink-bottle and rain drop effect, as shown in Figure 5.37. In the ink-bottle effect, as liquid enters a widening pore, the capillary forces change with the increasing diameter, which can trap a droplet. The rain drop effect is a result of

sNW (%) 100 6

80

60

40

20 sNWO 0

4 3 2

Drainage

Residual saturation of nonwetting fluid (sNW)

Irreducible wetting fluid saturation (sW)

5 Capillary pressure

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1

0

Figure 5.36 from [41].)

A

Inbibition

0

20 sWO 40 60 sW (%)

80

100

Typical wetting/drying curves for porous media illustrating hysteresis. (Reproduced

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ϕ1

ϕ2

(b) Figure 5.37 from [41].)

Illustration of hysteresis effects: (a) ink bottle effect; (b) rain drop effect. (Reproduced

gravity on nonhorizontal surfaces and can result in asymmetric droplet shape and capillary forces.

5.5.6

Phase Change in Porous Media: Capillary Condensation In very small pores, gas-phase pressure increases according to the Kelvin equation:
Ru T ln

Pv Po

 =

2γ V˜ cos θ r

(5.105)

where Pv is the increased pore vapor pressure, Po is the bulk vapor pressure, V˜ is the molar gas volume, γ is the surface tension of the liquid surface, and r is the radius of curvature of the liquid. Recalling the definition of relative humidity from Chapter 3, RH = φ =

Pvapor yH2 O PTotal = Pg,sat (T ) Pg,sat (T )

(5.106)

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So as Ptot increased, the RH increases, yv decreases, and condensation occurs in pores above the normal bulk condensation temperature due to increased pore-level vapor pressure. This is not a significant effect in most fuel cells and does not matter for any species besides water. For example, for a 50-nm (typical of a catalyst layer) pore at 80◦ C, water will condense at approximately 100.5◦ C. So capillary condensation is not a major effect in DM or catalyst layers but can be significant for vapor dissolving and condensing into solid polymer electrolytes with nanometer-size holes.

5.6 HEAT GENERATION AND TRANSPORT 5.6.1 Heat Generation In an operating fuel cell, even though the efficiency may be higher than a conventional combustion engine, there is still a considerable amount of the initial chemical energy dissipated as heat through operation. For a 50% efficient 100-kW engine, 100 kW still needs to be dissipated as heat. For high-temperature systems, such as the SOFC, the heat dissipation is not a major issue; in fact, the waste heat is high quality, because it can easily be used for some other purpose to raise the effective efficiency of the overall process, such as to convert water to steam and run a turbine or to heat a building. The process of using waste heat for another purpose is termed cogeneration and is explored in the Application Study at the end of this chapter. In high-temperature systems such as the MCFC and SOFC, fuel cell warm-up and maintaining a steady elevated temperature for operation are also important issues. Some dissipation can be achived using the reactant gas. For fuel cell systems with recirculating liquid electrolyte, significant cooling can be achieved through the electrolyte. Other large fuel cell systems usually require active coolant recirculation control systems. For low-temperature PEFC systems, heat rejection is challenging for the following reasons: 1. In a typical combustion engine, around 80% of the waste heat is removed by the exhaust gas flow. In a larger PEFC stack, the waste heat is primarily removed by the fuel cell coolant, and relatively little heat is removed by the exhaust flow. This puts additional heat rejection burdens on the system. 2. Due to the low operating temperature, the heat rejection rate to the environment is reduced compared to a combustion engine, since the heat transfer rate is proportional to the temperature difference between the heated source and the ambient. In Chapter 4, the heat generation flux in a fuel cell was shown to be related to the current and the departure of the cell voltage from the thermal voltage:

(W/cm2 ) = i(E th − E cell ) qheat

(5.107)

where i is the operating current density, Eth is the thermal voltage, and Ecell is the fuel cell operating voltage. The cell voltage is of course a function of activation, ohmic, and

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concentration polarizations. This heat generation includes the reversible heat generated by the entropy change, which is the difference in the thermal and Nernst voltages: 
G T S H

2 ◦ − = −i (5.108) qheat,rev (W/cm ) = i(E th − E ) = i − nF nF nF This entropy-generated heat is known as Peltier heating. The irreversible heat generated by activation, ohmic, and concentration polarizations is

qheat,irr (W/cm2 ) = i(E ◦ − E cell ) = i(ηa,a + |ηa,c | + ηm,a + |ηm,c | + η R + ηx )

(5.109)

where the various polarizations are defined in Chapter 4. The total heat generated by reaction polarizations is the sum of the reversible and irreversible components:

(W/cm2 ) = −i qtotal

T S + i(ηa,a + |ηa,c | + ηm,a + |ηm,c | + η R + ηx ) nF

(5.110)

As current density increases (corresponding also to reduced cell voltage), the thermal energy dissipation flux will increase. The first term on the right-hand side of Eq. (5.110) represents Peltier heating. The second term on the right-hand side represents the sum of the activation (kinetic), concentration, ohmic, and crossover contributions to the heat generation. 5.6.2

Single-Phase Heat Transport9 Conduction Conduction is heat transfer resulting from intermolecular collisions. At a molecular level, as a molecule with higher thermal energy collides with a molecule with lower thermal energy, some of the energy is transferred to the lower energy system. The governing equation for conduction heat transfer is known as Fourier’s law of heat conduction, which is analogous to Fick’s law of mass diffusion, written in three dimensions as

(W/m2 ) = −ki qheat,i

∂T ∂ xi

(5.111)

where subscript i represents the x, y, or z dimension, ki is the thermal conductivity in the

is the conduction heat transfer flux in the i direction. Expanded into i direction, and qheat,i three dimensions, Eq. (5.111) is written as

= −k x qheat,x

∂T ∂x



qheat,y = −k y

∂T ∂y



qheat,z = −k z

∂T ∂z

(5.112)

In many cases, the thermal conductivity is isotropic and therefore not a function of orientation. However, for some fuel cell materials, the value should be highly anisotropic based on structure and material orientation. An example of this is the woven diffusion media structure of the PEFC shown in Figure 5.38. The layered woven pattern should result in a much higher in-plane electrical and thermal conductivity than the through-plane direction. The thermal conductivity of many PEFC materials has been measured as a function of compression pressure and temperature [49]. Representative values of PEFC material 9 It

is assumed the reader has a cursory knowledge of basic heat transfer. The reader is referred to other texts for additional information, such as Fundamentals of Heat and Mass Transfer, 5th ed., by F. P. Incropera and D. P. DeWitt, Wiley, New York, 2002.

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Figure 5.38 Cross-sectional SEM of membrane electrode assembly, microporous layer, and paperbased macro diffusion media.

conductivity and other fuel cell material conductivity are given in Tables 5.14 and 5.15, respectively. A plot of the estimated thermal conductivity of Nafion electrolyte with water content is shown in Figure 5.39. For solids, the thermal conductivity is a combination of the transport of free electrons and vibration of bound lattice atoms [50]: k t = k e + kl

Table 5.14

(5.113)

Measured Thermal Conductivity of Polymer Electrolyte Fuel Cell Components.

Material

Measured k (W/m · K)

DuPont Nafion membrane (at 30◦ C) W. L. Gore reinforced electrolyte Toray carbon fibar paper diffusion media (TGP-H at 57◦ C) SIGRACET 0 wt % PTFE carbon-fiber paper diffusion media (AA series at 56◦ C) SIGRACET 5 wt % PTFE carbon-fiber paper diffusion media (BA series at 58◦ C) SIGRACET 20 wt % PTFE carbon-fiber paper diffusion media (DA series 58◦ C) E-Tek ELAT carbon cloth diffusion media (LT1200-W at 33◦ C) Catalyst layer (0.5 mg/cm2 platinum on carbon)

0.16 ± 0.03 0.16 ± 0.03 1.76 ± 0.30 0.48 ± 0.09 0.31 ± 0.06 0.22 ± 0.04 0.22a ± 0.04 0.27a ± 0.05

a Effective

thermal conductivity (includes thermal contact resistance with diffusion media) Source: From [49].

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Transport in Fuel Cell Systems Table 5.15 Thermal Conductivity of Fuel Cell Components Material Platinum Nickel 7% YSZ (SOFC electrolyte) Pure Graphite Stainless steel Aluminum Oxide Aluminum Carbon Steel TeflonTM Fiberglass Oxygen Nitrogen Hydrogen Water vapor Liquid water Methanol

Thermal Conductivity (W/m · K) @25 ◦ C 70 91 ∼2.0 [56] ∼90 16 30 250 1.7 46 0.25 0.04 0.024 0.024 0.17 0.016 0.58 0.21

Figure 5.39 Estimated thermal conductivity of Nafion 1100 EW at different humidity ratios. The thermal conductivity variation of pure water is shown as an upper bound for the theoretical moist Nafion thermal conductivity [49].

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For electrical conductors such as metals, the electron conductivity portion dominates, and the thermal and electrical resistances can be correlated by the Wiedemann–Franz law: kt = LT σe

(5.114)

where T is the absolute temperature, kt is the thermal conductivity, σ e is the electrical conductivity, and L is the proportionality constant known as the Lorenz number, determined from quantum mechanics to be L = 2.45 × 10−8 W · /K2

(5.115)

This result matches with experiment quite well for most metals above room temperature. For electrical insulators, however, such as electrolytes, the lattice vibration thermal conductivity dominates, and the more ordered and crystalline the structure is, the greater the thermal conductivity. For these materials, Eq. (5.114) does not hold true. For gases, the thermal conductivity generally increases with temperature. For fuel cells, it is noteworthy that the thermal conductivity of hydrogen is about 5–10 times greater than for air or water vapor. As a result, a greater fraction of the heat is transported through anode than through cathode flow, although the total transported by gas flow is much less than by direct conduction of heat through the lands.10 Convection: Internal Correlations and Definitions Mass and heat transport in fuel cells is not only by diffusion and conduction. There are numerous instances where mass and heat transport by convection is important, most notably in fuel cell flow channels or in fuel cells with recirculating electrolytes. Fundamentally, convection is a result of the motion of the fluid field. It should be noted that diffusion itself necessarily induces motion and thus convection, but this is accounted for in the diffusion flux. What we are talking about in this case is transport via motion of the bulk flow field. As an example, consider a stagnant glass of clear water in which a droplet of food coloring is placed. Slowly, the color diffuses through the water (by measuring the rate of radial transport in a static environment you can measure the diffusion coefficient). Now, consider stirring the same glass as the food coloring is added. Obviously, the mixing will occur more quickly. This is a result of the motion of the general fluid field. Convection transport can be modeled with a convective mass transport coefficient:
 mol

= h m (Cs − Cm ) (5.116) n˙ m2 · s where n˙

is the molar flux of the species, hm is a convective mass transfer coefficient and Cs and Cm are the surface and mean concentrations, respectively. The mass transfer coefficient is analogous to the heat transfer convection coefficient and is known for various geometries and flow regimes as shown in many undergraduate heat and mass transfer textbooks [e.g., 50]. At the fundamental level, heat transfer into a fluid is through conduction at the boundary of the interface, as shown in Figure 5.40. Within the flow, random molecular motion and 10 Recall

that the lands are the portion of the flow field that contacts the diffusion media/catalyst layer, providing direct contact for electrical and thermal conduction.

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q˝ = −k

∂T ∂y

δBL

vy vx

Convective heat flux

y x

T high Figure 5.40 Schematic of fluid flowing over heated interface showing local conduction at interface and advection of heat through boundary layer. The sum of the molecular-level interaction conduction and heat transfer by bulk motion (advection) is terms the convection heat transfer.

collisions still occur, resulting in conduction heat transfer. In a moving fluid, however, there is also heat transfer by the bulk motion of the flow, termed advection, that can dominate the transport of heat. The combination of conduction and advection is known as convection. To illustrate this, think of a cold pot of water on a heated stove. The water near the bottom of the pot will be heated first, and the heat will conduct to the top of the water, which is a relatively slow process (ignoring natural convection effects). To hasten the heat transfer, a simple stir of the water will bring the heated water from the bottom of the pot to a location near the top, adjacent to the cold water, heating the cold water by intermolecular collision. There are two main classifications of convection, forced and natural. Forced convection is fluid motion that is a result of forced input, such as a fan or pump. Natural convection is a result of density gradients in the flow which cause motion. In forced convection, there is also often a component of natural convection, but this is typically dominated by the forced convection effects. The density gradients in the flow, which are the genesis of natural convection, can be caused by either temperature or solutal buoyancy effects. Temperature effects are simply a result of the density–temperature relationship for a fluid. These effects can be illustrated by imagining a window in a warm apartment on a cold winter day (see Figure 5.41). At the inside surface of the window, the air in the room is cooled by the window and increases in density, sinks down along the window, and causes an uncomfortable draft. Solutal buoyancy forces are the result of the mixture changing its distribution of species and its density. For example, in a portable fuel cell, dry air is brought in from the ambient, and oxygen is consumed, while the mixture is simultaneously heated and humidified, as shown in Figure 5.42. The uptake of water (MW 18 g/mol) into a mixture of air (MW 28.85) Window Outside (cold)

Inside (warm) Local cooling air sinks, causing motion

Figure 5.41

Schematic of natural convection flowing from a cold window.

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Heat into Air

269

Increasing Temperature Buoyancy Force

Moisture into Air

Decreasing Molecular Weight Buoyancy Force

Dry Air Flow In

Figure 5.42

Schematic of thermal and solutal natural convection.

reduces the molecular weight and density of the mixture, which induces a solutal buoyancy convection motion in the flow in addition to any thermal or forced effects. Despite the relative complexity of convective heat transfer, it is often modeled with a bulk heat transfer coefficient h. The heat flux from a surface at temperature s to a fluid at temperature m is written as

(W/m2 ) = h(Ts − Tm ) qheat

(5.117)



where qheat is the local heat flux, h is the local convective coefficient, Ts is the surface temperature of the enclosure in contact with the fluid, and Tm is an appropriate mean temperature of the fluid. The mean temperature in a flow channel can be solved analytically from the following relationship [50]:  ρucv T d Ac

Tm =

Ac

˙ v mc

(5.118)

where Tm is the mean temperature difference of the fluid throughout the length of the flow channel. Here, Ac is the cross-sectional area, cv is the constant volume specific heat of the fluid, m˙ is the bulk mass flow rate of the fluid, and u is the velocity profile in the fluid. Note that all of these properties can in principle vary in distance along the flow channel. In thermally fully developed flow with constant specific heat, the heat transfer coefficient can be shown to be independent of axial location. From an energy balance on the enclosed channel, it can be shown that q

P P dTm = heat = h (Ts − Tm ) ˙ p ˙ p mc mc dx

(5.119)

where P is the perimeter of the enclosed channel (2 × width + 2 × height for a rectangular channel). For a constant surface heat flux condition, we can show from Eq. (5.119), that Tm (x) = Tm,i +



P qheat x ˙ p mc

(5.120)

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where x is the axial distance along the channel and Tm,i is the inlet mean fluid temperature. So for a constant surface heat flux condition, the temperature varies linearly in the channel. For a constant surface temperature condition, we can similarly derive from an integration of Eq. (5.119):
 Ts − Tm (x) Px = exp − h ˙ p mc Ts − Tm,i

(5.121)

So for a constant surface temperature condition, the temperature varies exponentially in the channel, asymptotically approaching the constant surface temperature value. Equations (5.120) and (5.121) can be used with Eq. (5.117) to determine the heat flux when the average convection heat transfer coefficient is known. The heat transfer literature is replete with correlations that relate the particular fluid and other parameters to the heat transfer coefficient. The most basic relationships most relevant to fuel cell study will be given here, but the student or engineer interested in a more thorough understanding should consult a heat transfer source for a more complete treatment. For free convection in gases, h is very low, ∼2–20 W/m2 ·K. For forced convection, h can be many orders of magnitude higher, controlled by the flow rate and fluid being convected. The Nusselt number Nu is an important dimensionless parameter related to the thermal conductivity and length scale of heat transfer to the convection coefficient: Nu =

hL kt, f

(5.122)

where L is the length scale relevant to the particular geometry (e.g., kt, f for a tube L is the diameter, for a rectangular channel L is the hydraulic diameter) and kt, f is the thermal conductivity of the fluid. There are a multitude of Nusselt number correlations for heat and mass transfer in different situations. Similar to the momentum boundary layer entrance length in a closed channel, there is a thermal boundary layer development region. For laminar fully developed flow (Re < ∼3000), an exact solution can be found for different boundary conditions. For fully developed and laminar heat transfer in a rectangular channel with equal depth and width, the heat transfer coefficient is constant and can be determined as follows For constant surface heat flux (laminar) Nu =

hL = 3.61 kt

(5.123)

For constant surface temperature (laminar) Nu =

hL = 2.98 kt

(5.124)

Since the true boundary condition in a fuel cell is not exactly isothermal or constant heat flux, an intermediate value is typically chosen for calculation for bulk analysis. For other

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5.6 Heat Generation and Transport Table 5.16

271

Nusselt Number for Various Rectangular Geometries Boundary Condition

Cross Section (b × a) Circular Triangular Rectangular Rectangular Rectangular Rectangular Rectangular Rectangular Rectangular

Uniform Heat Flux, Uniform Surface Temperature, Nu = hL/k Nu = hL/k

b/a NA, any diameter NA, equilateral triangle 1 1.43 2 3 4 8 ∞

3.11 4.36 3.61 3.73 4.12 4.79 5.33 6.49 8.23

2.47 3.66 2.98 3.08 3.39 3.96 4.44 5.6 7.54

Source: Adapted from [51].

common fuel cell channel geometries,11 some other Nusselt number values are given in Table 5.16. The heat transfer in the entry region is enhanced for the same fundamental reasons as the pressure drop is increased in the momentum boundary larger entry region. However, in fuel cells, the entry length heat transfer effect is typically small since the channels are generally very long, and a small minority of the total heat generated is transferred to the reacting gas flow streams anyway, so this effect can be neglected at an introductory level of analysis. The thermal entry length for laminar flow can be shown as L e,thermal ≈ 0.06 Re · Pr dh

(5.125)

L e,thermal ≈ 4.4 (Re · Pr)1/6 dh

(5.126)

For turbulent flow

The unitless Prandtl number Pr is the ratio of thermal to viscous dissipation forces, so that multiplying by the Reynolds number cancels out the momentum forces, leaving the thermal dissipation: Pr =

ρα µ

(5.127)

where the thermal dissipation of the fluid, α, is α=

11 In

kt kt ⇒ Pr = ρc p cpµ

(5.128)

this text, we will only discuss basic correlations of greatest relevance to fuel cells. For more detailed information, the reader is referred to advanced textbooks on convective heat transfer.

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For fully developed turbulent flow (Re > 10,000) in a channel, the Dittus–Boelter equation is recommended to find the heat transfer coefficient [50]: For Re > 10,000, 0.7 < Pr < 160, L/dh > 10, Nu =

hdh = 0.023 Re0.8 Prn kt, f

(5.129)

where n is 0.4 for flow being heated by the channel and 0.3 for hot flow being cooled by the channel. In a fuel cell, we often have a mixed case, where a portion of the channel near the catalyst layer is heating the flow and a portion on the back wall of the channel is cooling the flow. In this case, we must remember that the h values obtained are simply averaged correlations based on experimental data and generally measured for larger channels then used in fuel cells. The use of the heat transfer coefficient h is a simplified way of calculating the heat transfer compared to more fundamental calculation approaches. Thus, the solutions provided by these Nusselt number correlations already have inherent error and should not be treated as exact solutions. In the case of mixed conditions or odd geometries not exactly within the bounds of those prescribed by the particular correlation: (1) a more appropriate correlation may be developed and available in the literature or (2) some alternative approximation can be made. For example, in the laminar-to-turbulent transition region (3000 < Re < 10,000), a linear interpolation between the proper laminar Nusselt number and the Dittus–Boelter Nusselt number can be used. Example 5.17 Estimated Temperature Gradient inside a PEFC Consider a typical PEFC operating at 0.6 V generating around 0.6 W/cm2 waste heat flux. Determine the expected temperature gradient from the 400-µm-thick cloth DM to the cathode catalyst layer, assuming 50% of the waste heat is removed from the cathode side. SOLUTION From Table 5.14, we see the thermal conductivity for the cloth is about 0.22 W/m·K. Through the DM, heat transfer should be dominated by conduction, so for one-dimensional conduction between the catalyst layer and the edge of the DM

= −k x qheat,x

dT x

⇒ qheat,x = T dx kx

Plugging in the numbers, we find (0.3 W/cm2 )

400 × 10−4 cm = 5.45 K 0.0022 (W/cm · K)

So at a typical current density of 1 A/cm2 , we can expect >5 K temperature difference between the electrode and the edge of the DM for this DM. At higher current densities, the temperature difference can even reach >10◦ C, which has a significant effect on the water balance and evaporator mass transfer. COMMENTS: The fraction of heat removed from the cathode side was arbitrarily chosen as 50% in this example to simplify the analysis. However, this need not be the case and depends on the geometry, materials, and operating conditions. Obviously, the DM thickness

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also plays an important role. In the PEFC, the DM behave like insulation on the catalyst layers, limiting heat transfer to the lands with relatively low thermal conductivity values. Mass Transfer Analogy It is obvious by comparison that there is a direct analogy between heat and mass transfer: Each has a developing region, each can be transported by direct molecular collision (conduction or diffusion), and each can be transported by fluid motion (convection). Indeed, Fourier’s law of heat conduction is mathematically identical to Fick’s law of diffusion.

= −k qth,i

∂T ∂ xi

n i

= −D

∂C ∂ xi

As discussed, the Prandtl number is the ratio analogous to the Nusselt number and is the dimensionless mass concentration gradient. The Schmidt number is the ratio of momentum and mass diffusivities: v Sc = (5.130) D AB Therefore, appropriate correlations for the mass transport in enclosed channels can be obtained by taking the relationships shown for heat transfer and replacing Nu with Sh and Pr with Sc and the temperature with the concentration. Radiation Heat Transfer Radiation is heat transfer resulting from the emission of photons or electromagnetic waves from matter undergoing molecular transitions. Unlike the transmission of heat by conduction or convection, radiation does not rely on intermolecular collisions and therefore can be transferred in a vacuum. This quality is particularly handy considering all life on Earth relies on radiation from the sun. Radiation is a complex subject that will only be briefly discussed here. For more detailed analysis, the reader is referred to undergraduate-level [50] and graduate-level [52] references. Radiation is only a significant mode of heat transfer for high-temperature fuel cells, such as molten carbonate and solid oxide fuel cells. For an enclosed body, the net radiation exchange between the surface of the body at absolute temperature Ts and the surroundings at absolute temperature T surr is   4 q

= εσ Ts4 − Tsurr (5.131) where ε is the surface emissivity, which is the fraction of radiative energy emitted (0 < ε < 1) and is different for every surface. For a perfect emitter, this value can be assumed to be 1. The σ is the Stefan–Boltzmann constant (σ = 5.67 × 10−8 W/m2 · K4 ). This expression assumes that the body of exchange has the same emissivity as the surface. Here, T surr is the surrounding temperature the body is exchanging radiation with, which is different from the ambient temperature. For example, consider a SOFC outer shell at 1000◦ C and inside surface of the surrounding at 700◦ C. As a first approximation, the radiation exchange between the surfaces can be estimated as12    

4 = 5.67 × 10−8 12734 − 9734 = 98 kW/m2 qrad = σ Ts4 − Tsurr 12 This

is only a basic estimation. For a better approximation, the spectral emission, reflection, and absorption surface properties of the materials involved need to be incorporated into the analysis.

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This relationship assumes a perfect emitter in a fully enclosed surroundings. This value can be compared to a typical natural convection current from the surface, with h ∼ 5 W/m2 · K,

= h (Ts − T∞ ) = 5 (1273 − 973) = 1.6 kW/m2 qconv

So radiation can be quite important, but only when there is a high temperature difference between the surface and surroundings, as is the case for high-temperature fuel cells such as the molten carbonate and solid oxide fuel cells. Heat Dissipation from Stacks In many high-temperature systems, the high rate of heat transfer and operating temperature and the need to maintain a safe external environment require thermal insulation around the unit. For high-temperature systems, it is often desirable to operate the power system as a combined heat and power (CHP) source. This practice is common for stationary power systems, not just fuel cells. In a CHP system, some of the waste heat from reaction is used for some other intentional service, such as providing heated water or powering a steam turbine. High-temperature fuel cell systems are well suited for CHP use due to their quality recoverable waste heat. In 1998, Siemens Westinghouse began operation of a 100-kWe SOFC unit in Westervoort, The Netherlands. The system was also designed as a CHP unit, to deliver 65 kWh to the residential district as heated water. This early demonstration unit was able to achieve a direct electrical conversion efficiency of 46% at 109 kWe. When the additional recovery of heat is included in the overall efficiency, the CHP system achieved a remarkable 73% average energy conversion efficiency. Many more advanced systems now are in operation that improve on this early prototype. In many high-power fuel cells, the heat dissipation is high enough that some cooling is needed. Many fuel cell systems have a small range of operational design temperature for a variety of reasons. In some liquid electrolyte fuel cells (e.g., an alkaline fuel cell), the electrolyte itself can be circulated through a heat exchanger and act as the coolant. In PEFC systems with a solid electrolyte, the material and need for humidification of the electrolyte limit operating temperature to below 100◦ C. To avoid a large thermal gradient and possible overheating in PEFC stacks, coolant channels are typically integrated with the overall stack design, as illustrated in Figure 5.43. The coolant used is typically water (which can freeze) or some other coolant such as ethylene glycol with resistance to freeze. The heat transfer from the bipolar stack plate to the coolant flow can be simply estimated by consideration of an energy balance on the fluid: Q˙ = m˙ coolant ccoolant (Tout − Tin )

(5.132)

This simple relationship, derived from a conservation of energy around the coolant flow in the steady state, can be used to estimate temperature rise in the coolant for a given condition or adjust the coolant flow rate to achieve a desired temperature gradient across the bipolar plate. Because the thermal mass of the bipolar plates is so much larger than the gas in the flow channels, the gas temperature will follow that of the bipolar plate at the inlet and through to the exit. Example 5.18 Determination of Coolant Flow Rate Required Consider a 100-plate, 10kWe PEFC stack operating at 48% thermal efficiency, as determined from a stack voltage measurement. Each individual fuel cell is to be cooled by a flowing liquid water coolant channel. In order to balance the water generated in the fuel cell and prevent flooding, it is

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275

E

C A G

B D F

A: B: C: D: E: F: G:

Air in Air out Coolant in Coolant out H2 in H2 out Active area

Flow chimney

Figure 5.43

Stack plates manifolded with coolant flow channels.

desired for the coolant temperature to increase 10◦ C from the inlet to the exit of the fuel cell. Solve for an expression relating the coolant mass flow rate to the desired temperature increase. From measurement of the gas channel temperature you can assume 80% of the waste heat is absorbed by the bipolar plates and flows into the coolant and the remaining 20% is removed by the gas flow. The specific heat of liquid water is 4.18 J/g · K. SOLUTION ηth =

At 48% thermal efficiency, the stack is generating waste heat:

Q˙ e Q˙ e (1 − ηth ) 0.52 = 10.83 kWh ⇒ Q˙ waste = ⇒ Q˙ waste = (10 kWe) ηth 0.48 Q˙ waste + Q˙ e

With 80% of this waste heat into the coolant and a 10◦ C temperature increase, from Eq. (5.132), (kWh) 8.67 0.8 Q˙ waste = m˙ coolant = (1000 W/kW) = 207 g/s ccoolant (Tout − Tin ) 4.18 (J/g · K) (10 K) If the flow rate were increased, the temperature rise of the coolant would be decreased. As the power output of the fuel cell increases, the coolant flow rate can be increased to match the rising waste heat output. COMMENTS: Much of this example has been simplified to emphasize the use of Eq. (5.132). In a full-size stack, there would be temperature gradients from plate to plate in the stack resulting from the external heat loss and differences in the individual performances of the fuel cells in the stack. Although the overall thermal efficiency is measured at 48%, individual fuel cells can be operating with very different voltages. In some cases, individual fuel cells may degrade significantly and generate excess heat.

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5.7

SUMMARY

Char Count=

In this chapter the transport of uncharged and charged species (ions and electrons) was discussed. For charged and uncharged species, transport by diffusion (concentration gradient driven) and convection (velocity field driven) occurs. The addition of a voltage gradient can cause motion of charged species by migration. The governing transport equation combining these modes is the Nernst–Planek equation: n˙

j,i = −D j,i

∂C j zjF ∂φ D j,i C j + C j vi − ∂ xi Ru T ∂ xi

For most fuel cells, the ohmic region is dominated by the electrolyte conductivity. For a PEFC, the conductivity is a strong function of water content, temperature, and polymer molecular weight. For the SOFC, the electrolyte conductivity is mostly a function of temperature and material additives and is not normally ionically conductive at all until an elevated light-off temperature is reached. For liquid electrolytes, the ionic conductivity is a function of many parameters, including electrolyte concentration, temperature, ion type, and ion charge. Electron transport in a fuel cell is typically not limiting, and only contact resistance between components contributes to any significant voltage loss. In Section 5.3, gas-phase transport, which occurs by both diffusion and convection, was discussed. The characteristic transport times of diffusive transport were shown as τ=

l2 D

The characteristic diffusion time for gases is orders of magnitude faster than for liquids or in polymers, which can lead to instabilities and transient variations in low-temperature PEFCs. Several different methods for the determination of gas-phase diffusion coefficients were discussed, the simplest being derived from molecular theory: Dj ∝

T 3/2 P · MW1/2 σ 2

While this relationship is commonly used and shows proper qualitative trends, it is not completely accurate for polar molecules such as water vapor. Methods for improved estimation of binary diffusion coefficient and diffusion coefficients in mixtures including nonpolar and polar molecules are presented and should be used when quantitative precision is required. Using purely gas-phase diffusion, an expression for the gas-phase diffusion limiting current density was derived: il = −nFDeff

C∞ yi P/Ru T = −nFDφ 1.5 δ δ

This expression can be used to see the qualitative relationships between the variables, but due to film resistances, especially in multiphase PEFCs, the actual limiting current density is much less than that predicted through this relationship. The relationship can be extended to include the effects of film resistances and different layers (e.g., catalyst layer resistance) as well. Film resistances from an electrolyte layer or liquid on the catalyst layer can be

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277

accounted for using Henry’s law yi,liquid/membrane side =

yi,gas side Pgas side H (T )

Henry’s constant H is a strong function of temperature for liquids. At a phase boundary, the concentration of the reactant is decreased in the liquid or solid phase according to Henry’s law and then must diffuse to the catalyst. Any small film resistance on the catalyst of liquid effectively floods the catalyst location, so that almost no reactant can reach the catalyst. For ionomer coverage of the catalyst in a PEFC, some reactant penetration is desired. Although a high reactant diffusivity in the catalyst layer electrolyte is beneficial to increase the mass transfer limiting current density, it is deleterious for reactant crossover discussed in Chapter 4, so that a proper engineering balance of ionomer content in the electrolyte is used. In very small pores, Knudsen diffusion, dominated by molecule–pore surface collisions, can play a role or even dominate. The Knudsen number (Kn) is a dimensionless parameter that can be used to determine the relative role of Knudsen flow: Kn =

kB T l =√ d 2π σii2 Pd

Ĺ When Kn > 10, Knudsen flow dominates. Ĺ When Kn < 0.01, bulk diffusion flow dominates. Ĺ For 0.01 < Kn < 10, both Knudsen and bulk diffusion are important, and transitional flow exists. For Knudsen flow, the effective diffusion coefficient can be determined from the kinetic theory of rigid spheres [18]: DKn =

  d 2k B T 1/2 3 MWi

(5.133)

The pore size diameters where Knudsen flow dominates are below 0.05 µm, which is below the normal pore size seen in fuel cells. However, Knudsen flow can play a role within the catalyst layers of many fuel cells, in parallel with normal diffusion processes. The pressure drop along flow channels in a fuel cell is governed by frictional pressure drop, reactant consumption, product uptake, and two-phase slugs or blockages in lowtemperature PEFCs. For low-stoichiometry flows, the consumption can dominate pressure drop along the flow field. Some fuel cell designs even feature a dead-end anode, where the consumption is used to draw the hydrogen into the fuel cell. In terms of transport, the developing boundary layer enhances transport of mass and heat and increases frictional losses. Many fuel cell designs have a significant portion of the flow field within the developing region, although fully developed flow is normally assumed in analysis. Multiphase flow in gas channels is characterized by different regimes. In PEFC flow channels, slug, annular, and mist flow can occur depending on the flow velocity. In porous media, the description of multiphase transport is more complex. The momentum equation reduces to Darcy’s law: Q=

−kkr A P µ L

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where the permeability k is a function of the saturation and intrinsic permeability of the porous media, which can be related to the Carman–Kozeny relationship: k=

r 2φ3 18τ (1 − φ)2

and kr , the relative permeability for a phase, is typically shown as kr,nw = A(snw )n

and

kr,w = B(1 − snw )m

for the wetting (w) and nonwetting (nw) phases. Although m and n vary, typical values are around 2.0–3.0 for fuel cell porous media in PEFCs. The driving force in Darcy flow is the capillary force, which can be written as Pc = Pnw − Pw =

2γ cos θ r

This relationship shows the critical role that pore size and surface tension have in controlling the capillary flow through porous media. The smaller the pore size, the higher the capillary pressure. This fact is responsible for driving liquid from small-pore-size areas to areas with larger pore sizes. However, the capillary pressure is not solely a function of pore size. It is also a function of the level of saturation in the media. In order to link the saturation, capillary pressure, and liquid flow in porous media, a Leverett function has been written such that
1/2 φ J (sl ) PC = γ cos θ k where the Leverett function J(sl ) is an empirical best curve fit of data measured for a variety of soils. Although this general approach has been adopted in fuel cell studies, the particular form of the Leverett function is not appropriate for fuel cell media and can lead to large errors in calculations. Newer, more appropriate functions according to PTFE content, compression, and temperature have now been derived. The modes of heat generation include Peltier heating, Joule heating, and activation heating, a result of entropy generation or reduction, ohmic losses, and activation or concentration losses, respectively. In most larger stacks, some active cooling is needed to remove waste heat and prevent excessive temperature gradients. In low-temperature fuel cells, this can be achieved using a recirculating liquid coolant. In higher temperature SOFC systems, the gas-phase reactant flow can be used to achieve a more uniform internal temperature profile. In systems with recirculating liquid coolant, heat can be removed from the coolant bath.

APPLICATION STUDY: COGENERATION FOR FUEL CELLS In a cogeneration power plant, the effective overall thermodynamic efficiency of the plant is increased by utilizing a portion of the waste heat generated by the power generation

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process, that is: ηeff =

work + heat utilized maximum energy output

Such systems based on conventional power generation technology have been used for stationary power or larger grid power systems, not only fuel cells. For instance, the waste heat generated by a gas turbine can be used to heat the water or provide steam heat for a building, eliminating the need for a separate heating system by using some of the thermal energy dissipated as waste heat for a useful purpose. For this assignment, do some research and answer the following: 1. Which types of fuel cell systems are well-suited for cogeneration? Explain why. 2. Go online and determine what are the current cogeneration concepts and or working fuel cell systems. There are many of them. Write a brief summary of the three of the concepts or systems you find to be the most interesting.

PROBLEMS Calculation/Short Answer Problems 5.1 Discuss the physical meaning of the terms in the Nernst-Plank Equation. 5.2 When would Ohm’s law be invalid for an electrolyte solution? 5.3 Make a plot of water viscosity versus temperature in the range of 300–400◦ C. By what percentage does the viscosity change over this range? Make a plot of the conductivity of Nafion with respect to temperature for fully hydrated conditions. Do you expect the trends in the two plots match? 5.4 Discuss the physical reason why the conductivity of the Nafion PEFC electrolyte changes with water content and EW. If you were to design an electrolyte for low humidity conditions, would you choose a high or low value of EW electrolyte? What would be the drawbacks of this choice? 5.5 Why is the Grotthuss mechanism of ion transport more rapid than the vehicular mode?

5.8 Calculate the expected voltage gain (from ohmic polarization recovery only) would you expect from increasing the average fuel cell temperature of an SOFC from 700 to 900◦ C at 1 A/cm2 . What would the practical disadvantages of this change be? Use the ionic and electrical conductivity of 8% mole fraction yttria given in the text. 5.9 List some ways an SOFC system could rapidly achieve light off temperature in practice. 5.10 Discuss the physical reasons why the temperature, ion concentration, viscosity, ion radius and charge number has an effect on the ionic conductivity of liquid electrolyte solutions. 5.11 At high water content, the electrolyte in a solid polymer electrolyte membrane such as Nafion behaves similarly to a dilute electrolyte solution. Do you expect the conductivity of the Nafion electrolyte to always increase with water content, or would there be a physical limit? 5.12 Calculate the thickness of a bipolar plate (σ e = 10,000 S/cm) that will match the voltage drop caused by proton flux through a Nafion electrolyte at 80◦ C, 100% RH.

5.6 Calculate the expected voltage gain (from ohmic polarization recovery only) would you expect from increasing the average fuel cell relative humidity from 40 to 60% in a Nafion 112 at 80◦ C, 1 A/cm2 . What would the practical disadvantages of this change be?

5.13 Develop an equation like Eq. (5.33) for water vapor in air, and water vapor in hydrogen. Onto what side of a fuel cell will the moisture more readily go into the gas phase?

5.7 A new electrolyte is developed that needs only 20% relative humidity at 90◦ C to achieve a maximum conductivity of 8 S/cm. What is the RH required for an equivalent Nafion system to achieve the same level of conductivity?

5.14 Make a plot of the diffusion coefficient of oxygen into water vapor versus porosity using the Bruggeman relationship. At what level of porosity is the flow 90% restricted compared to pure gas-phase flow?

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5.15 Estimate the ratio of the time required for oxygen to diffuse through the same length in the gas-phase and in water. 5.16 Compare the expected diffusion coefficient of oxygen and hydrogen using Eq. (5.31). 5.17 Calculate the oxygen and hydrogen gas-phase transport limiting current density in a hydrogen SOFC for the anode and cathode sides at 900◦ C, 1 atm pressure operation with fully humidified gas streams and high stoichiometry. Assume the anode and cathode catalyst layers are 50 and 100 µm thick, respectively and 50% porosity. 5.18 Calculate the oxygen and hydrogen gas-phase transport limiting current density in a hydrogen PEFC for the anode and cathode sides at 80◦ C, 1 atm pressure operation with fully humidified gas streams and high stoichiometry. Assume the anode and cathode diffusion layers are 300 µm thick, 70% porosity. Ignore the catalyst layer restriction in this problem. If the pressure were increased to 3 atm on both sides, what would be the effect on the limiting current density. 5.19 Redo problem 5.18, but this time include the effects of a 30 micron thick anode and cathode with 50% porosity. Is the catalyst layer resistance important? Hint: Assume the reaction occurs, on average, at the middle of the catalyst layers. 5.20 Consider the case of a hydrogen-fed PEM fuel cell at arbitrary P and T with a porous gas diffusion layer, with a hydrogen mole fraction of 0.4. (a) What is the effect of doubled total pressure on the limiting current density? (b) What is the effect of doubled temperature on the limiting current density? (c) What is the effect of doubled hydrogen mole fraction on the limiting current density? 5.21 We discussed in this chapter about the limitations of the simplified model for determination of limiting current density based on the gas-phase diffusivity. In particular, besides the diffusion media, there is also diffusion resistance in the catalyst layer, which is in series with the gas diffusion layer, and the effects of a thin Nafion or liquid layer on the catalyst. Assume the anode and cathode catalyst layer porosity is 0.5 and thickness is 20 µm. Consider a system with a thin layer of flooding and an ionomer on the catalyst. Consider the cathode only, at a normal operating temperature of 80◦ C, and a pressure of 15 psig. Assume the average mole fraction of the oxygen in the flow channel 0.12. Develop an expression for, and solve for, the mass

transfer limiting current density at the cathode. Consider the catalyst has a 1 nm Nafion coating, and a 0.5 nm liquid water coating, and the DM is 250 µm thick (porosity 0.7). The catalyst layer is 20 µm thick, with a porosity of 0.4. 5.22 Calculate the molar flow rate of hydrogen crossover into and through a 51 µm thick Nafion electrolyte. The anode is operating at 383 K and 1 atm pressure with a mole fraction of 0.6 hydrogen. Determine the mass transfer limiting hydrogen crossover current density from this value. 5.23 Find the Reynolds number at the inlet of a pure H2 anode for a single path serpentine fuel cell flow field under the following conditions. λa = 1.5, w square channel = 1.0 mm, T = 80◦ C, Pinlet = 202,560 Pa, i = 1 A/cm2 , Aelectrode = 50 cm2 , w is the channel width, and the channel has a square x-section, µH2 = 8.8 × 10−6 kg/m·s (a) Is it laminar or turbulent flow in the anode? (b) Will parallelizing the flow channels increase or decrease the Reynolds number? (c) Will parallelizing the flow channels increase or decrease the pressure drop? 5.24 For many calculations of heat and mass transfer, we neglect the entrance region and assume fully developed flow. At what path length L, in the flow field, will the flow in problem 5.23 part a above become fully developed? What is the effect of the entrance length on pressure drop in the flow channel – will it be greater or less than we expect if we neglect the entrance effects? 5.25 Make a plot of the frictional pressure drop versus channel length for a single 1 mm x 1 mm channel with 5 m/s fully humidified air flow. Assume fully developed flow. On the same plot, show the pressure drop from consumption along the flow path if the stoichiometry is 2.0 on the air cathode. 5.26 Compare the ratio of pressure drop on the anode to the cathode side for a hydrogen/air fuel cell. 5.27 Compare the ratio of entrance length on the anode to the cathode side for a hydrogen/air fuel cell at 353 K, 1 atm pressure. 5.28 Given a fuel cell with a 1 mm width x 0.5 mm depth channel size and a flow stoichiometry of 2.0 on the air cathode side. Plot the entrance length per unit length of the channel at 353 K, 1 atm as a function of current density.

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References 5.29 Make a plot of absolute permeability versus porosity for a 50 micron pore size using the Carman–Kozeny relationship. 5.30 Make a plot of the liquid permeability in a porous media as a function of liquid saturation, with arbitrarily chosen parameters besides saturation. On the same graph, plot the gas-phase permeability as a function of liquid saturation. 5.31 In Example 5.14, the capillary pressure was calculated by the Leverett approach for a hydrophobic diffusion media. In this problem, repeat Example 5.14 using the modified Leverett approach given in Eq. (5.104) for a DM with 5, 10, and 20% PTFE content at a liquid saturation of 0.4. (a) Determine the change in PC when contact angle is changed from 110 to 150◦ . Compare to the results using the original Leverett approach. (b) Determine the change in PC when the porosity is increased to 0.9. Compare to the results using the original Leverett approach. 5.32 Consider a 2 kWe solid oxide hydrogen–air fuel cell operating at 0.6 V. What value of effective heat transfer coefficient h, must the surface of the fuel cell stack have with the environment at 298 K to allow it to remain at 800 ◦ C in steady state? Consider that the heat in the effluent is completely recovered in a recuperator so that none leaves the fuel cell stack through the exhaust. 5.33 Using typical fuel cell parameters, solve for the expected ratio of conduction heat transfer through the lands to convective heat transfer through the channel gas on the anode and cathode sides of a PEFC at 80◦ C. Assume Re = 200 in the anode, 2000 in the cathode, and fully humidified gas flow at 1 atm. Would changing the pressure make a difference? Assume a channel-to-land ratio of 1:1. 5.34 Estimate the ratio of the heat dissipation by natural convection, forced convection, and radiation from a PEFC and SOFC stack.

281

5.35 Use the Wiedemann-Franz Law to relate the thermal conductivity of a known thermal conductor copper to the electrical conductivity of copper. Check your result versus published values. How close is the approximation? Now check the approximation on a known insulating solid such as a ceramic. Is the approximation close? 5.36 Looking at Table 5.14, what can you say about the probable relationship between PTFE content and electrical conductivity. Does this make sense? 5.37 It has been found that the thermal conductivity of a PTFE treated diffusion media decreases with compression. Given that compression will decrease the effective porosity of the diffusion media, this seems like the opposite of what we expect. Can you explain why this happens?

Computer Problem 5.38 Update your computer simulation of PEFCs from Chapter 4 to include film resistances on the electrodes, and heat generation by the various polarizations. Plot the polarization curve along with the heat generation from the various terms separately, and compare them for a typical PEFC parameters.

Open-Ended Problem 5.39 Fuel cell start-up from cold conditions is a common challenge. Considering the various different fuel cell systems and operating temperatures, there are a multitude of engineering challenges including a damage free-start-up, a rapid start-up, and an efficient start-up. Looking at two examples, the low temperature PEFC, and the high temperature SOFC, how, in general engineering terms, would you address these issues for these two systems? For example, what general engineering system parameters would lead you to a rapid start-up? What factors could cause damage?

REFERENCES 1. J. S. Newman, Electrochemical Systems, 2nd ed., Prentice Hall, Englewood Cliffs, NJ, 1991. 2. F. M. White, Fluid Mechanics, 4th ed., McGraw-Hill, New York, 1999. 3. M. Doyle and G. Rajendran, “Pefluorinated Membranes,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 351–395. 4. J. S. Wainright, M. H. Litt, and R. F. Savinell, “High-Temperature Membranes,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 436–446.

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Transport in Fuel Cell Systems 5. A. Z. Weber, and J. Newman, “Transport in Polymer-Electrolyte Membranes I. Physical Model,” J. Electrochem. Soc., Vol. 150, No. 7, pp. A1008–A1015, 2003. 6. C. Chuy, V. I. Basura, E. Simon, S. Holdcroft, J. Horsfall, and K. V. Lovell, “Electrochemical Characterization of Ethylene tetra flouroethylene-g-Polystyrenesulfonic acid solid polymer electrolytes,” J. Electrochem Soc., Vol. 147, pp. 4458–4453, 2000. 7. T. A. Zawodzinski, Jr., M. Neeman, L. O. Sillerud, and S. Gottesfeld, “Determination of Water Diffusion Coefficients in Perflourosulfonate Ionomeric Membranes,” Vol. 95, pp. 6040–6044, 1991. 8. M. Doyle, M. E. Lewittes, M. G. Roelofs, and S. A. Perusich, “Ionic Conductivity of Nonaqueous Solvent-Swollen Ionomer Membranes Based on Flourosulfonate, Flourocarboxylate, and Sulfonate Fixed Ion Groups,” J. Phys. Chem. B., Vol. 105, pp. 9387–9394, 2001. 9. F. N. Buchi and G. G. Scherer, “Investigation of the Transversal Water Profile in Nafion Membranes in Polymer Electrolyte Fuel Cells,” J. Electrochem Soc., Vol. 148, pp. A183–A188, 2001. 10. A. Z. Weber and J. Newman, “Transport in Polymer-Electrolyte Membranes,” J. Electrochem. Soc., Vol. 151, p. A311–A325, 2004. 11. J. T. Hinatsu, M. Mizuhata, and H. Tekenaka, “Water Uptake of Perfuorosulfonic Acid Membranes from Liquid Water and Water Vapor,” J. Electrochem. Soc., Vol. 141, p. 1493–1498, 1994. 12. T. E. Springer, T. A. Zawodzinski, and S. Gottesfeld, “Polymer Electrolyte Fuel Cell Model,” J. Electrochem. Soc., Vol. 138, pp. 2334–2342, 1991. 13. N. Minh and T. Takahashi, Science and Technology of Ceramic Fuel Cells, Elsevier, New York, 1995. 14. O. Yamamoto, “Low Temperature Electrolytes and Catalysts,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1002–1014. 15. C. H. Hamann, A. Hamnett, and W. Vielstich, Electrochemisty, Wiley-VCH, New York, 1998. 16. X. Li, Principles of Fuel Cells, Taylor and Francis, New York, 2006. 17. J. Larmine and A. Dicks, Fuel Cell Systems Explained, 2nd ed., Wiley, New York, 2003. 18. M. F. Mathias, J. Roth, J. Fleming, and W. Lehnert, “Diffusion Media Materials and Characterization,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 517–537. 19. E. L. Cussler, Diffusion-Mass Transfer in Fluid Systems, 2nd ed., Cambridge University Press, New York, p. 101, 1997. 20. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 3rd ed., Wiley, New York, 1995. 21. J. C. Slattery and R. B. Bird, “Calculation of the Diffusion Coefficient of Dilute Gases and of the Self-Diffusion Coefficient of Dense Gases,” AIChE J., Vol. 4, pp. 137–142, 1958. 22. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., Wiley, New York, 2002. 23. E. N. Fuller, P. D. Schettler, and J. C. Giddings, Ind. Eng. Chem., Vol. 58, p. 19, 1966. 24. H. S. Salem, and G. V. Chilingarian, “Influence of Porosity and Direction of Flow on Tortuosity in Unconsolidated Porous Media,” Energy Sources, Vol. 22, pp. 207–213, 2000. 25. H. T. Bach, B. A. Meyer, and D. G. Tuggle, “Role of Molecular Diffusion in the Theory of Gas Flow Through Crimped-Capillary Leaks,” J. Vacuum Sci. Technol. A: Vacuum, Surfaces, and Films, Vol. 21, No. 3, pp. 806–813, 2003.

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26. S. Srinivasan, A. Parthasarathy, A. J. Appleby, and C. R. Martin, “Temperature Dependence of R Interface a Microelectrode the Electrode Kinetics of Oxygen Reduction at the Platinum/Nafion Investigation,”J. Electrochem. Soc., Vol. 139, pp. 2530–2537, 1992. 27. Z. Ogumi, Z. Takehara, and S. Yoshizawa, “Gas Permeation in SPE Method,” J. Electrochem. Soc., Vol. 131, pp. 769–773, 1984. 28. D. Bernardi and M. W. Verbrugge, “A Mathematical Model of the Solid Polymer-Electrolyte Fuel,” J. Electrochem Soc., Vol. 139, pp. 2477–2491, 1992. 29. Y. A. C ¸ engel and M. A. Boles, Thermodynamics, an Engineering Approach, 4th ed., McGrawHill, New York, 2002. 30. D. M. Bernardi and M. W. Verbrugge, “Mathematical Model of a Gas Diffusion Electrode Bonded to a Polymer Electrolyte,” AICHE J., Vol. 37, pp. 1151–1163, 1991. 31. C. F. Colebrook, “Turbulent Flow in Pipes, with Particular Reference to the Transition Between the Smooth and Rough Pipe Laws,” J. Inst. Civ. Eng. Lond., Vol. 11, pp. 133–156, 1938/ 1939. 32. D. P. Wilkenson and O. Venderleeden, “Serpentine Flow Field Design,” in Handbook of Fuel Cells, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 315–324 33. Q. Dong, M. M. Mench, S. Cleghorn, and U. Beuscher, “Distributed Performance of Polymer Electrolyte Fuel Cells under Low-Humidity Conditions,” J. Electrochem. Soc., Vol. 152, pp. A2114–A2122, 2005. 34. G. W. Govier and K. Aziz, The Flow of Complex Mixtures in Pipes, Van Nostrand Reinhold, New York, 1972. 35. E. C. Kumbur, K. V. Sharp, and M. M. Mench, “Liquid Droplet Behavior and Instability in a Polymer Electrolyte Fuel Cell Flow Channel,” J. Power Sources, Vol. 161, p. 333, 2006. 36. A. Turhan, J. J. Kowal, K. Heller, J. Brenizer, and M. M. Mench, “Diffusion Media and Interfacial Effects on Fluid Storage and Transport in Fuel Cell Porous Media and Flow Channels,” ECS Trans., Vol. 3, No. 1, Proton Exchange Membrane Fuel Cells, Vol. 6, T. Fuller, C. Bock, S. Cleghorn, H. Gasteiger, T. Jarvi, M. Mathias, M. Murthy, T. Nguyen, V. Ramani, E. Stuve, T. Zawodzinski, Eds., pp. 435–444, 2006. 37. T. A. Corey, Mechanics of Immiscible Fluids in Porous Media, 1st ed., Water Resource Publications, Highlands Ranch, CO, 1994. 38. T. Young, Philos. Trans. Res. Soc., pp. 65–95, 1805. 39. J. H. Nam and M. Kaviany, “Effective Diffusivity and Water-Saturation Distribution in Single- and Two-Layer PEMFC Diffusion Medium,” Int. J. Heat and Mass Transfer. Vol. 46, pp. 4595–4611, 2003. 40. M. Honarpour, L. Koederitz, and A. H. Harvey, Relative Permeability of Petroleum Reservoirs, 1st ed., CRC Press, Boca Raton, FL, 1986. 41. J. Bear, Dynamics of Fluids in Porous Media, American Elsevier, New York, 1972. 42. E. C. Kumbur, K. V. Sharp, and M. M. Mench, “On the Effectiveness of the Leverett Approach to Describe Water Transport in Fuel Cell on the Diffusion Media” J. Power Sources, Vol. 172, pp. 816–830, 2007. 43. U. Pasaogullari, C. Y. Wang, and K. S. Chen, “Two-Phase Transport in Polymer Electrolyte Fuel Cells with Bilayer Cathode Gas Diffusion Media,” J. Electrochem. Soc., Vol. 152, pp. 1574–1582, 2005. 44. S. Litster, D. Sinton, and N. Djilali, “Ex situ Visualization Liquid Water Transport in PEM Fuel Cell Gas Diffusion Layers,” J. Power Sources, Vol. 154, pp. 95–105, 2006.

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Transport in Fuel Cell Systems 45. K. S. Udell, “Heat Transfer in Porous Media Considering Phase Change and Capillarity—the Heat Pipe Effect,” Int. J. Heat Mass Transfer, Vol. 28, pp. 485–495, 1985. 46. M. C. Leverett, “Capillary Behavior in Porous Solids,” Am. Inst. Mining Met. Eng. Petroleum Dev. Technol., pp. 142–152, 1994. 47. E. C. Kumbar, K. V. Sharp, and M. M. Mench, “A Validated Leverett Approach to Multiphase Flow in Polymer Electrolyte Fuel Cell Diffusion Media: Part 3, Temperature Effect and Unified Approach,” J. Electrochem. Soc., Vol. 154, pp. B1315–B1324, 2007. 48. E. C. Kumbar, K. V. Sharp, and M. M. Mench, “A Validated Leverett Approach to Multiphase Flow in Polymer Electrolyte Fuel Cell Diffusion Media: Part 1, Hydrophobicity Effect,” J. Electrochem. Soc., Vol. 154, pp. B1295–B1304, 2007. 49. M. Khandelwal, and M. M. Mench, “Direct Measurement of Through-Plane Thermal Conductivity and Contact Resistance in Fuel Cell Materials,” J. Power Sources, Vol. 161, pp. 1106–1115, 2006. 50. F. P. Incropera and D. P. De Witt, Fundamentals of Heat and Mass Transfer, 3rd ed., Wiley, New York, 1990. 51. W. M. Kays and M. E. Crawford, Convection Heat and Mass Transfer, McGraw-Hill, New York, 1980. 52. M. F. Modest, Radiative Heat Transfer, 2nd ed., Academic, New York, 2003.

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Fuel Cell Engines Matthew M. Mench

6

Copyright © 2008 by John Wiley & Sons, Inc.

Polymer Electrolyte Fuel Cells Market forces, greenery, and innovation are shaping the future of our industry and propelling us inexorably towards hydrogen energy. Those who don’t pursue it . . . will rue it —Frank Ingriselli, President, Texaco Technology Ventures, April 23, 2001

Throughout this textbook, the PEFC has been emphasized because it is a likely candidate for power replacement for portable, auxiliary, stationary, and automotive power systems. As shown in Figure 6.1, the PEFC class of fuel cells includes the hydrogen, direct methanol, direct alcohol, and other fuel cell systems utilizing a solid polymer electrolyte. While the higher temperature molten carbonate and solid oxide fuel cell systems are well-suited for steady power systems, only the low-temperature PEFC offers the rapid startup and lower operating temperatures (20–90◦ C) required for transient operation of portable, reserve, and automotive power applications.

6.1 HYDROGEN PEFC The primary advantages of the hydrogen PEFC system compared to other fuel cell systems include the following: 1. High relative performance: H2 PEFCs can reach >1.3 kW/L fuel cell power density, >0.6 kW/L system power density, and >0.6 kW/kg mass specific power density. 2. Low-temperature operation: H2 PEFCs can start and operate in subfreezing temperature, although normal operating temperatures are 20–90◦ C. 3. Facile anode kinetics for the HOR: As a result, H2 PEFCs have the lowest precious metal loadings of all the PEFC types (typically 0.2–0.8 mg/cm2 total active area; i.e. anode plus cathode). However, the H2 PEFC has many complex technical issues that have no simple solution. Besides issues of manufacturing, ancillary system components, control, cost, and market acceptance not treated in this text, the main technical design issues for the H2 PEFC system include the following: 1. Water and Heat Management Due to the low-temperature operation of PEFCs, the water generated by reaction often condenses into liquid phase, flooding parts 285

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Polymer electrolyte fuel cell

Hydrogen fuel cell (H2 PEFC)

Direct alcohol fuel cell (DAFC) Direct methanol fuel cell (DMFC)

Figure 6.1

2.

3.

4.

5. 6.

6.1.1

Subclassifications of PEFCs.

of the electrodes, DM, and flow channels. At a typical operating temperature of 80◦ C, the saturation pressure of water changes by almost 5% for every 1◦ C change at 1 atm. Therefore, the two-phase flow and heat generation are inexorably linked for all situations but very low power (<∼0.2 A/cm2 ), where isothermal conditions can be assumed. The presence of liquid water or hot spots in the fuel cell can also negatively impact lifetime durability and should be minimized. Durability The performance of every fuel cell gradually degrades with time due to a variety of phenomena. The year 2005 U.S. Department of Energy goals for longevity of fuel cell systems are given in Table 6.1. The automotive fuel cell must withstand load cycling and freeze–thaw environmental swings with an acceptable level of degradation from the beginning-of-lifetime (BOL) performance over a lifetime of 5000 h (equivalent to 150,000 miles at 30 mph). A stationary fuel cell must withstand over 40,000 h of steady operation under vastly changing external temperature conditions. Durability here also refers to tolerance to a variety of environmental poisons that can harm performance. Manifolding and Stack Design The flow to each fuel cell within the stack should be uniformly distributed to avoid performance degradation, which is a particularly challenging aspect of design for a fuel cell with multiphase flow. Materials There is a strong interaction between the material choices, fuel cell design, durability, and water/heat management for all fuel cell components, including bipolar plates, DM, seals, catalysts, and electrolytes. Achieving Higher Efficiency and System Power Density As in any power source, there is a continual need to achieve a smaller system profile with better efficiency. Dynamic Performance and Rapid Power Availability Compared to higher temperature fuel cell systems, the startup time to full power of the PEFC is rapid, but nearly immediate response from all ambient conditions is desired.

Components and Materials of PEFC Recall the general components of a PEFC shown in Figure 6.2. The fuel and oxidizer flow through the flow fields, diffuse through the thin (∼200–400-µm) porous diffusion media (DM) [also known as a gas diffusion layer (GDL) or porous transport layer (PTL)] and to the ∼5–20-µm-thick porous catalyst layers.

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Table 6.1 Department of Energy Goals for Fuel Cell Systems and Durability Automotive Scale: 80 kWe (Fuel Cell System, Net)

Units % s s

2005 Status

2010 Goal

2015 Goal

50 1.5 120

50 1 30

50 1 30

−20 470 500 1000 110

−40 650 650 5000 45

−40 650 650 5000 30

Efficiency at rated power Transient response time (10–90% rated power) Cold startup time (to 50% rated power) from −20◦ C Unassisted start Specific power (system) Power density (system) Durability with load cycling Cost

◦ C W/kg W/L h $/kWe

Auxiliary Power: 3–5 kWe (Fuel Cell System, Net)a

Units

2005 Status

2010 Goal

2015 Goal

Efficiency at rated power Specific power Power density Durability Cost

% W/kg W/L h $/kWe

15 50 50 100 >2000

35 100 100 20,000 400

40 100 100 35,000 400

Stationary Scale: 250 kWe (Fuel Cell System, Net)

Units

2005 Status

2011 Goal

32 75 <3 <90

40 80 <3 <30

Efficiency at rated power Combined heat and power efficiency Transient response time (10–90% rated power) Cold startup time (to 50% rated power) from −20◦ C Survivability (min/max ambient temperature) Noise output Durability <10% rated power loss Cost

% % s s ◦ C dB h $/kWe

−25/40 >65 at 10 m 20,000 2,500

−35/40 >55 at 10 m 40,000 750

Consumer Electronics: subwatts – 50 W (Fuel Cell System, Net)

Units

2005 Status

2010 Goal

Specific power (system) Power density (system) Energy density Lifetime Cost

W/kg W/L Wh/L h $/kWe

20 20 300 >500 40

100 100 1000 5000 3

a Based

on SOFC systems, not PEFCs. Source: From [1].

As shown in Figure 6.2, the PEFC consists of the following basic materials: 1. Solid polymer electrolyte 2. Catalyst layers (anode and cathode)

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Figure 6.2 Schematic of typical H2 PEFC and its components.

3. Diffusion media, usually including a microporous layer 4. Bipolar plates with flow channels for reactants and coolant in larger stacks Solid Polymer Electrolyte The most common solid polymer electrolytes consist of a hydrophobic and inert polymer backbone which is sulfonated with hydrophilic acid clusters to provide adequate conductivity as discussed in Chapter 5. In order to ensure adequate performance, some membrane hydration is required. However, excess water in the electrodes can result in electrode flooding, so that a precarious balance must be achieved. Modern perflourosulfonated ionomer electrolytes for H2 PEFCs are 18–25 µm thick with a practical operating temperature limit of 120◦ C, although PEFC operation is rarely greater than 90◦ C due to excessive humidity requirements and operational low lifetimes. Catalyst Layer Catalyst layers (CLs) in PEFCs consist of a porous, three-dimensional structure, with a thickness of 5–30 µm (see Figure 6.3). For supported CLs, the 2–10-nm catalyst is physically supported on considerably larger, 45–90-nm carbon particles. As discussed in Chapter 2, the CL is the most complex structure in the PEFC. It must have facile transport of ions, electrons, reactants, and products with a high electrochemically

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Figure 6.3 Transmission electron micrograph (TEM) of 40 wt% platium/chrominum catalyst on carbon support. (Reproduced with permission from [2].)

active surface area (ECSA), where the reactants, catalyst, proton, and electron conduction are all available. To facilitate these requirements, the CL is highly porous (typical porosity 0.4–0.6), with a high connectivity in the carbon and catalyst particles to promote electrical conduction. The CL typically contains a considerable fraction of ionomer (up to ∼30% by weight) to promote ionic transport to/from the main electrolyte membrane. The CL normally has some fraction of polytetrafluouroethylene (PTFE) additive as well to promote water removal. However, like the DM, it is not totally hydrophobic because the basic components besides PTFE are hydrophilic. Therefore, the CL consists of a mixed network of hydrophobic and hydrophilic surfaces. To manufacture the CL structure, several techniques are employed and summarized briefly here: 1. Physical Spray Deposition on DM or Electrolyte Surface In this method, a slurry of catalyst, support, PTFE, solubilized polymer ionomer, and alcohol compounds (to

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Catalyst slurry

Doctor blade Catalyst layer Electrolyte

Figure 6.4 Tape casting technique for catalyst layer preparation.

tailor the slurry viscosity) are sprayed directly onto the DM or electrolyte surface. The spray can be applied by a simple nozzle or via electrodeposition, sputter deposition, or other techniques [3]. The slurry is then held at high temperature in an oven to evaporate the remaining alcohols. This method has the advantage of being relatively rapid, but tolerances are not precise compared to other methods. 2. Slurry Tape Casting In this method, a slurry or catalyst layer ink similar to that used in the spray deposition technique is spread onto the DM or directly onto the electrolyte via a doctor blade (Figure 6.4). This method produces high dimensional tolerance but is slower than physical spray deposition and less suitable for mass production. 3. Decal Method In this technique, thin CLs are cast or spread onto a nonadhesive medium, and decal transferred onto an electrolyte by hot-press compression (similar to a clothes iron). This method is suitable for mass production of catalyst layers, with high tolerance and batch processing capability, although the physical bond between the electrode and the electrolyte must be carefully maintained. Diffusion Media The diffusion media (DM) consists of a carbon fiber or woven cloth macroporous layer and possibly a highly hydrophobic microporous layer (MPL) that we will treat separately in this text. The flexible DM is a critical component in the PEFC and was originally developed to enable better electrical contact between the catalyst layer and lands but really serves four primary functions: 1. To provide electron conduction to and from the catalyst layer. The through- and in-plane electron resistivity varies with DM type and PTFE content but has been measured to be around 0.08
· cm and between 0.055 and 0.009
· cm, respectively [4]. 2. To provide reactant transport to and product removal from the catalyst layer. A DM has a typical porosity of 0.7–0.8 and gas-phase permeability of 5–55 Darcys [4]. 3. To provide heat transport from the catalyst layer to the current collector. The throughplane thermal conductivity of cloth and paper DM varies with PTFE content but has been measured to be between 0.2 and 1.8 W/m · K [5]. At this level it acts as a thermal insulation on the catalyst layer. 4. To provide mechanical support for the electrolyte structure and avoid tenting into the channels, which results in poor catalyst–DM conductivity, elevated channel pressure drop, catalyst layer damage, and local water pooling.

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Figure 6.5 SEM of nonwoven fiber paper and woven carbon cloth DM structure: (a) nonwoven fiber; (b) woven carbon cloth. (Image by Soowhan Kim, Penn State Fuel Cell Dynamics and Diagnostics Laboratory.)

The DM consists of a woven carbon cloth or a nonwoven fiber paper or felt structure held in a carbonized resin binder to provide good electrical conductivity. In the paper DM, the resin may have a distribution of very small pores that can also contribute to flow. Figure 6.5 shows pictures of nonwoven carbon paper and a woven carbon cloth from scanning electron microscopy (SEM), respectively. Carbon cloth materials are manufactured using weaving technology from the textile industry [4] while carbon paper products are manufactured using technology similar to that used to manufacture paper products. The cloth DM are as flexible as any textile, but the paper DM are fairly brittle due to the presence of thermoset polymer resin and can easily be broken under strain. The webbing seen in the SEM of the nonwoven paper is not PTFE, but the carbonized resin used to bond the paper fiber together. Some common properties of various DM are given in Table 6.2. As discussed, the basic carbon fiber in the DM is hydrophilic and thus will spontaneously imbibe liquid water into the porous structure. Because this results in flooding in H2 PEFCs, a hydrophobic additive, typically PTFE (TeflonTM ), is added to prevent pore blockage and manage internal water distribution. At the DM surface, the net effect of the PTFE additive and surface roughness is a generally hydrophobic surface contact angle, at least from a macroscopic perspective, as shown in Figure 6.6. Since the base carbon fiber material is hydrophilic, however, the resulting PTFE-treated DM structure is really a mixed hydrophobic–hydrophilic structure with channels favoring gas-phase and liquid phase transport, despite the overall hydrophobic surface behavior. Diffusion Media Compression During assembly, the fuel cell is compressed and the DM material is deformed under compressive strain. Generally, cloth DM are more compressible than paper DM, but both materials suffer irreversible strain of 5–20% upon release from the high compression pressure of 2.75 MPa [4]. Although this compression pressure is relatively high, significant residual strain has also been observed at normal compression pressures of 1–2 MPa. Due to the strain, the initial, uncompressed porosity is decreased under the lands to a compressed value. Assuming all of the compression is a result of lost

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Polymer Electrolyte Fuel Cells Table 6.2 Typical Properties of Commonly Used Diffusion Media Property

Cloth Value

Paper Value

Thickness Porosity In-plane gas-phase permeabilitya Through-plane gas-phase permeabilitya In-plane electrical conductivity Through-plane specific electrical resistancea PTFE content (by wt %, typical)

250–450 µm 0.7–0.9 10−12 –10−11 m2 10−14 –10−12 m2 100–200 S/cm 15–30 m
· cm2 5–30%

175–400 µm 0.7–0.9 10−12 –10−11 m2 10−14 –10−12 m2 50–200 S/cm 5–20 m
· cm2 5–30%

a Values

depend on PTFE content and compression.

pore volume (i.e., the carbon fibers and resin or other additives are incompressible), an expression for the effective compressed porosity can be derived as φ eff = 1 −

1−φ 1−δ

(6.1)

where δ is the fractional strain on the DM material under compression, δ=

t − t∗ t

(6.2)

and t is the uncompressed and t* the compressed DM thicknesses, respectively. A normal range of strain on the DM is 10–20% at 1.5–2 MPa compression pressure.

Figure 6.6 Water droplet on hydrophobic paper DM structure. (Image by E. C. Kumbur, Penn State Fuel Cell Dynamics and Diagnostics Laboratory.)

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Example 6.1 Typical DM Compressed Porosity Values Calculate a typical range of compressed DM porosity and the effect on the effective gas-phase diffusivity through the compressed media. SOLUTION From Table 6.2, we see a normal uncompressed porosity is around 0.8. Then, assuming the compressed strain is 10–20% on the DM, from Eq. (6.1), we can calculate φ eff = 1 −

0.2 1−φ =1− = 0.75δ=0.2 , 0.78δ=0.1 1−δ 1 − δ0.1−0.2

Assuming a Bruggeman correlation is appropriate, the fractional gas-phase diffusivity change for the case of 20% strain is eff Dcompressed eff Duncompressed

=

1.5 Dφcomp 1.5 Dφuncomp

=

0.75 = 0.94 0.80

So the gas-phase diffusivity under the lands in a compressed DM is retarded by around 6–7% compared to uncompressed values. COMMENTS: We could extend this analysis to look at the effect of strain on the mass transfer limiting current density and a variety of other effects. One relevant question regarding treatment of the compressive strain is whether or not to consider the compression uniform over the surface of the DM or only under the lands. There is likely to be some strain experienced by the entire DM material, not just under the lands, although when viewed under a microscope, it is clear that brittle paper DM suffer plastic, irreversible damage upon high compression so that the strain is not uniform over the whole area. Cloth DM are typically more pliant and suffer greater strain under similar compression pressure, so strain transmission under the channels is less prevalent for these structures. Another effect of compressive strain is on the capillary flow of liquid. We know from Chapter 5 that, as the pore radius decreases in a hydrophobic media, the capillary pressure increases. Therefore, for the same level of saturation, water in strained DM under the lands will have a higher capillary pressure and tend to flow lateraly into the channels. Microporous Layer The addition of a thin (∼5–20-µm-thick), highly dense MPL with pore sizes of 100–500 nm is commonly used to help water management. There are two basic types of MPLs employed, as illustrated in Figure 6.7. The slurry-based MPL consists of (5–20 %) carbon particles, polymeric binder, and 5–20 % PTFE that is applied to the catalyst side of the DM surface. The other type of MPL is a porous polymer sheet bonded to the outer surface of the catalyst layer. The MPL can be physically bonded to the catalyst layer or DM inner surface but resides between the catalyst layer and the DM. The MPL was originally designed to provide improved electrical conductivity between the catalyst layer and DM but has since become used primarily to aid in water management for hydrogen and DAFCs. The MPL structure is highly hydrophobic, and its role in water balance is discussed in detail later in this chapter. The slurry-based MPL is manufactured in a similar manner to the catalyst layer. In fact, some MPLs have catalyst in them to help improve performance. The MPL also functions to protect the catalyst layer from carbon fiber intrusion damage from the DM.

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Figure 6.7 Schematic of microporous layers used to enhance water management in PEFCs: (a) slurry-based MPL consists of carbon particles, polymeric binder, and PTFE that is applied to the catalyst side of DM surface; (b) porous polymer sheet bonded to outer surface of catalyst layer.

Bipolar Plate/Flow Field The bipolar plate materials and manufacturing techniques used are also a subject of intense development. The bipolar plate requirements were described in Chapter 2. Some stack developers and laboratory-scale fuel cells utilize a polymer-sealed high-conductivity graphite material. The polymer sealing is used to ensure the normally porous graphite is impermeable to water. For high power density, low weight, and robust stack design, however, metallic plates are needed. Where graphite flow plates can be as thin as 2 mm, a stamped metal plate can be almost an order of magnitude thinner, stronger, inexpensive, and much more manufacturable. The technical difficulties with metal bipolar plates include difficulty scaling and corrosion, which results in rapid electrolyte degradation and poor electrical contact resistance.

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6.1.2 System Components and Subsystems Within the overall system, the hydrogen fuel cell may occupy considerably less than 50% of the system volume. The overall hydrogen fuel cell system includes the following subsystems and control tasks, as illustrated in Figure 6.8: 1. Reactant Storage, Delivery, and Recycling This includes the pumps and blowers required to supply the stack with prescribed flow rates of fuel and oxidizer and to recycle unused fuel back into the anode inlet stream. Typically only fuel storage and recycling are needed as air is used as the oxidant. 2. Humidification This system is responsible for humidification of the flow of reactants, as described in the following section. Some systems (especially portable designs) are designed to be passively humidified and eliminate this subsystem completely at the expense of reduced performance. 3. Cooling Smaller, low-power portable systems can be passively cooled or even require insulation. However, systems larger than 1 kWe power typically require active liquid cooling of the stack to remain within membrane material tolerances and achieve uniform performance. The choice of coolant is an active area of research. Distilled water can be used but will freeze at subzero temperatures. Ethylene glycol (EG) is the coolant of choice for contemporary automotive applications and can

U6 Traction motor control

TM

Power management U5

U4 Humidity control

Power conditioning

Energy storage (battery)

U3 Temperature control

U1 Hydrogen flow control S Hydrogen tank U2 Air flow control Motor Compressor

Humidifier

Backpressure valve

Fuel cell stack

Water separator Water tank

Figure 6.8 Schematic of typical hydrogen PEFC system and control tasks. (Courtesy of Manish Sinha of General Motors.)

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operate at subzero temperatures, but contact of EG with the electrolyte can cause irreversible damage. 4. Hydrogen Reformation If a liquid hydrocarbon or alcohol fuel is reformed to provide the hydrogen gas, a hydrogen generation system is required. The reformation process is described in greater detail in Chapter 8. For stationary systems, a fuel reformer is often used. For automotive or portable applications, on-board reformation is typically avoided due to excessive complexity, cost, and transient control limitations. 5. Power Conditioning and Control The power from a fuel cell stack is in the form of direct current (DC) which must normally be inverted to AC and conditioned into a suitable voltage range to power most electric motors and equipment. The fuel cell control system is quite complex and is responsible for all system monitoring and maintaining stable and safe operation though feedback from a variety of flow, pressure, voltage, current, and temperature sensors, as illustrated in Figure 6.8. 6. Startup Power Systems Fuel cells normally need some external power input to assist startup. An auxiliary high-power battery to run pumps and heaters during startup or to provide power to overcome voltage transients and reversals in the fuel cell stack is often used. System Humidification A natural question for a student to ask is: Why do we need to humidify the PEFC at all? After all, it is a net water generation device, and yet so much of the design is ultimately meant to remove water from the cell. Since the fuel cell has a precarious balance between a moist electrolyte needed for high ionic conductivity and a flooded cell that degrades performance, it is entirely possible that some sections of the same fuel cell or individual plates in a stack will be overly dry and other sections in the cell or different plates in a stack will be flooded. Because of this, some humidification is typically needed at the inlet of the fuel cell to ensure adequate performance. Additionaly, strong humidity gradients in the electrolyte can result in internal stresses that limit durability. Humidification is accomplished by two main approaches, passive and direct humidification. In passive humidification, the water generated by reaction is used to maintain a proper moisture balance and humidify the incoming flow without external power. In active humidification, a separate humidifier is used to directly provide the humidification of the incoming flow with stored or recycled water. Methods of Active Humidification Active humidification requires a discrete, external humidification system. In a laboratory environment, a sparge-type humidifier, as illustrated in Figure 6.9, is often used. In this system, gas is sparged through a porous rock and into heated water to absorb moisture before entering the fuel cell. This system is not useful outside the laboratory because it is dependent on orientation and almost never 100% efficient. Care must be used to ensure proper humidification is achieved and careful calibration is neccessary. In a membrane humidification system, dry air is forced through a moist membrane with small pores to absorb moisture. The membrane humidification system can have very high efficiency but also has a higher pressure drop compared to sparge systems. A third type of

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Figure 6.9

Hydrogen PEFC

297

Schematic of sparge-type laboratory humidifier.

active humidification is direct injection of liquid droplets (Figure 6.10). This technology is based on gasoline injection systems. Additional advantages of this approach are that the liquid added to the flow is precisely metered, and the energy required to evaporate the droplets can be used to cool the flow. This can be especially useful in pressurized systems where flow from the compressor can be at significantly elevated temperature. Methods of Passive Humidification Because the humidification system is an additional complexity and the fuel cell itself is a net water producer, there is a tremendous potential to develop passive humidification systems that eliminate parasitic humidification altogether. One such method of passive humidification is the use of an external membrane to absorb and transfer moisture from the cathode effluent, as illustrated in Figure 6.11. At the exit, an absorbent membrane captures the water through condensation on the cooler surface, and a concentration gradient between the dry inlet flow and wet effluent produces a net flux into the inlet flow, recirculating the product moisture. This approach can also be adapted for larger stacks by filtering condensate water into a central condensation collection plenum, and then used to supply a membrane humidifier, or by exchanging the exit water through a membrane to directly humidify incoming flow, so humidifier water refilling is unnecessary. Water can also be internally recirculated, as shown in Figure 6.12, with the use of a counterflow arrangement. Although the net water generated that must ultimately be removed from the stack is the same, a counterflow arrangement facilitates transport of water from the wet cathode exit, through the electrolyte, to the dry anode inlet. Similarly, at the anode exit, the moisture balance is reversed, and diffusion drives the flow of moisture toward

Water in Figure 6.10

Injection pump

Injector

Schematic of direct injection humidification system.

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Atmospheric air in Inlet air getting warmer and more humid To atmosphere

Outgoing air cooling and losing water

Membrane Humidified product gas from fuel cell

Figure 6.11 Passive humidification with external water recirculation. This system can be used to recycle water produced by fuel cell stack into incoming fuel or oxidizer stream, eliminating need for separate water storage container.

the cathode. This internal recirculation through a counterflow arrangement is utilized on many portable applications to eliminate the humidifier and on larger systems to reduce the humidification load required. The high humidity gradients are not generally suitable for long-term use, however. In another novel method of internal humidification, originally proposed by Watanabe et al. [6], platinum particles are embedded into the main electrolyte. The crossover hydrogen and oxygen react on these surfaces, generating water and maintaining membrane hydration despite low external humidity, as illustrated in Figure 6.13. This has the added benefit of converting crossover gases into water before reaction on the electrodes. A variation of this concept has been used in an attempt to generate higher temperature membrane materials by using a water-absorbent additive such as SiO2 to the perflourinated membrane material, so that it retains moisture in a higher operating temperature membrane [7]. Various composite membrane technologies have had some success in achieving a higher conductivity in lowhumidity environments.

6.2

WATER BALANCE IN PEFC A key element in PEFC performance is the water balance. There is a complex relationship between moisture content and performance in PEFCs. For high ionic conductivity, the polymer electrolyte membrane must have high moisture content [8]. However, as discussed in Chapter 5, liquid accumulation can restrict reactant availability at the electrode,

Figure 6.12 Passive humidification with internal water recirculation. This counterflow configuration is used for portable and underhumidified arrangements.

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Figure 6.13 Passive humidification via internal membrane water generation from embedded platinum particles.

resulting in performance loss. Performance loss resulting from liquid water accumulation is generically referred to as flooding. More specifically, flooding can occur as a discrete event in the anode or cathode catalyst layers, DM, or flow channels, as illustrated in Figure 6.14. At low current, anode and cathode side-channel level flooding from slug blockage has been observed [9] as a result of the inability to remove slugs from the

Figure 6.14 Schematic of possible locations of flooding in PEFC including catalyst layer, diffusion media, and channel level flooding.

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Figure 6.15 Schematic of complex interactions among fuel cell design, material, and operational parameters that influence water distribution and flooding behavior. Flooding interactions and behavior are not yet a complete science.

channels at low channel velocities. At higher current densities, where the gas-phase flow in the channels is sufficiently high to remove most slug formations, flooding is more likely to occur in the cathode catalyst layer or DM. Flooding can be a result of channel design, operating conditions, or material properties. In fact, a complex interaction between many design, operational, and material parameters exists, as summarized in Figure 6.15. A fuel cell that floods at a given condition may not flood with slightly different operating conditions, a different DM or microporous layer, or a modification to the channel design. A fuel cell polarization curve, with and without flooding losses, is shown in Figure 6.16. In this figure, a polarization curve for a single 50-cm2 fuel cell was taken at 80◦ C, where significant flooding losses were observed at 1.5 A/cm2 . From this point, the operating temperature of the fuel cell was increased to 85◦ C to eliminate the flooding. The performance at 80◦ C was 141 mV lower than at 85◦ C, where more of the water was vaporized. The flooded cell had a total of 381 mg (∼7.6 mg/cm2 ) of liquid water, while the dry cell had only 206 mg (∼4 mg/cm2 ) of liquid water [10]. A side-by-side comparison of the liquid water distribution in this fuel cell is shown in Figure 6.17. Interestingly, a significant amount of water exists even in a nonflooded state, stored in the pores of the DM, electrolyte, and catalyst layer and in the channels. The difference of only a few milligrams of water per square centimeter active area can have a significant impact of performance [10]. From a study of flooding and water content, it has been deduced that simple pore flooding blockage in the DM is not alone responsible for the voltage drop seen, and some film resistance is required to account for the observed voltage loss.

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Figure 6.16 Polarization curve for PEFC with and without flooding losses; the only difference in the operating conditions is the fuel cell temperature. Between 80 and 85◦ C, there is 115 mV difference in performance directly attributable to flooding. (Adapted from Ref. [10].)

Figure 6.17 Side-by-side comparison of (a) flooded and (b) unflooded liquid water distribution. Images are taken using neutron imaging technology. The brighter areas represent liquid water accumulations. Upon close inspection, the flow pattern in the fuel cell is visible. This is a result of accumulation of liquid water under the lands, where there is typically a high liquid saturation. (Adapted from Ref. [10].)

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Overall Water Balance: Fuel Cell Mass Balance Although flooding is a localized phenomenon, for a fuel cell to operate at steady state, an overall state of water balance must be achieved. Consider a control volume mass balance of the water in a single fuel cell, illustrated in Figure 6.18. From a conservation of mass on the water, we can show that
dm

= (m˙ in − m˙ out )H2 O,anode + (m˙ in − m˙ out )H2 O,cathode + m˙ gen (6.3) dt
cv The term on the left-hand side of Eq. (6.3) represents the time rate of change in the water mass in the fuel cell. The two sets of terms in parentheses on the right-hand side of Eq. (6.3) represent the net water flow out of the fuel cell on the anode and cathode, respectively. The generation rate of water (from Faraday’s law) is given as m˙ gen =

iA MWH2 O 2F

(6.4)

Therefore, to achieve water balance in steady state, (m˙ out − m˙ in )H2 O,a + (m˙ out − m˙ in )H2 O,c =

iA MWH2 O 2F

(6.5)

In terms of the steady-state molar mass balance, (n˙ out − n˙ in )H2 O,a + (n˙ out − n˙ in )H2 O,c =

iA 2F

(6.6)

The net outlet flow can contain slugs of liquid, flow of capillary films into the manifold and humidified gas, that is,     (6.7) n˙ out,H2 O = n˙ out,a + n˙ out,c liquid + n˙ out,a + n˙ out,c gas If we assume the slugs and capillary flow of liquid water at the exit are insignificant (which may not be the case in a flooded condition), we can solve for the steady-state water balance.

Anode in Cathode in

Anode out

Cathode out

CV

Figure 6.18 Basic control volume of fuel cell.

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From the material in Chapter 3, we can derive an expression for water vapor carried by the flow: Pv yH2 O P = Psat (T ) Psat (T ) n v,H2 O n˙ v,H2 O = yv,H2 O P = P= P n˙ v,H2 O + n˙ others n v,H2 O + n others

RH = Pv,H2 O

(6.8) (6.9)

where n˙ others represents the molar flow rate of anything but vapor (reactant and inert gas) and P is the total gas-phase pressure. For the incoming flow, n˙ others,in =

λreactant,in i A yreactant,in,dry n F

(6.10)

Here, yreactant,in,dry is the mole fraction of reactant in the incoming flow on a dry, nonhumidified basis. For air, yO2 ,in,dry = 0.21. After humidification, the mole fraction of oxygen in the air will be something less, but the dry value is used in Eq. (6.10). The consumption of reactant is simply iA/nF. If we neglect the crossover and leakage, which are typically small relative to the overall flow rate, the outgoing flow of nonwater species is n˙ others,out

iA = nF



λreactant,in

 −1

(6.11)

n˙ others [RH · Psat (T )/P] 1 − RH · Psat (T )/P

(6.12)

yreactant,in,dry

Rearranging Eqs. (6.8) and (6.9): n˙ v,H2 O =

which is appropriate for inlet and exit flows, providing the RH and total pressures at the appropriate locations are used. Solving for the net water out of the anode and cathode sides and including liquid water slugs and film flow out of the cell, the net molar flow rate of water out of the cathode is   n˙ out,c − n˙ in,c H2 O = n˙ slugs,out,c   λO  i A  RHin,c ·Psat (Tin )  λO 2 iA sat (Tout ) 2 − 1 RHout,cP·P 4F yO2 ,in,dry y 4F Pin,c out,c O ,in,dry  + − 2 RHout,c ·Psat (Tout ) RHin,c ·Psat (Tin ) 1− 1− Pout,c Pin,c (6.13) and for the anode, the net water flux out is   n˙ out,a − n˙ in,a H2 O = n˙ slugs,out,a   +

iA 2F

λH 2 yH2 ,in,dry

1−

·Psat (Tout ) − 1 RHout,aPout,a RHout,a ·Psat (Tout ) Pout,a

λH 2

−

 i A  RHin,a ·Psat (Tin ) 

yH2 ,in,dry

1−

2F

Pin,a

RHin,a ·Psat (Tin ) Pin,a

 (6.14)

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Letting χ = RH · Psat (T )/P we can show that  iA  λO 2 λO 2 iA − 1 χout,c χin,c 4F yO2 ,in,dry yO2 ,in,dry 4F − 1 − χout,c 1 − χin,c  iA  λH 2 λH 2 iA − 1 χout,a χin,a 2F yH2 ,in,dry iA yH2 ,in,dry 2F + − + n˙ slugs,out,a + n˙ slugs,out,c = 1 − χout,a 1 − χin,a 2F (6.15) Surprisingly, if the stoichiometry is constant and there are no liquid slugs out of the cell, we can cancel out iA/2F from each term, eliminating current from the overall gas-phase water balance. This is because the water generation and the stoichiometry both scale directly with current. For the general case with liquid water slugs, we can show that in steady state    λO 2 λO 2 λH 2 χout,c χin,c − 1 − 1 χout,a yO2 ,in,dry 2 yO2 ,in,dry 2 yH2 ,in,dry − + 1 − χout,c 1 − χin,c 1 − χout,a   λH 2 χin,a n˙ slugs,out,a + n˙ slugs,out,c yH2 ,in,dry

− + =1 (6.16) 1 − χin,a i A 2F and without liquid flow that     λO 2 λO 2 λH 2 λH 2 χout,c χin,c χin,a − 1 − 1 χ out,a yO2 ,in,dry 2 yO2 ,in,dry 2 yH2 ,in,dry yH2 ,in,dry − + − =1 1 − χout,c 1 − χin,c 1 − χout,a 1 − χin,a (6.17) This convenient reduction occurs for constant-stoichiometry operation only, since the flow rate and generation are both linearly proportional to current and thus cancel each other out. In a general transient case, there would also be a mass storage/depletion term in Eq. (6.17). There are some possible simplifications to Eq. (6.16): 1. Zero Liquid Water Out This is appropriate for relatively dry conditions with little or no continuous flooding, where there will not be any liquid slugs liquid films, or liquid entrained as a mist in the reactant flow. Equation (6.16) reduces to Eq. (6.17), eliminating the current dependency and the liquid water term. 2. Zero Net Drag This assumes there is no net flux of water from the anode to cathode. The modes of water transport in the electrolyte are discussed in detail later in this chapter. This assumption uncouples the anode and cathode flows and is most appropriate for very thin electrolytes with a fully humidified anode and isothermal conditions. In this case, all the water uptake to balance the generated water must come from the cathode flow. 3. Isothermal This assumes the inlet and outlets are at the same temperature and thus the saturation pressure is constant. This approximation is most valid at low power or with a very high coolant flow rate. 4. Viscous Drag Dominates Pressure Loss In lieu of experimental data, the Hagen–Poiseuille relationship in Chapter 5 can be used to estimate anticipated pressure drop from inlet to outlet, although minor losses, species consumption, and water uptake will also affect the pressure drop.

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5. Full Humidity Saturation at Exit Although the flow at the exit of a flow channel is not necessarily fully humidified, if the flow field is long and the initial conditions are not overly dry, an exit RH = 1 can be used as a simplifying assumption in the initial analysis. An overall water balance can be achieved in practice through a variety of methods. Looking at the parameters we can control in Eq. (6.16), there are several possibilities: 1. Control of the inlet RH and stoichiometry of the reactants to exactly remove the water generated by reaction. This approach can lead to local drying at the inlet and potentially accelerate degradation, however [11]. 2. Engineer the temperature gradient through the fuel cell by coolant flow rate and channel design. If the coolant flow rate and channel design are such that the flow channel temperature increases from the inlet to the outlet, the increase in temperature can be used to absorb the excess moisture generated into the gas phase by the increasing saturation pressure. This is a common method of moisture control in larger stacks, where around 10–15◦ C variation in coolant temperature from inlet to outlet is achievable at high current just from excess heat removal requirements. 3. Engineering the pressure gradient through the fuel cell flow field design. From Eq. (6.8), as the total pressure is decreased at a given temperature, the mole fraction of vapor allowable in the gas phase at a given RH increases. That is, lower pressure flow holds a greater amount of water. This approach is more difficult to achieve in practice than temperature gradient or RH control and generally only works at a given operating point, since the velocity and pressure drop will change as a function of current. Also, intentionally engineering a high pressure drop in the flow channels results in undesirable parasitic losses. While achieving an overall water balance in a PEFC will generally improve performance compared to a highly flooded or dry condition, the liquid water distribution in a PEFC is generally highly nonuniform, and small accumulations or areas of drying can result in substantially reduced performance and durability. Example 6.2 Calculating the Global Water Balance (a) Calculate the net rate of water vapor uptake into an air cathode flow at the given conditions for a 250-cm2 fuel cell operating at 1.2 A/cm2 . Compare the cathode uptake to the water generation. What drying rate would the anode have to share to obtain a steady-state global balance? (b) Determine the cathode exit temperature that would achieve a global balance, assuming all uptake occurs in the cathode and there are no water slugs at this balanced condition.

Cathode Condition

Inlet

Outlet

RH Temperature Pressure Stoichiometry

0.25 78◦ C 3.2 atm 2.0

1.0 80◦ C 2.7 atm —

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SOLUTION (a) Since we are assuming all uptake at the cathode,   λO iA sat (Tout ) 2 − 1 RHout,cP·P   4F yO2 ,in,dry out,c n˙ out,c − n˙ in,c H2 O =  − sat (Tout ) 1 − RHout,cP·P out,c

λO 2

 i A  RHin,c ·Psat (Tin ) 

yO2 ,in,dry

1−

4F

Pin,c

RHin,c ·Psat (Tin ) Pin,c



From Chapter 3 Psat (T) (Pa) = −2846.4 + 411.24 T(◦ C) − 10.554 T(◦ C)2 + 0.16636 T(◦ C)3 . Plugging in Psat (78) = 43,966 Pa and Psat (80) = 47,684 Pa results in     2.0  1×47,684 0.25×43,966 2.0 1.2×250 1.2×250 − 1   0.21 4×96,485 324,240 4×96,485 0.21 273,577  n˙ out,c − n˙ in,c H2 O =  − 1 − 1.0×47,684 1 − 0.25×43,966 273,577 324,240 = 0.001399 mol/s The water generation rate at these conditions is n˙ H2 O =

iA = 0.00155 mol/s 2F

So in order to reach a steady-state gas-phase water balance, the anode would have to uptake 0.00151 mol/s of water, or the cell would accumulate water with time. (b) To determine the cathode exit temperature that would exactly balance the water generated, we rearrange Eq. (6.17), assuming no net uptake from the anode side and no liquid ejection:   λO 2 λO 2 χout,c χin,c − 1 yO2 ,in,dry 2 yO2 ,in,dry 2 − =1 1 − χout,c 1 − χin,c where χ = RH · Psat (T )/P. All of the conditions are known except the Psat (T) at the exit. To solve this problem by hand, solve for the exit saturation pressure from this equation as the only unknown and then use the saturation pressure relationship to solve for the proper temperature. Otherwise, a computer program can easily be generated to iteratively solve for the solution. When the exit temperature is ∼ 85.4◦ C, the steady-state water balance is approximately achieved. COMMENTS: Although we assume all the water uptake occurs at the cathode, there can be some net transport of water across the membrane, as discussed later in this section. There will be some pressure drop in the anode due to viscous losses and reactant consumption which will result in uptake into the anode flow. Transient Operation It should now be obvious to the reader that, to obtain perfect water balance, very precise temperature, flow rate, pressure, and humidity control are needed. During normal operation, the transient term in Eq. (6.3) is usually nonnegligible. In molar

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terms, the mass balance becomes
    dn

I (t) = n˙ in,a − n˙ out,a H2 O + n˙ in,c − n˙ out,c H2 O +
dt cv 2F

307

(6.18)

In this expression, the total cell current is left as a function of time, and the water out of the anode and cathode represents the gas- and liquid-phase contributions. During operational transients, the stored water in the porous DM, catalysts, and flow channels is depleted or increased and a new equilibrium is reached. Overall, during operation we can have three possible global water balance conditions:
dn

>0 dt
cv This represents an accumulation of water mass in the fuel cell media and flow channels. Eventually, this excess must be removed or performance will suffer via flooding. A drying condition is reached when
dn

<0 dt
cv This is a state of water depletion, or drying of the fuel cell. Liquid stored in the electrolyte, DM, catalyst layer, and channels will be depleted with time. Eventually, this condition will result in a dryout of the membrane and greatly reduced performance. A net balance is, of course,
dn

=0 dt
cv This is the ideal state of a water balance represented by Eq. (6.16). If the fuel cell is operating in a net flooded or drying condition, the fuel cell will adjust over time until a new global balance is reached. During operation or after load changes, it is actually rare to be at an exact water balance condition, and the fuel cell is generally operated in a slightly flooding or drying condition until a new equilibrium adjustment is reached. Flooding Condition Adjustment When the water balance is accumulating liquid water mass, a periodic ejection of droplets can maintain the water balance in the fuel cell since the liquid droplers are so dense compared to gas phase ejection. An illustration of the process of water buildup and ejection from the DM is shown in Figure 6.19. In the steady state, the water from generation must be exactly balanced by that removed. Although water droplet ejection is a periodic process, a H2 PEFC can be operated in a net flooding condition and still achieve relatively stable performance with periodic ejection. If the liquid water accumulation restricts gas-phase flow to the catalyst surface, performance instability will occur, however, until a new equilibrium is achieved. Drying Condition Adjustment When the fuel cell is operated in a net drying condition, the stored water content in the membrane, porous media, and channels will decrease until a new balance is achieved. In general, the outlet relative humidity of the low streams will adjust themselves, and any dryout of the membrane will result in reduced performance.

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Figure 6.19

Process of water buildup and ejection from diffusion media during operation.

Memory Effect The process of water balance adjustment involves liquid water accumulation or depletion in pores, capillary flow through the DM, condensation, evaporation, and gas-phase mass transfer. The liquid-phase adjustment has a much longer time scale than gas-phase flow adjustment. This mixed time scale can result in a so-called memory effect. Figure 6.20 is an example of this—a polarization curve that was taken for conditions of an underhumidified anode and cathode inlet flow. The rapid downward polarization curve was obtained by starting at open-circuit conditions and reducing voltage in 0.05-V increments at 10-s intervals. After 20 s dwell time at 0.5 V, the rapid upward polarization curve was obtained by increasing the voltage in 0.05-V increments at 10-s intervals. The upward polarization performance is slightly better than the downward scan, since the water generated at the 0.5-V conditions self-humidified the membrane before the upward polarization scan. The steady-state polarization curve was obtained by waiting until sufficient time had passed

Figure 6.20 Polarization curves taken for H2 PEFC. Anode/cathode: RH is 0/50% at 80◦ C, pressure 3/3 atm, λa /λc = 1.2/2.5.

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for a true steady state to be achieved at each voltage (sometimes >30 min per data point). At high voltage, the three performance curves are very similar. But at lower voltages, due to some liquid accumulation, the steady-state polarization curve is much lower than the other two. Because the time scale of liquid water accumulation and motion is on the order of minutes while that of gas-phase transport is on the order of seconds, the performance at a given state is a function of the previous recent history of the fuel cell. This effect can complicate transient performance and control in stacks. As discussed, one of the matters complicating operation and control of PEFCs is the time-scale difference between liquid- and gas-phase water accumulation and motion. While observed liquid slug velocities in the channel are lower than gas-phase velocities, they are usually of similar magnitudes. However, the time scale for liquid buildup and drying from the gas DM and of water uptake and loss from the electrolyte can be very slow. Consider the time scale for 1 mg/cm2 to accumulate in the DM, an amount of liquid likely to begin to restrict flow and reduce performance [10]. The time the fuel cell takes to generate that amount of water can be found from Faraday’s law. For 1 A/cm2 , it takes around 11 s to accumulate this amount of water; for 0.2 A/cm2 , it takes nearly a minute (see Example 6.3). Thus, the time scale of liquid accumulation is on the order of a minute, while the time scale of gas-phase transport can be calculated as τ=

(0.04)2 l2 ≈ D 0.1



cm2 cm2 /s

 = 16 ms

(6.19)

where a typical gas-phase diffusion coefficient of 0.1 cm2 /s was used and 400 µm represents a typical distance from the gas channel to the catalyst layer. From this result, the gas-phase transport is extremely rapid. Water uptake into the electrolyte also has a relatively long time scale that depends on the temperature, partial vapor pressure, and initial membrane state but can also be on the order of minutes or even hours. Ionic conductivity, water diffusivity in the electrolyte, and electro-osmotic drag are directly related to the electrolyte water uptake, which can also contribute to the observed performance memory effect and hysteresis. Example 6.3 Time Scale for Liquid Water Accumulation in PEFC Calculate the approximate time required for 1 mg/cm2 liquid water to accumulate in a fuel cell at 0.2 and 1.0 A/cm2 , assuming all the water generated remains in the liquid phase. SOLUTION A rough calculation can be done to show the time scale needed to see a buildup from water generation of a significant amount of water in the cell from Faraday’s law: m H2 O n F n H2 O = n˙ H2 O MWH2 O i A     1 mg/cm2 2 e− eq/mol 96,485 C/e− eq 2 (1 g/1000 mg) ≈ 53 s = 0.2 A/cm = 18 g/mol 0.2 A/cm2      1 mg/cm2 2 e− eq/mol 96,485 C/e− eq (1 g/1000 mg) ≈ 11 s = 1.0 A/cm2 = 18 g/mol 1.0 A/cm2 t =

 t i  t i

Only on the order-of-minutes time frame allows liquid water accumulation.

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COMMENTS: This calculation assumes all water generated goes directly to liquid and none to vapor, which is unlikely to be true, so that the time scale required for liquid water accumulation will be even greater than calculated. In a PEFC, this slow time scale, the slow time scales of evaporation or drainage from the porous media and electrolyte, coupled with the nearly instantaneous electrochemical and gas-phase response times lead to hysteresis in a polarization curve and the fuel cell memory effect discussed. 6.2.2

Local Water Balance We have just discussed the global water balance in a PEFC, but we have also mentioned that actual flooding loss is a localized phenomenon that can occur as a film resistance and pore filling in the catalyst layer, DM, and channels. To grasp the localized flooding phenomenon, it is also important to understand the macroscopic water transport processes which occur within the fuel cell media. Water Flux in Polymer Electrolyte Membranes Water flux in the solid electrolyte membrane of the PEFC must be understood to grasp the concept of a local water balance in the fuel cell. From Chapter 5, we know that the ionic conductivity of perfluorosulfonic acid–based solid polymer electrolytes is a strong function of water content. Within the electrolyte, there are four basic modes of transport, as schematically illustrated in Figure 6.21: 1. 2. 3. 4.

Diffusion—concentration gradient driven flow Electro-osmotic drag—voltage gradient driven flow Hydraulic permeability—gas or capillary pressure gradient driven flow Thermo-osmosis—temperature driven flow

Condensed Water Droplet

Hydrophobic Channel

Hydrophilic Channel Thermo-osmosis Diffusion Electro -osmotic drag Hydraulic permeation

H 2O vapor H 2O liq H 2O H 2 O generated H 2O vap

H 2O vap

H 2O liq Diffusion Medium

Micro-porous Layer

Figure 6.21

Cathode Catalyst Layer

Membrane

Different modes of water transport inside fuel cell.

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Water Balance in PEFC

Diffusion in Nafion Diffusion into Nafion (and other perfluorosulfonic acid–based membranes) can be modeled according to Fick’s law: n˙ W = −DW

m dC W dx

(6.20)

The water diffusion in the ionomer phase, DW , as a function of ionomer water content λ has been measured by several groups, including Springer et al. [8]. Gong and co-workers [12] also reported water self-diffusion coefficients for Nafion with pulse field gradient NMR. Motupally and co-workers expanded the data from [8] to include changes in temperature [13].     −2436 −3 0.28λ for (0 < λ ≤ 3) (6.21) exp DW = 3.10 × 10 λ −1 + exp T (K )     −2436 DW = 4.17 × 10−4 λ 1 + 161 exp−λ exp for (3 ≤ λ < 17) (6.22) T (K ) where λ is the water content of the membrane per sulfonic acid site: λ=

H2 O SO3 H

(6.23)

and is defined in Eq. (6.26). The water activity, a, needed to solve for λ is defined as a=

yv P = RH Psat (T )

(6.24)

This relationship is shown in Figure 6.22 and is an alternative to the relationship given in Chapter 5. At low water content, the diffusion coefficient increases with water content until a peak value around λ = 3, and then decreases with increasing water content until 14 12

Diffusivity x 10-6 (cm2/s)

c06

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353 K

6 4

303 K 2 0

0

2

4

6

8

10

12

14

16

18

Membrane water content, λ , (H2O/SO3H)

Figure 6.22 [14].

Diffusion coefficient as a function of membrane water uptake from Zowadzinski et al.

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around λ = 6, and finally gradually increases. The diffusivity is a decreasing function of temperature. Water Uptake in Nafion In order to determine a relationship between the gas-phase relative humidity and the ionomer water content, a relation between the ionomer water m and the gas-phase water vapor mole fraction is needed. If we neglect concentration C W the volume change of the ionomer caused by water uptake, the water concentration in the ionomer phase can be expressed by the ionomer water content λ as m = CW

ρdry λ EW

(6.25)

where ρ dry is the density of dry ionomer, EW is the equivalent molecular weight of the ionomer material, and the water content λ is defined as the ratio of the number of water molecules to the number of sulfonic acid groups within the ionomer. As discussed in Chapter 5, Zawodzinski et al. [14] showed 2 3 λ = 0.043 + 17.81aW − 39.85aW + 36.0aW

(6.26)

where aw = RH. For gas-phase contact of vapor with the membrane, the water activity in the gas phase is equivalent to the gas-phase relative humidity at the cell operating temperature, as discussed in Chapter 5. For contact with liquid water, λ increases to 22, despite the same thermodynamic activity as water vapor due to Schroeder’s paradox. Hydraulic Permeability Hydraulic permeation of water through the membrane occurs as a result of a pressure difference between the anode and cathode. The molar flow rate of water from the cathode to the anode can be written from Darcy’s law: n˙ H2 O,cathode =

kkr Pc−a µl

(6.27)

where k is the effective permeability of the membrane µ is the liquid viscosity, kr is the relative permeability of the membrane, l is the membrane thickness, and Pc−a is the gas-phase pressure difference between the cathode and anode. Water flux through the membrane can occur by gas- and liquid-phase transport, respectively. Transport of water through the membrane can occur as a result of a gas pressure gradient across the membrane or the capillary pressure gradient across the membrane. The gas-phase term is typically small because the anode and cathode pressures are usually similar, so this effect can be ignored. In the liquid phase, however, a capillary pressure difference between the anode and cathode can result in a net flux of water via this mode of transport [15]. The DM properties are often tailored to achieve the desired capillary flux effect, depending on the operating conditions. Electro-osmotic Drag Electro-osmotic drag of water is the mass flux resulting from a polar attraction of the water molecules to the positively charged protons moving from the anode to the cathode through the electrolyte, as illustrated in Figure 6.23. As each proton

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SO – SO3– 3 SO3– SO3– H2 O SO3– H+ SO3– H2O SO3– SO – SO3– 3

Figure 6.23

SO3– – 3

SO

SO

– 3

– 3

SO

SO3

313

Water Balance in PEFC

SO3–

–

SO3– SO3– SO3–

SO3– SO3– SO3– SO3– SO3–

SO3–

SO3– SO3–

Schematic of electro-osmotic drag in electrolyte membrane under a current.

travels through the electrolyte from the anode to the cathode by Grotthuss and vehicular mechanisms described in Chapter 5, the surrounding cloud of polar water molecules will be dragged along. Water transport by electro-osmotic drag is always from the anode to the cathode. Since the drag is proportional to the current (protons), an expression for the flux of water by electro-osmotic drag is written as n˙ H2 O = n d

iA F

(6.28)

where nd is the electro-osmotic drag coefficient in units of water molecules per proton. Many studies have been conducted to determine the drag coefficient. A drag coefficient of 1–5 H2 O/H+ of Nafion membranes has been shown for a fully hydrated Nafion 117 membrane [16]. Zawodzinski et al. [17] have investigated the electro-osmotic drag coefficient of Nafion 117 and other ionomeric polymer electrolyte membranes at 30◦ C under conditions relevant to PEFCs. For a Nafion 117 membrane fully hydrated in liquid water (λ = 22), they obtained nd = 2.5. For a nearly fully hydrated membrane with a water content of λ = 11, a much smaller value, nd = 0.9, was obtained. Fuller and Newman [18] obtained nd = 1.4 for λ values of 5–14. From the same kind of measurement, however, Zawodzinski et al. [17] obtained a convenient value of nd =1.0 for λ < 14 at 30◦ C. Ise and Kreuer et al. [19] also measured the electro-osmotic drag coefficients in Nafion and obtained nd = 2.6 for λ = 20, which is very close to the value reported by Zawodzinski et al. [17]. In summary, if equilibrated in moist vapor (0 < λ < 14), the value of nd is around 1.0–1.5. For Nafion equilibrated in liquid water, however, the membrane water uptake is much greater, and the electro-osmotic drag coefficient is around 2–5. Example 6.4 Comparison of Generated and Drag Water Compare the total water delivered to the cathode by electro-osmotic drag to that generated by reaction at a given current density, assuming the membrane is in contact wit vapor-phase water only. SOLUTION Eq. (6.28):

For water drag, the net molar flux of water to the cathode is shown from

n˙ H2 O,drag = n d

iA F

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where n d has been shown to be ∼1.0–1.5. For water generation, we have Faraday’s law: n˙ H2 O,gen =

iA 2F

Comparing the two, we have n˙ H2 O,drag (1–1.5) × 2 n d (i A/F) = = = 2–3 n˙ H2 O,gen i A/(2F) 1 Thus, water transport by electro-osmotic drag is always from the anode to cathode and is two to three times greater than the water generation at the cathode for vapor-equilibrated membranes! In terms of flooding at the cathode, the electro-osmotic drag to the cathode results in more water than the electrochemical generation. COMMENTS: In hydrogen PEFCs, much of the water driven to the cathode by electroosmotic drag is removed by back diffusion to the anode, especially in thin membranes. In DAFCs with a liquid fuel solution, however, back diffusion does not occur and the cathode flooding problem can be much more severe. Temperature and Heat Flux Driven Flow A fourth mode of transport that has been shown to drive water flux in the membrane is heat flux driven flow. As a general rule, water will move through the membrane toward a colder location. This occurs in a freezing process due to capillary forces [20, 21], and nonfreezing processes [22, 23]. The nonfrozen mode of transport is poorly understood but is likely a result of the combined effects of capillary pressure change with temperature and thermo-osmosis in membranes. There may also be a phase change phenomena associated with the motion of water in the membrane under a temperature gradient, since Bradean et al. [22] showed an exponential relationship between liquid flux and the temperature gradient and heat flux, but the exact nature of this is not fully understood. This mode of transport has not commonly been included in the analysis of normal operation, since this effect is obscured by the net diffusive and electro-osmotic drag transfer. Under startup or shutdown conditions, however, where larger gradients in temperature can exist, the net water flux from this mode can be significant, and has been exploited to passively drain the DM on shutdown to a frozen state [22]. Net Transport Coefficient The overall water transport through the membrane can be written as the combination of the various modes of transport: n˙ H2 O,net,a−c = n˙ H2 O,drag + n˙ H2 O,diff + n˙ H2 O,perm,gas + n˙ H2 O,perm,cap + n˙ H2 O,temp

(6.29)

The net drag coefficient α d is a parameter used to express the net drag of water from the anode to the cathode and accounts for the total effect of the modes in Eq. (6.29): n˙ H2 O,net,a−c = αd

iA F

(6.30)

The net drag coefficient represents the total transport of water to the cathode. In an ideal situation for water management, α d would be uniformly −0.5 along the electrode. In this case, the exact amount of water generated by reaction is exactly balanced and moved

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Figure 6.24 Measured local and net effective drag coefficients along gas flow channel of PEFC operating at 0.7 V, with a dry anode inlet and cathode inlet at 50% RH at 9◦ C. The net drag is negative, indicating a net drag of water toward the dry anode. Toward the exit, however, the local effective drag becomes positive. (Adapted from Ref. [24].)

through the electrolyte from the cathode to the anode. There would be the possibility of anode flooding, but the membrane would retain maximum moisture content. In practice, for the thin (∼15–25-µm) membranes used in automotive applications with uniform anode and cathode inlet humidity, the high back diffusion to the anode nearly completely compensates for the electro-osmotic drag, and the net drag is nearly zero [25] or slightly negative [24]. For thicker membranes used in stationary applications, the net drag coefficient can be slightly positive because the back diffusion is limited. Another point should be made that the assumption of uniform net drag within the fuel cell is rarely justified. Figure 6.24 shows the measured net drag coefficient distribution along the flow channel of a PEFC operating at either relatively dry anode or dry cathode inlet conditions, with a thin 18-µm electrolyte membrane [11]. In this case, even though the electrolyte is very thin, the net drag coefficient is not near zero because of the initial imbalance between anode and cathode humidity. For this dry anode inlet case, the overall net drag coefficient is −0.12, representing a net back-diffusion flow toward the anode. However, after the initial 40% of the fuel cell flow channel, the net flux is slightly positive, toward the cathode, since the anode has become humidified, reducing the diffusion concentration gradient. As a result of Schroeder’s paradox, there is a very high electro-osmotic drag coefficient of 2–5 H2 O/H+ in applications where the anode is in contact with liquid-phase water such as the DMFC. This and the lack of back diffusion result in a very positive net drag coefficient and more severe cathode flooding without special engineering of the DM to provide a strong capillary pressure gradient toward the anode. Local Water Balance: Catalyst Layer Mass Balance In this section we discuss the local water balance, which can be (and usually is) highly nonhomogeneous throughout the fuel

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CV Cathode

nin,

dn/dt iA/2F

c

nout,

c

Figure 6.25 Control volume mass balance applied to cathode catalyst layer.

cell. From a mass balance on the cathode catalyst layer (Figure 6.25),
dn

I = n˙ in,c − n˙ out,c + dt
2F

(6.31)

cv

In steady state, the water generated will be exactly equivalent to the net water out of the catalyst layer. The transport in and out of the catalyst layer involves many modes of transport: 1. Transport into or from the electrolyte by diffusion, electro-osmotic drag, hydraulic permeation, and temperature effects. 2. Transport of liquid and gas into the porous media between the catalyst layer and the channel/land locations. Example 6.5 Calculating Internal Water Balance Given a net drag coefficient of 0.1, determine the molar rate of water accumulation at the catalyst layer that must be removed to prevent flooding. SOLUTION


I iA iA iA dn

(αd + 0.5) = 0.6 + = = n˙ H2 O,net,a−c + n˙ gen = αd dt
cv F 2F F F

This value must be removed from the cathode exit of the fuel cell to obtain a condition of water balance. If this value is not removed, saturation of liquid in the catalyst larger will increase, raising the local capillary pressure until it is pushed into the DM, or electrolyte, or the active area is sufficienty reduced to flood the electrode and reduce the current. The balance can be achieved through a variety of methods already discussed. COMMENTS: For thin membranes in fully humidified conditions, we can typically assume a net drag value close to zero. If there is an imbalance in the inlet RH values between the anode and cathode, the diffusion flux will change the net drag coefficient. If the anode flow is relatively underhumidified compared to the cathode flow, the net drag

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Figure 6.26

Water Balance in PEFC

317

Typical liquid water accumulation behavior under lands and channels in PEFC.

coefficient generally becomes slightly negative. In the case of an underhumidified cathode, the net drag value will become slightly positive. Liquid Distribution and Transport in Catalyst, Microporous, and Diffusion Layers A basic question of PEFCs is, where is the flooding occurring? The answer is that it depends on the porous media properties, flow conditions, and fuel cell geometry. The exact nature of the liquid water structure in the DM is not precisely known, but it is generally believed from capillary theory that the liquid water flows through large hydrophobic and hydrophilic pores, and the gas phase flows through small hydrophobic pores. However, evaporation and condensation also play a role, so that a unified understanding based on capillary pressure arguments alone is insufficient. Figure 6.26 is an illustration of the typical water distribution in the fuel cell porous media under the lands and channels. Since the coldest location during operation is generally under the lands, water condenses there first. As the saturation increases, water pushes out laterally from under the lands and forms connections between the lands under the channels, resulting in DM flooding and performance degradation. The removal of water from under the lands into the channels is important to avoid flooding, as lateral connectivity between the water under adjacent lands in the DM can induce severe performance loss through reactant blockage. Besides under the lands, there are other locations in a fuel cell where liquid water tends to accumulate. These locations have been identified primarily using neutron imaging, which enables a direct nonintrusive quantification of the liquid water content in the operating fuel cell and is used by several research institutions for this purpose [26–28]. Liquid accumulation also commonly occurs around channel switchbacks, as shown in Figure 6.27. This is a result of flow recirculation, stagnation, and pressure drop at locations of sudden momentum reversal. Additionally, the local flow separation near the corner accelerates the core flow, promoting annular flow of liquid water. Interestingly, even in very dry operating conditions, there tends to be an accumulation of liquid water under the lands, as shown in Figure 6.28. This is because the most efficient heat transfer is conduction through the lands, and access to the channel is blocked.

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Figure 6.27 Neutron radiograph showing liquid water accumulation along corners of 180◦ switchback in operating PEFC. Water is often observed to preferentially accumulate at switchback locations and along the channel walls. (Adapted from Ref. [9].)

Therefore, during normal operation, there is typically liquid water storage in the gas DM under lands, since lands are the coolest location. At low current density, channel-level flooding is prevalent due to slug formation and the lack of sufficient gas-phase velocity to remove channel droplets via drag force. As the current density (and channel flow rates) increase, the channels are more efficiently cleared, and the porous media begin to accumulate liquid from generation. At this point, flooding may occur in the catalyst layer, DM, or some portion of both depending on the materials and conditions. From Chapter 5, we know that the capillary pressure liquid saturation relationship depends on the net hydrophobicity of the DM. Since the carbon materials in the catalyst layer and DM are hydrophilic and the PTFE additive is hydrophobic, there are regions of mixed hydrophobic and hydrophilic behavior, and no single surface contact angle describes the internal structure or multiphase flow within the mixed wettability media. Instead, flow in these structures takes place along separate hydrophilic–hydrophobic pathways, each with different behavior for liquids and gases (Figure 6.29). From porosimetry studies, a typical range of hydrophobic to hydrophilic pores in PEFC diffusion media with PTFE

Land Channel

Figure 6.28 Neutron image showing modest liquid water accumulation under the lands in a seven channel parallel flow configuration fuel cell at an underhumidified condition. Lighter areas represent the accumulation are under lands, while the generally black areas indicate a relatively liquid dropletfree situation under the channels. The total water mass in the 14.5 cm2 cell was 79 mg at 0.35 A/cm2 . (Adapted from Ref. [29].)

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319

Hydrophobic pore

air air

Water imbibed automatically

Higher capillary pressure

Figure 6.29 Schematic of different liquid water imbibitions and transport behavior in hydrophilic and hydrophobic pores. The catalyst layer and diffusion media are typically mixed wettability media; thus hydrophilic and hydrophobic pathways exist for transport of liquid and gas phases.

additive is 20–40% hydrophilic and 60–80% hydrophobic [30], so that the net condition of a PTFE-treated DM is hydrophobic. It is clear based on experimental studies that, while critical, flooding is not solely a result of capillary flow, and phase change, morphology, and interfacial properties also play key roles. In order to develop a heuristic of the capillary flow related flooding in the catalyst layer and DM, we should recall from Chapter 5 that the capillary pressure is inversely proportional to the pore radius through the Laplace equation for capillary tubes:   2γ cos θ (6.32) Pc = r∗ For hydrophobic media, the capillary pressure is elevated in the liquid phase and increases with liquid saturation. In all cases, liquid tends to move along a path toward a lower capillary pressure, which, for hydrophobic media, means liquid will move toward locations of (a) lower liquid saturation, (b) a more hydrophilic location, or (c) a larger, equally hydrophobic location. For a hydrophilic media, the liquid phase is nonwetting, a lower liquid-phase pressure exists and provides a suction force to draw the connected liquid into smaller pores, where it will remain until removed by convection or evaporation. Capillary flow through a hydrophilic porous media will flow in the direction of (a) higher liquid saturation (until fully saturated) (b) a more hydrophilic surface, or (c) a smaller hydrophilic pore.

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SGDL

SMiPL

iA at SS 2F out

iA 2F in

SW 0

CL

MiPL

GDL

Channel

Figure 6.30 Typical water distribution in fuel cell porous media under steady state after sufficient time to allow equilibrium in porous media between stored and flowing liquid. The discontinuities in the saturation level are a result of the changing pore size and hydrophobicity between the different layers. Hydrophobic layers are shown, and all water generated is assumed to leave through a single channel.

It should be emphasized that the capillary motion will be induced only for droplets along a connected fluid path. That is, isolated droplets which have condensed on a surface will feel no force other than that from the droplet interaction with the surface. Therefore, some fraction of liquid can remain as isolated droplets despite capillary effects in the continuous liquid phase. At equilibrium conditions, a pressure balance in the gas and liquid phases across interfaces must exist. Therefore, we can predict the water distribution and flooding locations depending on the hydrophobicity of the surfaces and the pore size distribution. Figure 6.30 shows the liquid water saturation distribution in the porous media assuming an isothermal condition with no phase change and hydrophobic surfaces at steady state. In steady state, there is a flow of water from the catalyst to the channel and out of the fuel cell as condensed slugs and vapor. Discontinuities in the liquid saturation due to the pore size variations result in a saturation jump for the same capillary pressure. At each interface, the liquid-phase capillary pressure is balanced (in steady state). The typical pore size distribution in the fuel cell soft goods (membrane, electrode, and DM) is as follows: catalyst layer (∼50 nm) < microporous layer (∼100 nm) < DM (∼100–500 µm). For the same interfacial liquid pressure and hydrophobicity, the media with the smallest hydrophobic pores (catalyst layer) will have the lowest liquid saturation. If there were similar levels of hydrophobicity in each larger, the capillary pressure gradient will drive the liquid flow from the catalyst layer through the microporous layer and DM into the flow channel. Recall however that the microporous layer is typically much more hydrophobic. Therefore, the MPL can act as a barrier for liquid flow unless the break though pressure is reached. Typical MPLs have a break through pressure around 5–10 kPa. In hydrophilic pores of the CL and DM, liquid will accumulate until removed by evaporative or convective forces and will not spontaneously drain into channels. In our discussion so far, we have not included the possibility of phase change and temperature gradients which play a large role as well. While isothermal conditions may be true at low current density, higher current densities include phase change and temperature

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gradients. Under current, the polarization losses will generate a majority of the heat dissipated by the fuel cell. Since most of the entropy change and activation polarization are generated at the cathode, this is typically the hottest location in the fuel cell, by up to 5◦ C or more under high current depending on the thermal properties of the DM. At the cathode catalyst layer, vapor-phase water will be transported into the electrolyte and back to the anode or outward to the cathode flow channel. As the temperature cools, there will be a saturation plane that develops where liquid water condensation occurs and fills the porous media. The location of condensation will have a tremendous effect on the flooding. For the mixed wettability catalyst layer, the condensation would tend to take place in the predominantly hydrophilic pores first, flooding them, while the hydrophobic pores remained mostly liquid free. If the condensation plane is beyond the catalyst layer and in the microporous or diffusion layer, the highly hydrophobic nature of the MPL will prevent backflow into the catalyst layer. Some have also suggested the MPL acts to force liquid water toward the anode, preventing dryout [31, 32]. This can be true of filled hydrophilic connected networks in the catalyst layer. When the CL is flooded and cannot overcome the breakthrough pressure into the cathode MPL, then back flow to the anode by pressure-driven flow can occur. Gas-Phase Transport in Catalyst, Microporous, and Diffusion Layers The role of the different porous media in the fuel cell (catalyst layer, microporous layer, and diffusion media) in liquid transport can be grasped by understanding capillary flow behavior in mixed wettability porous media. The role of these porous media in controlling gas-phase flow can be simply understood through gas-phase transport relationships. Recall from Chapter 5 that the diffusivity in porous media must be modified to account for the tortuosity and porosity of the porous media: Deff = D

φ τ

(6.33)

Thus, the higher the tortuosity and the lower the porosity of the porous media, the more the diffusion will be restricted. Therefore, from a gas-phase transport perspective the microporous layer in the fuel cell restricts transport from the DM to and from the catalyst layer. Lands also play an important role in restricting gas-phase transport to the catalyst layer. The proper landing width is a balance beween reactant flow restriction and electrical contact limitation. 6.2.3 Overall Role of Materials in Maintaining High-Performance Electrode Based on our understanding of the gas- and liquid-phase transport in the fuel cell, a unified view of the role of the various porous media can be constructed and is shown in Figure 6.31. It should be noted that due to the lack of direct experimental observation of the very small microporous and catalyst layers, there exist several different theories to resolve the observed influences of the material properties on fuel cell performance. Microporous Layer: Cathode Side A MPL on the cathode side has been experimentally determined by many to enhance performance under high-current-density and high humidity

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Figure 6.31

Schematic of roles of different porous media in PEFC.

conditions, where catalyst layer and DM flooding is prevalent. Since the performance in this situation is generally limited by the flooding, and not the gas-phase oxygen transport, the additional diffusion resistance of the MPL does not significantly reduce performance. Based on the schematic shown in Figure 6.31, it is believed that the MPL serves as a highly hydrophobic boundary to prevent water flow back into the catalyst layer after condensation and can also force water back to the anode by capillary pressure forces. The capillary pressure gradient through the hydrophobic microporous and macroporous layers also favors flow toward the lower pressure channel, draining the DM and preventing catalyst layer flooding. The DM also serves as an intermediate transition between the very small pore catalyst layer and the macroporous layer. With no MPL, small water droplets emerging from the catalyst layer into a macroporous layer will see the equivalent of an open channel, and capillary flow will stop, pooling liquid in this location. The MPL therefore provides a continuous, connected flow of liquid emerging from the catalyst layer to flow to the macroporous DM and into the channel. In low RH conditions, the cathode MPL can force flow through the membrane into the anode by capillary pressure forces, reducing dryout and increasing performance. The backflow of water would occur primarily through the hydrophilic pore network in the catalyst layer, since complete pore saturation in the catalyst layer would result in nearly total performance loss, and high saturation in the hydrophobic pores of the CL would likely

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overcome the breakthrough pressure of the MPL, resulting in sporadic liquid slug emission, a phenomenon which has been observed to occur experimentally. Microporous Layer: Anode Side The role of the MPL on the anode side is completely different from that on the cathode side, although use of a MPL on the anode side has also been observed to enhance performance in low-humidity environments where the water in the anode ionomer can be easily lost to the dry hydrogen stream. The mass diffusivity of water vapor into hydrogen is up to four times greater than into air, as shown in Chapter 5. Thus, combined with electro-osmotic drag of water from the anode to the cathode, local anode dryout is a common reason for low performance and reduced longevity in low-humidity conditons. The use of an anode MPL limits the moisture removal from the anode by acting as a diffusion barrier, reducing this dryout effect, as illustrated in Figure 6.31. Under high-humidity conditions, the use of an anode MPL does not normally have much of an impact on performance, which has been validated experimentally [33]. Mechanically, the MPL has also been suggested to serve to protect the electrolyte from puncture from protruding fibers from the macroporous layer. Diffusion Media: Anode and Cathode Sides In terms of optimizing gas-phase transport in the macro–diffusion layers or the MPLs, there is a key engineering trade-off to consider. Obviously, high diffusivity of reactant to the catalyst is desired to promote reaction and limit concentration polarization. However, high moisture in the electrolyte is also desired. High-temperature and low-humidity conditions simplify system design but can lead to anode dryout with accelerated degradation and poor performance. For high reactant diffusivity, liquid saturation must be minimized, and there must be a high hydrophobic porosity. On the cathode side, oxygen transport is already limited by a low initial mole fraction, high water saturation, and reduced diffusivity coefficient, compared to hydrogen. Here, the focus is generally on prevention of flooding. On the anode, however, water vapor diffusivity loss into hydrogen can be severe, there is very little concentration polarization limitation at the anode, and hence a flow-restricting structure is preferred. The dominating role of the DM depends on the operating conditions. Under high current conditions, the oxygen transfer to the electrode is limiting performance, and an open hydrophobic structure promoting gas-phase transport with good liquid water removal on the cathode is necessary. In low-humidity environments, the lack of moisture dominates, and a closed-pore, less hydrophobic structure is needed to restrict vapor loss to the flow channel. From an overall porous media design perspective, the various porous media should be tailored to achieve the desired liquid- and gas-phase transport behavior. In the examples mentioned, and in most common materials, the properties are mostly uniform. However, the potential for enhanced vapor and liquid flow with hydrophobicity or pore size gradients exists and has been exploited in some specialized materials. Overall, different membrane electrode assembly configurations and materials are preferred by different manufacturers, and the exact nature of transport in these regions is not yet perfectly understood. Complicating factors that must be considered include the tightly coupled heat transport phenomena, nonisotropic material transport properties, and highly nonhomogeneous current density along the electrode. Since phase-change plays a key role, the thermal conductivity is another

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Figure 6.32 SEM of PEFC catalyst layer with relatively large scale macro cracking. (Image by Soowhan Kim, Penn State Fuel Cell Dynamics and Diagnostics Lab.)

design parameter of interest. Other factors include assembly sag into gas channels, which has been linked to flow maldistribution. Thus, a stiff DM is generally preferred for case of assembly and prevention of interfacial gaps. Mud Cracking, Interfacial and Morphological Effects Although it is easy to think of pore size as a constant in the various porous media, there is a distribution of pores in the DM and MPLs, and the catalyst layer can have significantly large cracks and gaps between interfaces in the catalyst surface, as shown in Figure 6.32. Catalyst layer surface cracking is typically present from manufacture and is a result of the presence of volatile compounds in the catalyst slurry. The viscous catalyst slurry is heated in an oven after application, removing these volatiles and shrinking the catalyst layer, causing what some have termed “mud cracks” to appear. From a multiphase flow perspective, this situation is very different than a continuous homogeneous phase, and some larger gaps and cracks may dominate flow physics in these regions. These cracks and gaps are orders of magnitude larger (they can be upto ∼10 µm wide) than the normal pore size in the catalyst layer, and these cracks would be regions of reduced capillary pressure, promoting liquid pooling. In terms of gas-phase transport, these macrocracks may enhance reactant transport to catalyst regions by reducing flow resistance. These cracks also increase the effective catalyst layer porosity, enabling high reactant species flux to the catalyst surface. From a durability perspective, however, these cracks have been linked to enhanced degration. In PEFCs, the interface between the channel, land, and DM, and the interface between the DM and catalyst layer can also affect transport of liquid. If there is a gap, this can serve as a pooling location for water. At the interface between the land and the DM, water stored in the DM can be drawn out with a hydrophilic surface or retained in the DM by a hydrophobic surface (Figure 6.33). Neutron imaging has also been used to confirm the important role the land interface has on the liquid water content stored at equilibrium. For fuel cells with otherwise identical operating conditions, the greater the number of hydrophilic land interfaces, the less liquid water content there is in the DM [34]. On the other hand, hydrophobic land surfaces have been shown to retain water under the lands, and promote flooding by restricting drainage from the DM.

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Figure 6.33 Liquid water removal from under land location. With hydrophilic channel wall surfaces, there is a net suction from the DM to the channel. If the wall is hydrophobic, however, liquid is retained in the diffusion media, causing earlier flooding.

6.3 PEFC FLOW FIELD CONFIGURATIONS AND STACK DESIGN Design Considerations There are many different flow field configurations that have been used for fuel cells in general and PEFCs in particular. The design of a flow field is a complex balance between many coupled constraints, many with opposing functional dependencies on the fuel cell performance, so that trade-offs must be made. The design constraints include the following: 1. Gas-Phase Transport and Parasitic Pressure Loss The channel and stack manifold design directly affects the flow and mass transport to the catalyst surfaces as well as the parasitic pressure drop. The flow through the DM and to the catalyst surface must be adequate to limit mass transport losses, and the pressure drop must be minimized. 2. Electron Transport For acceptable fuel cell performance, the electrical resistance must be low. This is provided by adequate contact area and material choices between the land and DM material. 3. Heat Transport Since a vast majority of the heat generated by fuel cell operation must be removed by the fuel cell and not through the exhaust gas, the landing–DM interface area carries much of the heat into the coolant. Local hot spots caused by poor design can cause dryout and lead to premature membrane failure. The coolant and reactant flow channels should be designed in tandem to minimize flooding and hot spots. 4. Liquid Water Storage and Transport The particular cell design has an impact on the amount of liquid water stored in the PEFC during normal operation and the ease with which it is removed. The presence of liquid water has a critical impact on the

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5.

6.

7.

8.

operating performance, pressure loss, degradation via ionic contaminants, and time to start and degradation from a frozen condition in a fuel cell stack. Gas-Phase Vapor Transport For low humidity operation, dryout of the ionomer into the channel flow can severely limit performance. Large channel widths promote dryout, while limiting dead zones under thinner lands. A channel to land ratio must be found to balance the oxygen restrictions with dryout for low RH operation. Degradation Mitigation There are many different modes of degradation in PEFC performance, as discussed in more detail in Section 6.5. The fuel cell system must be designed to avoid unacceptably high performance loss rate from irrecoverable losses (e.g., a pinhole in the membrane) and be capable of sensing and mitigating recoverable losses (e.g., a flooded electrode). Freeze–Thaw Damage Mitigation/Rapid Start-up If the fuel cell will be operated in ambient environments, survivability at subfreezing temperatures and rapid power availability at startup are required. Other Constraints Many other factors can affect the ultimate performance of the PEFC stack. In this context, the term “performance” is meant to be a general measure of the overall effectiveness of the fuel cell design, including power density, cost, and durability.

It should be emphasized that the constraints listed are not independent. In many cases, design to satisfy one constraint will impact others. An excellent example is the channel to land width ratio, discussed below. Design Constraints: Using Extremes to Illustrate Trade-offs Often in engineering systems the basic trade-offs can be best illustrated by consideration of extreme cases. Consider the generic fuel cell channel design with typical geometric parameters shown in Figure 6.34. The lands are an obstruction for mass transport that can potentially cause dead zones where reactant is unavailable. In the extreme case, the entire flow channel would be land, and no reaction could take place. At the other extreme, as shown in Figure 6.35, the entire fuel cell is open in design, with no mass transfer obstruction from lands. However, the performance of this design is poor, resulting from lack of electron conduction contacts provided by lands, and DM sag into the channel volume is likely. The best case is a balance between the two constraints that

W d L = land width W = channel width θ = draft angle d = depth W:L

L

θ

(typically 0.2–2.5 mm) (typically 0.5–2.5 mm) (typically 0–15o) (typically 0.5–2.5 mm) (typically 3:1–1:1)

Figure 6.34 Typical PEFC channel/land design features. The draft angle can be used to tailor the channel cross-sectional area without affecting the depth (stack volume) or land contact area.

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Current collector

Open

Figure 6.35 Extreme-case design-maximum channel width current collector along boundary and otherwise open. This design has the least obstructed mass transfer but the worst electrical contact and would suffer severe DM tenting.

minimizes the presence of both dead zones and electrical contact resistance losses. Under low humidity conditions, a balance between vaper loss and heat transfer is also required. Another common trade-off is channel velocity versus parasitic pressure drop. As discussed in Chapter 5, flow in channels is typically laminar, so that pressure drop, ignoring entrance and turbulence effects, can be written as P =

32µL V dh2

(laminar flow)

(6.34)

Some turbulence and minor losses from channel switchbacks and entrance effects are common. For a given cell design, an empirically derived relationship that combines the main laminar losses and minor losses can be used as P = av + bv 2

(6.35)

On one extreme, a high channel velocity (and stoichiometry) ensures nearly uniform reactant concentration from inlet to outlet and helps to remove any liquid droplets by shear force. However, very high flow rate results in higher parasitic pressure losses and can also lead to unintended maldistribution of flow throughout the stack. At the other extreme of very low flow rates, liquid water slugs will not be removed by channel shear forces, and reactant concentration losses will be severe near the fuel cell exit. The normal range of balance in H2 PEFCs is laminar flow with a stoichiometry of 1.2–1.5 in the anode and 2.0–2.5 in the cathode. Many more trade-offs exist and involve complex interactions and multiple considerations, so that no true optimal channel design exists. However, it is clear that a prespective involving understanding of the coupled capillary, phase-change, heat transfer, and gas phase flows must be used to arrive at an ideal design. PEFC Flow Field Designs qualities:

The ideal fuel cell flow field design results in the following

1. Excellent mass transport of the reactants to and products from the catalyst layer with a proper water balance to achieve a moist electrolyte with minimal flooding of the DM and channels under a wide range of operating conditions. 2. Excellent electron transport to and from the catalyst layers. 3. Adequate heat transport to the coolant channels. 4. Low pressure drop from inlet to exit. 5. Low cost of manufacture. 6. Compact design.

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Figure 6.36 Schematics of some common flow field design patterns. Many other basic design features have also been tried as well, including fractal and spotted post designs. (Image by Soowhan Kim.)

The particular fuel cell design has a great deal of influence on the transport of reactants to the electrode. Some basic fuel cell flow channel designs are illustrated in Figure 6.36, with additional details on the inherent trade-offs in Table 6.3. Most standard fuel cell designs are a combination of parallel and serpentine designs, like that shown in Figure 6.37. By tailoring the channel size and parallelization, the channel velocity and pressure drop can be balanced. Table 6.3 Channel Designs in PEFCs Flow Field Design

Advantages

Disadvantages

Serpentine

High channel velocity, good water removal, high performance Low pressure drop, more even concentration distribution Can balance advantages of serpentine and parallel design High performance, excellent water removal from under landings

High pressure drop, uneven species concentration distribution Low channel velocity, poor liquid water removal Combination of parallel and serpentine disadvantages High pressure drop for forced flow through DM, possible long-term damage to structure Expensive design, coolant used must be freezable water Dead zones and water accumulation away from path of least resistance Unintentional reactant bypass between low-pressure exit can high-pressure inlet channels Higher pressure drop

Parallel Parallel–serpentine combination Interdigitated

Porous plate

Excellent water uptake capabilities

Mesh

Low pressure loss, controllable total contact area Lower humidity load since exit channels run by inlet channels

Spiral

Metal foam plate Radial

Uniform compression on DM surface, ease of manufacture Lowest diffusion path length for passive designs

Only used in passive system

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329

Figure 6.37 Photographs of graphite 50 cm2 active area parallel–serpentine flow field used for laboratory studies. The laboratory flow field plates are over 1 cm thick to improve durability in a laboratory environment. Actual fuel cell stack flow field plates are considerably thinner to improve power density.

The interdigitated design is a unique design that has no continuous channels. Through a series of dead-end channel inlet fingers, as shown in Figure 6.36, flow is forced into the DM and under the lands into the outlet channel fingers. A crosssection of the interdigitated design is shown in Figure 6.38. In the process, liquid water is removed from the DM, and the reactant transport to the surface is greatly facilitated by forced convection. Performance with the interdigitated design is very good, but the parasitic pressure drop is also increased. United Technologies has developed a unique porous plate flow field technology, illustrated in Figure 6.39. The flow channels have a typical parallel and serpentine design, but the landings have many small hydrophilic capillary columns, which allow the cell to wick water from the DM surface by capillary action. When the DM becomes saturated, the porous plate wicks water away and into the coolant channels, maintaining a low saturation level and improving high-current-density performance. This design is a passive method to manage water transport and flooding using capillary forces. Naturally occurring capillary forces are quite effective to transport water (consider that trees have no pumps). Interestingly, natural forces are very rarely the first possible solution considered by engineers, although they can often be exploited, as in this unique design.

Figure 6.38 Schematic of cross section of interdigitated design to force flow convectively to catalyst surface under land locations.

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Water reservior

Channel

Channel

Channel

DM

Figure 6.39 [35].

Schematic of United Technologies porous plate fuel cell design concept, based on

Mesh designs are another attempt to reduce parasitic pressure losses, which can consume up to 30% of the gross system power. Since flow tends to follow the path of least resistance, the mesh design can leave corner areas as deadzones. The spiral design is an attempt to have exit channels, typically high in humidity, adjacent to inlet channels, so that moisture can be exchanged in-plane between channels, reducing the humidity load required for optimal performance. Unfortunately, aligning channels from near the inlet with channels near the output is rarely wise because the pressure drop in the channels will induce unintentional reactant bypass between the lower pressure exit and higher pressure inlet, leaving portions of the active area without sufficient reactant. The metal foam is a highly porous structure designed to completely eliminate the channel/land structure of the flow field and landing combination. Instead, a highly porous, conductive material is used as the flow field. This system has similar draw backs to the mesh design. Radial designs have been proposed for use in portable applications. Fuel is pumped through an interior annulus of the radial stack, and air diffuses along the cathode surface. The radial design minimizes the diffusion distance of the air, which is helpful when no active pump is used. An emerging concept in flow field design is that of asymmetric channel properties. In this type of design, a basic pattern is adopted, such as the parallel–serpentine combination. However, varying channel–land ratios or channel depths are applied to maximize performance and stability. This advanced design approach requires a deep understanding of the engineering trade-offs and nonuniformities along the flow field so that the unique features can be properly implemented. For example, the channel width can be varied along the channel or between various channels to control pressure drop, flow distribution, or liquid water accumulation inside the flow field. The disadvantage of this approach is that manufacture of the flow fields is generally more complex. Stack Orientation and Flow Direction In PEFCs, the anode and cathode flow fields should have some similar landing locations, so that most of the lands of the anode press against the lands of the cathode, forming a good overall compression and reducing sag of the membrane electrode assembly (MEA) into channels. Although flow in the fuel cell porous media is dominated by capillary forces, the channel-level and manifold liquid flow is strongly influenced by gravitational forces. If the fuel cell stack is oriented in a nonneutral position with gravity (e.g., the fuel cell plates are aligned vertically or at an angle), the inlets should be higher than the exits to allow water slugs to flow from the cell into the exit manifold. Additionally, the flow field should avoid local low points, where the water can pool in the channels due to gravitational effects. The flow should either be gravity neutral or follow a path of continually decreasing height with respect to gravity from inlet to exit for the anode and cathode.

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331

Anode in Cathode in (a) Anode in Cathode in (b)

Figure 6.40 Schematic of single channel (a) coflow and (b) counterflow design. In stack plates, the flow is often not exactly one or the other, but a mixture, since the anode and cathode flow designs can be quite different from one another.

The direction of the fuel and oxidizer flow can be coflow, counterflow, or a mixture of both. In the coflow case, the fuel and oxidizer inlets follow the same path, with reactants depleting from inlet to exit, as shown in Figure 6.40a. For underhumidied inlets, the qualitative humidity, performance, and mole fraction distributions are illustrated in Figure 6.41. The flooding shown will generally only occur after the saturation limit is reached, which may not actually occur depending on the operational parameters, such as flow rate, temperature, and inlet humidities on the anode and cathode. In the counterflow case, the inlets of the oxidizer and fuel are at opposite ends and flow against each other, as shown in Figure 6.40b. Depending on the stack and plate design, the flow pattern may not be completely coflow or counterflow and is some combination of both. The reasons for choosing a particular flow geometry are varied. The traditional view has been to design the fuel cell flow channel to minimize variations in the properties; that is, the coolant flow channel would be designed to minimize temperature gradients in the fuel cell. However, if a cell is properly designed to take advantage of pressure, temperature, or humidity gradients, these gradients can be used to effectively manage the water balance or cooling requirements. For underhumidied inlets, the qualitative humidity, performance, and mole fraction distributions are illustrated in Figure 6.42. For nonbalanced inlet humidity combinations, the local distributions can be more complex, as discussed in Section 6.6. In

RH saturated limit

RH

i

i (flooding loss)

yO2 , yH2

Figure 6.41 Schematic of typical distributions of species, current, humidity, and temperature in PEFC with purely coflow design and underhumidified anode and cathode inlets. The flooding loss portion does not necessarily have to occur, depending on inlet conditions, temperature, etc.

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i RH anode/cathode yO2, yH2

Figure 6.42 Schematic of typical distributions of species, current, humidity, and temperature in PEFC with counterflow design with underhumidified anode and cathode inlets.

some cases, the mole fraction of the hydrogen can actually increase along the flow path if the inlet flow is dehumidified along the flow path. Unintentional Reactant Flow Bypass Reactant bypass, or in-plane gas shorting, is described as a phenomenon of unintentional reactant penetration through the backing layer, underneath a current collecting land, and into another flow channel. Optimal performance without bypass is shown in Figure 6.43, where the reactant gases follow the intended flow path and utilize the fuel cell’s entire active area. In the case where bypass occurs, portions of the cell’s active area do not continuously receive a sufficient amount of reactants and a local dead zone is created, as illustrated in Figure 6.44. The bypass phenomenon is commonly observed in fuel cells with serpentinestyle flow fields and may be caused by a variety of circumstances in a fuel cell, including poorly designed flow field plates, water droplet accumulation, poor assembly, and large

Figure 6.43 Schematic of normal reactant flow without bypass around 180◦ switchback channel turn. (Adapted from Ref. [36].)

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333

Figure 6.44 Schematic of unintentional bypass that leaves a dead zone. The bypass can be a result of poor compression, excessive channel pressure drop, or poor flow field design. (Adapted from Ref. [36].)

pressure differentials along a given flow channel [36–39]. In terms of the flow plate design, if some flow channels with a high local pressure (e.g., inlet locations) are adjacent to channels with lower pressure (e.g., exit locations), excessive shorting can occur. The spiral design in Figure 6.36 is an example of this. As the flow comes into the cell and goes into the second turn, it is adjacent to the exit portion of the channel that is at the lowest overall pressure in the flow field. In this case, resultant pressure mismatch can lead to significant reactant bypass and low performance. The amount of bypass flow is controlled by the ratio of the pressure drop through the channel to the pressure drop through the DM. If the pressure drop through the DM to the bypass emergence point is relatively low compared to the pressure drop through the channel, significant bypass will occur. Assuming laminar flow, the pressure drop though the channel a distance L from the bypass location to the bypass emergence point can be derived from laminar flow theory [40]: Pflow path =

32L V µ dh2

(6.36)

where V is the channel bulk flow velocity and we have ignored turbulent, entrance, or secondary flow losses. An estimate of the pressure drop through the porous backing layer can be estimated with Darcy’s law [41]: PBacking =

Uave µ S k

(6.37)

where µ is the viscosity of the fluid, U ave is the bulk average velocity through the porous medium, S is the porous medium thickness in the direction of flow (equivalent to the land width), and k is the permeability of the backing layer. The DM permeability is a highly nonlinear function of porosity, as discussed in Chapter 5.

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A dimensionless parameter termed the bypass ratio (BPR) can be defined as the ratio of pressure drop through the channel to the backing layer [42]: BPR =

32L V k S

dh2 Uave

(6.38)

Obviously, the channel bulk flow velocity and the average bypass velocity U ave will be related, but the basic physics can be understood with this simple relationship. If BPR is much greater than unity, significant bypass should occur; if BPR is much less than unity, significant bypass can be avoided. Channel pressure, flow viscosity, and temperature should have little or no effect, while the hydraulic diameter, channel length, land width, DM permeability, and liquid saturation are the key controlling physical parameters. Stack Design Considerations for Portable and Automotive Applications cell stack design has the following qualities:

The ideal fuel

1. Compact design for maximum power density. 2. Proper flow manifolding to deliver flow evenly to all fuel cells in the stack without reversal of flow. 3. Proper sealing of reactants and coolant channels. 4. Low-cost, robust components. 5. High durability under a variety of operating environments. 6. Simplified purge and drainage of liquid water on shutdown. For stationary and automotive PEFCs, the most common stack design is simply a vertically stacked fuel cell plate configuration. Figure 6.45 shows an individual fuel cell flow plate

Figure 6.45 Serpentine stack plate field design showing manifolding of coolant, hydrogen, and air through middle of cell arrangement. (Reproduced with permission from Ref. [37].)

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6.3 PEFC Flow Field Configurations and Stack Design

Figure 6.46 Ref. [37].)

335

Fuel cell corrugation stacking for compact design. (Reproduced with permission from

used in a hydrogen PEFC flow field design patented by Ballard. Typical power densities of the fuel cell stack are now on the order of 1.3 kW/L and higher not including the balance of the plant. Typically, coolant flow channels are placed every or every second fuel cell to provide uniform heat removal and temperature distribution. Cells are stacked as efficiently as possible to provide a compact design. One way to increase stacking density is with corrugated designs, as illustrated in Figure 6.46. The corrugated design is very efficient for the stack, but sealing and proper flow manifolding are difficult to achieve. Coolant flow channel designs are typically simpler than the hydrogen or air flow field designs but should be tailored in concert with the anode and cathode flow fields to achieve proper heat and water management. For portable fuel cells, as used in small consumer electronics, the shape of a common vertical stack is usually not desirable to replace many of the thin batteries currently used. Therefore, a planar stack design is often used, as shown in Figure 6.47. In this design, the passive air flow cathode faces the open air, and the perforated metal cover serves as the current collector. The main issue with this configuration has been limitations in the effectiveness of the electrical connection between adjacent cells, since the path length for electron travel is longer than in a traditional vertical stack design.

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Polymer Electrolyte Fuel Cells Anode H2 flow

Cathode air flow

Anode 1

Cathode 1

i

Anode 2

Cathode 2

i

i

Bipolar plate/cell interconnect Anode 3

Cathode 3 i

Figure 6.47 Planar stack design with open cathode design for natural breathing. Note the use of cell-to-cell interconnects instead of structural bipolar plates common to PEFC designs.

Several different radial fuel cell stack designs have been developed. The primary reason to develop a radial system is to have the same form factor as a common battery. The radial design is typically fed fuel from an inner hollow core and air from the ambient around the unsealed cathode edges of the cell, as shown in Figure 6.48. An advantage of the radial design in this instance is that the diffusion path length is minimized. Many other portable designs exist, although almost all follow the basic planar, radial, or conventional stack design with some modifications. Stack Manifold Flow One of the most difficult engineering challenges in fuel cell stack design is the proper manifold design for fuel, oxidizer, and coolant flow. The manifold design challenge centers around three main constraints: 1. The manifold must be compact to minimize stack volume yet have minimal pressure loss. 2. The manifold must deliver flow evenly to all fuel cell plates, or flow maldistribution can occur, leading to significant performance degradation. 3. The manifolds must be properly sealed to prevent mixing of air, fuel, and coolant.

Cathode Anode Air in

Cathode Anode H2 out

H2 in

Figure 6.48 Schematic of portable design with radial open channels. The hydrogen flows upward through the inner distribution tube and outward into the closed anode chambers. The cathode flow field is an open structure, drawing air in from the ambient. Interconnects are not shown for clarity, and different variations of this concept exist.

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337

Figure 6.49 Schematic of chimney design utilized in most stack configurations for flow manifolding. Generally, an air, hydrogen, and coolant inlet and outlet chimney is used.

The manifold design challenge is further exacerbated by the fact that most fuel cell stacks contain over 100 fuel cells in series. In PEFCs, the presence of liquid water presents a multiphase flow and instability problem that further complicates design. Despite the myriad flow field patterns, the vast majority of vertical stacks employ some sort of chimney manifold, as illustrated in Figure 6.49, with flow for coolant, fuel, and air running through the periphery or the middle of the stack. The manifold exchanges between the individual cells must be sealed with O-rings, gaskets, or permanent glues to prevent crossover or coolant leakage. In the chimney manifold design, the pressure drop in the manifold must be much less than the pressure drops through the flow field plates, so that flow is evenly distributed among the plates. In an ideal situation, each parallel flow field plate would have an identical pressure drop, providing uniform flow distribution. However, multiphase flow will exisit in PEFC operation during startup, shutdown, and even regular operation, and assembly conditions or DM sag can result in slight difference in plate-to-plate or channel-to-channel pressure drop. The flow inside an exit manifold is highly complex and nearly impossible to analytically describe. The presence of liquid water droplets in the flow fields increases the pressure drop for droplet removal and causes transient pressure variations between the flow field plates in the stack. The flow from the manifold and through the fuel cells is analogous to current flow through a parallel resistance network, as illustrated in Figure 6.50. If one of the individual cells has a slightly different pressure drop due to liquid accumulation or DM sag, the flow

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Polymer Electrolyte Fuel Cells R1 R2

Inlet manifold flow

R3

exit manifold flow

R4 R5

etc.

Figure 6.50 Flow from manifold into fuel cell stack plates is analogous to resistor in parallel network. Minute variations in the pressure drop through any of the plates can result in flow redistribution and cause severe damage.

into that cell will be reduced, possibly below the minimum required flow to produce the stack current. In this case, that cell voltage will go to zero or even a negative value (voltage reversal), reducing the efficiency of the stack and increasing the heat release. Voltage reversal can lead to rapid cell degradation from excessive heat release and undesired side reactions that take place to produce the necessary stack current. While impossible galvanically for a single cell, an individual fuel cell in a stack can undergo voltage reversal by using available power from the properly functioning cells to drive undesired electrolytic reactions. Voltage reversal can occur when the conditions are such that it is not possible to generate the stack current in a galvanic mode. Since the individual cells are generally in series electrically, each cell must carry the same current, but the voltage in each cell can be different. As long as the total stack voltage is greater than zero, individual cells in the stack can be powered electrolytically by the rest of the stack to produce the required current through alternative electrochemical reactions. Essentially, if the current cannot be produced by the available galvanic cell voltage, the cell will be powered by the other cells in electrolytic mode to a negative voltage where the current is produced by some other electrochemical reaction. In some cases, the alternative reaction can be benign, such as water electrolysis. In other cases, the reaction is irreversible and permanently degrades the electrode. For example, if the anode flow is blocked, the anode potential will rise, reducing the fuel cell voltage. The first significant electrolytic reaction that will occur at the anode to produce current is water electrolysis: H2 O → 2H+ + 2e− + 12 O2

(6.39)

This reaction is benign and will not cause irreversible damage in small quantities. If this reaction cannot generate enough current, the anode potential will continue to rise, eventually driving the anode to oxidize the carbon in the electrode support at sufficiently negative cell voltages: C + 2H2 O → CO2(g) + 4H+ + 4e−

(6.40)

Normally, this reaction occurs so slowly at PEFC temperatures and potentials that it is not a concern. However, under a reversal situation the cell voltage can become negative enough to accelerate this reaction to appreciable levels.

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6.4

Direct Alcohol Polymer Electrolyte Cells

339

If there is oxidant starvation, the anode oxidation continues, but due to the absence of oxygen, the cathode potential is decreased to around 0–100 mV, where protons are reduced. This is called a hydrogen pump and is benign: 2H+ + 2e− → H2

(6.41)

In general, voltage reversal must be avoided during operation to prevent accelerated degradation.

6.4 DIRECT ALCOHOL POLYMER ELECTROLYTE CELLS Hydrogen is a high-efficiency fuel for fuel cells but has several technical drawbacks which engender an alternative fuel in certain applications. Ĺ Storage and transportation of hydrogen are not yet established or simple. Ĺ Storage of hydrogen is bulky in the gas phase, heavy stored in solid-phase hydrides, and cryogeninc and expensive in the liquid phase. Ĺ Hydrogen is highly flammable and has an invisible flame. Broad mixes of hydrogen in air between 4 and 74% hydrogen are flammable. Ĺ The H2 PEFC requires ancillary components such as humidifiers and coolant recirculators that can be larger than the fuel cell stack itself. Chapter 8 discusses the hydrogen storage, generation, and delivery in greater detail. For now, we can identify two major applications where the use of stored hydrogen fuel may not be the best solution: 1. Portable applications, where system compactness and not efficiency is the most valuable design parameter. 2. Stationary and distributed power applications, where delivery of hydrogen is not readily available, but natural gas is. For stationary applications, the most common solution is to use a stream of reformed hydrogen as fuel. In fuel reformation, a hydrogen carrying liquid fuel such as methane or ethanol is partially oxidized into a hydrogen-rich mixture including carbon dioxide, water vapor, and other species. If operating on reformed gas, the PEFC is still technically a hydrogen fuel cell. For portable applications, a liquid alcohol solution can be directly used as fuel, and the reformation process occurs internally at the anode. The ultimate charge transfer at the anode and the cathode for the DAFC is the same as the hydrogen fuel cell. That is, protons and electrons are produced at the anode to generate current, and oxygen is reduced at the cathode. Unlike hydrogen oxidation, there are many intermediate reactions which occur in the DAFC anode to break the bonds of the original fuel until oxidation and charge transfer occur. This logically means the electrochemical efficiency of the DAFC is lower than a hydrogen PEFC, since the electrochemical oxidation reaction is more complex than hydrogen oxidation, and will therefore have comparatively higher activation losses. However, since the density of the liquid is much greater than gas-phase hydrogen, fuel storage is much more compact that compressed hydrogen. Additionally, with the use of liquid fuel, other ancillary systems

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(a)

(b)

R Figure 6.51 9-cm3 Mobion direct methanol fuel cell chips, which are used by Mechanical Technology, Inc. (MTI) as the power source for consumer electronics applications. The Mobion technology is based on a passively fed DMFC, with 100% methanol fuel. A power density of over 50 mW/cm2 can be achieved. (Image courtesy of MTI.)

such as the coolant and humidification subsystems can be eliminated. In the simplest case, the system contains only fuel storage and delivery/recirculation systems, the fuel cell, and microelectronics. By elimination of various subsystems, the portable fuel cell system profiles can become extremely compact, even though the fuel cell stack (without ancillary components) could be smaller if operating on pure hydrogen. Figure 6.51 shows 9-cm3 DMFC chips used to power consumer electronics. Direct alcohol fuel cells do suffer some drawbacks compared to hydrogen PEFCs: 1. Low operating efficiency 2. Reduced performance, due to more complex kinetics, and flooding issues 3. Increased cost per kilowatt due to much higher catalyst loadings, on the order of 1–8 mg/cm2 total (anode plus cathode) precious metal loading, compared to 0.2– 1.0 mg/cm2 total loading for the H2 PEFC However, considering the portable market, efficiency and cost are less important than system size, so these trade-offs are acceptable. The most developed DAFC is the direct methanol fuel cell (DMFC). Many prototype and nearly commercial DMFC systems exist for powering small electronics, laptop computers, cell phones, hand-held electronics, and other devices. Direct alcohol fuel cells are expected to occupy a growing market for portable power for years into the future. The search for high-performance alternative fuels to hydrogen has led to many candidates. Table 6.4 provides a summary of safety, thermodynamic, and other data collected on the potential candidates. Some fuels are potentially attractive alternatives due to ease of handling or improved safety ratings. As with any fuel cell, there is no perfect solution, and each potential fuel has its own limitations. Alternative fuels to hydrogen are an attempt to eliminate one or more of the disadvantages of another fuel. One way to think about alternative fuels is as hydrogen carriers. That is, they are high in hydrogen content but with a greater hydrogen density than hydrogen gas because they are typically stored in liquid or solid form. There are many potential fuels that can be used in portable applications where the desire is for a compact size and low efficiency and higher cost per kilowatt can be absorbed.

106.078 90.0468

118.0468 94.0468

C4 H10 O3 C3 H6 O3 CH2 O2 CH2 O (CH3 )2 O C2 H6 O2 C4 O4 H6 C2 O4 H2

Formic Acid Formaldehyde Dimethyl Ether (DME) Ethylene Glycol (EG)

Dimethyl Oxalate (DMO) Oxalic Acid

46.0156 30.0156 46.0468 62.0468

76.0624

C3 H8 O2

Dimethoxy-methane (DMM) Trimethoxy-methane (TMM) Trioxane

32.0312 46.0468

CH3 OH C2 H5 OH

Methanol Ethanol

1

1.148

1.1155

1.21 1.09

1.17

0.97

0.086

0.791 0.789

Density (g/mL)c

10 g/100 mL

N/A

> 10 g/100 mL at 20 ◦ C Completely Miscible Very Soluble 55 g/mL Soluble Miscible >= 10 g/ 100 mL at 17.5 ◦ C Limited

N/A

N/A

2.1 N/A N/A 0.01

N/A

14.4

4.6 N/A

Evaporation Rate (relative to butyl acetate = 1)c

N/A

Completely Miscible Miscible >= 10 g/ 100 mL at 23 ◦ C 33 g/100 mL

Solubility in Waterc

−18 13

−105/42 −53/101–102

189/190

52/163.4

8.3/100.7 −118/−19.5 −138.5/−22 −13/195

N/A

75

69 60 −41 111

45

12 12

−98/64.6 −114.1/78.3

64/114.5

Flash Point (◦ C)c

Freezing/ Boiling Point (◦ C)c

(Continued)

43 Ah/ga

3.18 Ah/ga

N/A N/A N/A 4.32 Ah/ga

N/A

N/A

N/A

5.03 Ah/ga N/A

Theoretical Capacity

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Molecular Weight (g/mol)c

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Chemical Composition

Properties of Various Methanol Alternatives Being Considered for Portable Fuel Cell Use

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c06 Char Count=

341

342 Can evolve formaldehyde when heated strongly or in contact with strong acids. Permitted as an additive in food for human consumption. Toxic. Proved very harmful to test animals. Cancerous Mild anesthetic. Large quantites can cause bloodthining.c Mildly toxic by skin contact. A suspected carcinogen. N/A

Oral irritant (poisonous if swallowed) C2 O4 H2 + 1/2O2 → 2CO2 + H2 O

N/A 2/2/0b

3/2/0b 2/4/0b 2/4/1c 1/1/0b N/A 3/1/0b

Formic Acid

Formaldehyde Dimethyl Ether (DME)

Ethylene Glycol (EG)

Dimethyl Oxalate (DMO) Oxalic Acid

Peled (A38 - A41) b http://www.orcbs.msu.edu/nfpa/nfpa.html c http://chemfinder.cambridgesoft.com/ Source: Adapted from Ref. [43].

N/A

C4 O4 H6 + 1/2O2 → 4CO2 + 3H2 O

C2 O2 H6 + 2H2 O → 2CO2 + 2H2 O

Lower Energy Conversion than Methanola Lower Energy Conversion than Methanola N/A

CH2 O + O2 → CO2 + H2 O N/A (CH3 )2 O + 3H2 O → 2CO2 + 12H+ + 12e− N/A

CH2 O2 + 1/2O2 → CO2 + H2 O

Hydrolyzes in the fuel cell to produce methanol Hydrolyzes in the fuel cell to produce methanol N/A

20:1

a E.

C4 H10 O3 + 5O2 → 4CO2 + 5H2 O

N/A

1/3/2c

Dimethoxymethane (DMM) Trimethoxymethane (TMM) Trioxane

Membrane Crossover (causes mixed potential, parasltic O2 consumption) Carbon-Carbon bonds make CO2 formation very difficult

Efficiency Losses

January 26, 2008

C3 H6 O3 + 3O2 → 3CO2 + 3H2 O

Concentrations below 1000 ppm C2 H5 OH + 3O2 → 2CO2 + 3H2 O usually produce no signs of intoxication. It is a central nervous system depressant in humans. Irritates Eyes, Skin, and Airways C3 H8 O2 + 2O2 → 3CO2 + 4H2 O

0/3/0c

CH4 O + O2 → CO2 + 2H2 O

Ethanol

Skin/Eye irritant, Poisinous in large quantities

Global Reaction

1/3/0

c

NFPA Hazard Rating (H/F/R) Toxicity

Methanol

(Continued)

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Table 6.4

c06 Char Count=

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6.4.1 Direct Methanol Fuel Cell The global electrochemical reactions for the DMFC are as follows: Anode oxidation reaction: CH3 OH + H2 O → 6e− + 6H+ + CO2

(6.42)

Cathode reduction reaction: 6H+ + 32 O2 + 6e− → 3H2 O

(6.43)

CH3 OH + 32 O2 → 2H2 O + CO2

(6.44)

Overall cell reaction:

Notice that at the anode some water is consumed in the global oxidation reaction, although the overall fuel cell is still a net water generator. On the cathode of the DMFC, the main reactions are the same as for the hydrogen fuel cell. Even though methanol and water are used as the fuel, charge transfer at the anode catalyst and through the electrolyte is still the same; hydrogen protons are generated by the methanol oxidation and travel though the electrolyte. The DMFC has similar design features as the hydrogen PEFC, except that a liquid solution of methanol and water is used as the fuel, rather than hydrogen gas. A schematic of the various transport phenomena in a DMFC is shown in Figure 6.52. In the DMFC, a liquid solution of methanol and water is fed to the anode and air is supplied to the cathode. At the anode side, a countercurrent flux of carbon dioxide bubbles formed via electrochemical reaction fights through the DM against the liquidphase transport of methanol from the flow channel to the catalyst layer. Due to the potential

Figure 6.52 Schematic of direct methanol fuel cell and associated mass transfer processes. (Courtesy of K. Sharp, Penn State University.)

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blockage effect and the need to efficiently transport methanol solution to the anode surface, the anode-side DM material is typically highly hydrophilic porous carbon cloth or paper. On the cathode side, the same flooding issues prevalent in the hydrogen PEFC are even more severe, since the diffusion gradient from the anode to the cathode is always toward the cathode and the electro osmotic drag coefficient is higher (∼2–5) for liquid contact with the membrane due to Schroeder’s paradox. To mitigate flooding and achieve a more favorable net water transport coefficient, a highly hydrophobic microporous layer and DM are typically used. For the DMFC, both anode and cathode activation polarizations are significant. However, reduced performance compared to the H2 PEFC is tolerable in light of other advantages of the DMFC, namely: 1. Because the anode flow is mostly liquid (gaseous CO2 is a product of methanol oxidation), there is no need for a separate cooling or humidification subsystem. 2. Liquid fuel used in the anode results in lower parasitic pumping requirements compared to gas flow. In fact, many passive DMFC designs operate without any external parasitic losses, instead relying on natural forces such as capillary action, buoyancy, and diffusion to deliver reactants. 3. The highly dense liquid fuel stored at ambient pressure eliminates problems with fuel storage volume. With highly concentrated methanol as fuel (>10 M), passive DMFC system power densities can compare favorably to advanced Li ion batteries. 4. No reformer system is needed. 5. Methanol is ubiquitous and transportable, and an infrastructure already exists. The DMFC solves many problems associated with the hydrogen PEFC system; however, there are of course limitations to the DMFC. The main technical issues affecting performance and design are as follows: 1. Water Management Even though external humidification is not needed in the DMFC, prevention of cathode flooding is critical to ensure adequate performance. 2. Methanol Crossover There is a high crossover rate of methanol from anode to cathode because of the high concentration of methanol at the anode side. This results in a mixed potential at the cathode from crossover methanol oxidation and greatly reduces the open-circuit voltage of the DMFC from the theoretical value of ∼1.2 V to around 0.7–0.8 V. 3. Poor Anode Kinetics The kinetics are inherently slower because of the more complex anode oxidation reaction. Tafel kinetics are appropriate at both electrodes, and compared to the H2 PEFC, an order-of-magnitude higher precious metal loading is typically used. 4. Counterflow and Removal of Carbon Dioxide Carbon dioxide is produced at the anode surface, resulting in countercurrent two-phase flow in the anode DM that can block access to the catalyst layer. 5. Methanol Safety Methanol is slightly toxic, spreads more easily into the ground than gasoline, and is highly flammable and miscible in water so that contamination with reservoirs is very simple.

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Water Management in DMFC In DAFCs, some water is needed at the anode to provide additional oxygen for the oxidation reaction. As a result, flooding at the cathode can be more severe because the diffusion gradient will favor flow toward the cathode and electroosmotic drug is enhanced. From Eq. (6.42), 1 mol of water is needed per mole of methanol for the overall oxidation reaction. One can define an anode methanol and an anode water stoichiometry in this case: λCH3 OH =

n˙ CH3 OH

i A 6F

λH2 O =

n˙ H2 O

i A 6F

(6.45)

Ideally, some of the water generated in the reaction at the cathode can be directed to the anode, and concentrated methanol can be used as the feed fuel, reducing the fuel storage volume requirements. This balance can be achieved passively if the net transport coefficient can be maintained to the proper level using capillary pressure management or other techniques. For the DMFC n˙ H2 Onet,a−c = αd

iA F

(6.46)

From Eq. (6.45), if α d = −0.17, then operation on neat methanol with only product water back-fed to the anode can be theoretically achieved. Each DAFC will have a different value for this coefficient, depending on the number of electrons exchanged in the fuel oxidation. This condition must be achieved with a capillary or gas-phase pressure difference, since the electro-osmotic drag and diffusion are always toward the cathode in the DMFC. Practically, methanol crossover reduces performance, so that some methanol dilution is typical, as described in the next section. External humidification is not needed in the DMFC, due to the liquid anode solution, but prevention of cathode flooding is critical to ensure adequate performance. To combat flooding and methanol crossover in the DMFC, several approaches have been used, as schematically shown in Figure 6.53: 1. Increased Electrolyte Thickness diffusion through Fick’s law:

This also limits the methanol crossover from

n˙ x-over = D A

Ca − Cc δPEM

(6.47)

where δ PEM is the electrolyte thickness and D is the diffusion coefficient of methanol in the electrolyte. As δ PEM increases, the diffusion rate of water decreases. However, this solution reduces performance since the path length of ion travel is increased. In typical DMFCs, the electrolyte thickness is greater than 100 µm to limit methanol and water crossover. 2. Capillary Pressure Management Use of a highly hydrophobic microporous layer on the cathode can be used to maintain a capillary pressure difference between the liquid-filled hydrophilic pores of the cathode and anode, and pump water (and crossover methanol) back toward the anode by capillary pressure forces. 3. High Cathode Flow Rate The crossover water and generated water can be removed by a high flow rate of dry air. This has the drawback of increasing parasitic losses for the cathode flow. However, many compact fans provide adequately high flow rate.

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Polymer Electrolyte Fuel Cells Diffusion barrier DM CL

CCH3OH

PEM

CL

DM

Crossover CH3OH

Air flow

Sharp drop

Methanol solution (a) DM

CL

PEM

CL

DM

CCH3OH Air flow

Methanol solution (b)

DM

CCH3OH

CL

PEM

CL MPL

Capillary backflow of water/CH3OH

DM

Air flow

Methanol solution (c)

Figure 6.53 Schematic of various water and methanol management approaches used in DMFC: (a) diffusion barrier approach, (b) thicker membrane approach, and (c) capillary back flow management.

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To prevent flooding by airflow, the cathode air flow must be adequate to remove water at the rate that it arrives and is produced at the cathode surface. The water arrival and production at the cathode surface by diffusion, electro-osmotic drag, and hydraulic permeability can be expressed by Eq. (6.46). For the case where the cathode is just flooding, the diffusion to the cathode will be minimal. Therefore, an estimate of the minimum amount of water that must be removed by the cathode to avoid flooding without capillary pressure management can be derived by balancing the water generated and dragged by electro-osmosis to the cathode with the drying capability of the cathode flow. The maximum amount of water vapor that can be removed at the exit for an air cathode can be shown as [44]   Pg,sat (T ) iA (6.48) n˙ H2 O,removed = (λc − 1) 0.84F Pt − Pg,sat (T ) where λc is the cathode stoichiometry at operating conditions and Pg,sat is the saturation pressure. In this calculation, the assumed oxidizer is air, which results in the factor of 0.84 in the denominator. This does not allow for water removal in the liquid phase. For the case of flooding just at the exit, Pt is equal to the total pressure of gas leaving the fuel cell. The minimum stoichiometry required to prevent liquid water accumulation in the limit of zero water diffusion through the membrane can be shown as  2.94     Pg,sat /(Pt − Pg,sat ) + 1 in air λcathode, min = (6.49)  14   + 1 in O2  Pg,sat /(Pt − Pg,sat ) The factor of 1 in Eq. (6.49) is a result of the consumption of oxygen in the cathode by the electrochemical oxygen reduction reaction. A plot of this minimum boundary as a function of pressure over the relevant temperature range is shown in Figure 6.54. This boundary serves as a baseline for discussion purposes. Depending on the use other methods to control the net drag coefficient of water, this boundary can shift considerably.

Figure 6.54 Plot of minimum stoichiometry requirements for flooding avoidance as function of operating temperature and pressure for DMFC. (Adapted from Ref. [44].)

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It can be seen that, without capillary pressure management, the minimum cathode stoichiometry for a DMFC is determined by flooding avoidance rather than by electrochemical requirements. Therefore, cathode stoichiometries in the DMFC are typically much greater than unity. Also note from Figure 6.54 that the lowest curve is that of air at 3 atm pressure with no electro-osmotic drag. For this curve, Eq. (6.49) was modified to eliminate the electro-osmotic drag term, which represents a result achievable by capillary pressure management. This results in a vast reduction in the required cathode flow rate to avoid flooding and shows the potential of capillary pressure management to improve performance. Methanol Crossover Another critical issue in the DMFC is methanol crossover from the anode to the cathode from diffusion, electro-osmotic drag, and hydraulic permeation. Methanol crossover from the anode to the cathode results in the following performancelimiting effects: 1. A mixed potential on the cathode and oxidation of methanol at this location both poison the cathode catalyst, consume oxygen, and greatly reduce the OCV, even more so than hydrogen crossover in H2 PEFC systems. Typical OCVs of DMFCs are significantly below 0.8 V. 2. The parasitic leakage of fuel through the membrane without current generation represents an inefficiency. Without special design, or purging on shutdown, the leakage will continue and consume methanol under idle conditions. Methanol crossover to the cathode is quickly oxidized to CO2 via Eq. (6.42). This consumes O2 , dilutes the cathode flow, and creates a mixed potential parasitic current (Ip ) reaction at the cathode: I p = 6F n˙ CH3 OH,cathode

(6.50)

The loss from this equivalent current can be modeled in the same way as hydrogen crossover shown in Chapter 4. Methanol crosses from anode to cathode by diffusion, hydraulic permeability, and electro-osmotic drag: n˙ CH3 OH = −D A

 kkr Pc−a iA  Cc−a + λdrag − A x F µ l

(6.51)

Typically, the hydraulic permeability is either neutral or directed toward the anode by capillary pressure management. Of the three modes of methanol crossover, diffusion (estimated as 10−5.4163-999.778/T m2 /s [45]) is dominant under normal conditions, especially at higher temperatures. Since the driving potential for oxidation is so high at the cathode, the methanol that crosses over is almost completely oxidized to CO2 , which sets up a sustained maximum activity gradient in methanol concentration across the electrolyte. The electro-osmotic drag coefficient of methanol is estimated to be 0.16 CH3 OH/H+ [46], or 2.5y, where y is the mole fraction of CH3 OH in solution [47]. The electro-osmotic drag coefficient is relatively weak compared to water, which is a result of the nonpolar nature of the molecule.

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In order to combat methanol crossover, several approaches have been used: 1. Use of Dilute Methanol Solutions Use of a low-molarity solution (0.5–2 M) of methanol reduces the concentration of methanol at the anode, thus reducing the crossover. However, this approach results in unacceptably large fuel storage tanks and excessive water-pumping requirements. 2. Use of Thicker Electrolyte Similar to the water crossover, a thick electrolyte can restrict crossover but also limits performance via increased ohmic losses through the electrolyte. 3. Diffusion Barrier on Anode A diffusion barrier (shown in Fig. 6.53) is an alternative to the use of a thicker electrolyte that places the diffusion restriction at a location that will not affect ionic transport. With a diffusion barrier, there is a steep concentration gradient from the DM through barrier, so that the methanol concentration at the catalyst layer is minimized, reducing crossover [48]. 4. Capillary Pressure Management This establishes a hydraulic pressure gradient favoring liquid flow toward the anode (Figure 6.53). The use of capillary pressure management and an anode diffusion barrier permits simultaneous methanol and net water crossover management, so that highly concentrated methanol solutions can be used as the fuel source. Of the various methods to restrict methanol crossover, typically a combination of thicker electrolyte (∼100 µm) with diffusion barriers and capillary pressure management is used. This approach is the most successful because it simultaneously enables water and methanol management, with a high-concentration methanol solution at the anode, resulting in a compact system design. Anode Kinetics Since the cathode ORR is the same in DMFCs as it is in H2 PEFCs and the anode methanol oxidation is a complex series of intermediate reaction steps, Tafel kinetics are generally valid for both the anode and the cathode. The theorized intermediate reaction pathways are given in Figure 6.55 from [49]. There are believed to be two main routes to methanol oxidation. The preferred pathway is to generate formaldehyde (CH2 O), followed by formic acid (CH2 O2 ) oxidation to carbon dioxide (CO2 ). The nonpreferred route is also initiated by generation of formaldehyde, which then oxidizes to carbon monoxide (CO), finally oxidizing to produce carbon dioxide. The overall oxidation pathway (either preferred CH3OH

CH2OH

CH2O

COH

CH2O

COH

CO

HCOOH

COOH

CO2

Figure 6.55 Proposed methanol electrochemical oxidation pathway at DMFC anode. (Adapted from Ref. [49].)

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or nonpreferred) results in a six-electron, six-proton generation, but certainly not in a single step. The CO oxidation pathway is not preferred since CO is a known poison of platinum catalysts. Typically, a different catalyst, platinum ruthenium, is used because it facilitates oxidative removal of the CO at lower overpotentials than pure platinum [50] and therefore mitigates poisoning from the nonpreferred pathway. There have been myriad research efforts aimed at reducing the precious metal loading for DMFCs and decreasing the anodic activation polarization, with some success. However, even with advanced catalyst selection, the anodic reaction generally requires a high precious metal loading of 10 times a hydrogen fuel cell. Around 2–4 mg/cm2 of catalyst is typically needed (compared to ∼0.2 mg/cm2 for the H2 fuel cell) for the anode and cathode. The cathode electrode generally has to have additional catalyst loading to withstand the methanol crossover oxidation. Because of the high metal loading in the catalyst layers, use of a carbonsupported structure results in a prohibitively thick electrode (and high ionic transport losses) therefore, an unsupported catalyst electrode (i.e., without carbon supporting particles in the CL) design is typically used. The bottom line is that the DMFC anode kinetics are poor compared to hydrogen oxidation and require a higher catalyst loading. This probably eliminates the DMFC for all but portable applications. Carbon Dioxide Blockage and Removal At the anode side, a countercurrent flux of carbon dioxide bubbles formed via electrochemical reaction must travel through the anode, into the diffusion media, and out through the channel, against the liquid-phase transport of methanol solution from the flow channel to the catalyst layer (Figure 6.56). Because the vapor-phase density of CO2 is so much lower than the liquid fuel solution (∼1000 times!), the CO2 bubbles can quickly fill flow channels. At high current densities, the volume fraction of the carbon dioxide bubbles in the flow channels can reach up to 95% [51], reducing the area through which liquid-phase reactant can penetrate to the catalyst layer. Blockage of methanol solution transport to the reactive surface in the DM and flow channels can result in mass-limited performance. In portable system applications, a hydrophobic microporous membrane is often used to passively separate and reject the product CO2 to the atmosphere from the methanol solution flow that is recycled back to the anode.

Figure 6.56 Photograph of carbon dioxide bubble produced in anode reaction in anode flow channel of transparent DMFC. (Adapted from Ref. [52].)

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Table 6.5 Health Effects for Average 70-kg Human of Methanol Exposure Exposure

Amount in Body and Result

Background methanol in body Hold liquid methanol in hand for 2 min 0.8 L of aspartame-sweetened diet drink Drink 0.2 mL of methanol Drink >25 mL of methanol Inhale 40 ppm vapor for 8 h Inhale 15 ppm vapor for 15 min Inhale 2.5% vapor for 1 s

∼35 mg 170 mg 40 mg 170 mg >20,000 mg, Death 170 mg ∼150 mg Very dangerous, possible damage

Source: Based on data from the Methanex Corporation [53].

Methanol Safety Methanol safety is an issue in the design of DMFCs. Methanol itself is toxic in liquid and vapor form if imbibed orally or inhaled in large quantities and absorbs through skin, as shown in Table 6.5. It is also highly flammable and spreads more rapidly into groundwater than gasoline. Its colorless flame is difficult to detect, and the solution itself is more corrosive than gasoline. To be fair to methanol advocates, this is no different in most ways to the gasoline used by millions for automotive transportation on a daily basis or the caustic materials used in the batteries the DMFCs would replace. However, the fact that methanol vapor and liquid are not benign means that special precautions must be taken to provide safe power, and the system should be designed with little potential for leakage. 6.4.2 Other DAFCs Although the design and operation of the hydrogen and direct methanol fuel cells are the most developed among PEFCs, both the DMFC and the H2 PEFCs have significant limitations. Since the power density of a pure hydrogen PEFC is higher, the use of hydrogen alternatives is meant to overcome hydrogen system drawbacks and eliminate ancillary system components for system compactness. The particular designs of DAFCs are very similar to the DMFCs, except that other catalysts besides Pt–Ru may be used to have slightly better anode kinetics, and a different membrane electrode assembly and DM configuration may be used to manage water or crossover more effectively. In terms of kinetics and catalysts for DAFCs, a few general trends are notable: 1. In general, the more complex the molecule (i.e., the more bonds), the higher the activation polarization since there are more intermediate steps required for complete oxidation. 2. An intermediate reaction pathway in the carbon-containing fuel oxidation will include carbon monoxide, which poisons platinum catalysts at the low temperatures of PEFCs. Thus, a catalyst such as Pt–Ru that has a CO tolerance will generally be more effective than pure platinum. 3. A molecule with a carbon–carbon (C–C) bond is generally more difficult (higher polarization) to electrochemically oxidize than one without a C–C bond. Methanol and some other fuels do not have a C–C bond, while ethanol and other hydrogen alternatives do [54].

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Polymer Electrolyte Fuel Cells 1.0 21 oC operation 30 oC operation

0.8

Voltage (V)

c06

0.6

0.4

0.2

0.0 0

200

400

600

800

1000

1200

2

Current density (A/cm)

Figure 6.57 Polarization curve of a fuel operating at 21 and 30◦ C with a 10 M formic acid solution as fuel. Anode catalyst palladium, with platinum cathode catalyst. (Adapted from Ref. [55].)

Formic Acid and Formaldehyde The use of formic acid (HCOOC) or formaldehyde (CH2 O) for a DAFC has the potential to achieve better anode polarization kinetics than methanol, since formic acid and formaldehyde are intermediate reaction products in the overall methanol oxidation process and have no C–C bonds (Figure 6.55), so that lower activation losses should be achievable. The formic acid fuel cell has a particular potential because it may avoid significant CO generation and poisoning by avoiding the undesired pathway to CO oxidation proposed for methanol shown in Figure 6.55. A polarization curve from a formic acid fuel cell is shown in Figure 6.57. Besides the DMFC, the formic acid fuel cell is the most developed DAFC [e.g., 55–57]. The formaldehyde fuel cell had some early interest but is no longer being developed. From a health standpoint, formic acid and formaldehyde are undesirable choices because these are known toxins with a National Fire Protection Association (NFPA) health rating of 3. Formaldehyde is also chemically unstable, making it even more difficult to work with. While both are very soluble in water (formic acid is completely miscible), these compounds pose considerable health risks and have relatively low energy storage densities, considering the low electron transference numbers (n) of 4 and 2 for formaldehyde and formic acid, respectively. Dimethyl Ether Another potential alternative fuel is dimethyl ether (DME, CH3 OCH3 ), presently used as an aerosol and propellant for spray paints and agricultural chemicals and cosmetics and a potential diesel fuel replacement [58, 59]. The storage and handling of DME is similar to standard propane; DME can be stored as a liquid at 0.6 MPa in standard propane tanks, and it throttles to a gas at atmospheric pressure. This is similar to the fuel

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Throttle to lowpressure gas phase

Liquid butane under pressure

Figure 6.58 Butane and DME are both stored as liquid under pressure but are easily throttled to gas phase at atmospheric pressure.

in a butane cigarette lighter (Figure 6.58). Table 6.6 presents some basic thermochemical parameters of DME and other fuels for comparison. Besides the fuel storage advantage, following are some other specific benefits of the use of DME for fuel cells [60]: Ĺ High electron transfer number of 12 for complete oxidation (methanol is 6 and hydrogen is 2), resulting in reduced theoretical fuel requirement. However, this does also indicate a more complex molecule requiring a greater number of intermediate reaction steps and pathways and generally worse kinetics. Ĺ Lack of C–C bond makes complete direct electro-oxidation possible with minimal kinetic losses. Ĺ Reduced net crossover rate due to the reduced dipole moment of DME compared to methanol. Ĺ The low toxicity of DME is comparable to that of liquid propane. Comparatively, methanol is toxic upon skin contact and ingestion. Dimethyl ether has a higher autoignition temperature and lower flammability limit than gasoline [61], however. Table 6.6 Properties of DME and Comparative Fuels

Chemical Formula Boiling Pt, ◦ C Liquid density, g/cm3 @20◦ C Gas specific gravity relative to air Saturated vapor pressure at 25◦ C, atm Ignition temperature, ◦ C Explosion limits, % Net heating value, kcal/kg

DME

Propane

Methane

Methanol

Diesel Fuel

CH3 OCH3 −25.1 0.67 1.59

C3 H8 −42.0 0.49 1.52

CH4 −161.5 NA 0.55

CH3 OH 64.6 0.79 NA

N/A 180–370 0.84 NA

6.1

9.3

246

NA

NA

235 3.4–17 6,900

470 2.1–9.4 11,100

650 5.0–15 12,000

450 5.5–36 4,800

250 0.6–6.5 10,000

Note: Hydrogen lean flammability limit = 4%.

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Ĺ Handling properties are similar to those of propane and butane; therefore, existing liquid propane infrastructure and handling technologies can be used to store and transport DME. Ĺ Dimethyl ether will not spread into groundwater as does methanol. Ĺ The DME lower explosion limit is higher than that of propane, and DME has a visible flame. In comparison, hydrogen and methanol flames are nearly invisible. Ĺ Dimethyl ether can be produced with very low greenhouse gas emissions, especially if produced from biomass. M¨uller and co-workers examined DME fuel cell performance and fuel utilization compared to the DMFC at high pressure (5 atm) and temperature (130◦ C) and found performance similar to DMFC under these operating conditions [62], although the high pressure and temperature studied are not suited for portable applications. A few groups have published research on the DME PEFC and have shown substantial performance enhancement for elevated temperature (100–130◦ C) and pressure (4.5 atm) [60, 63]. Also, DME has been applied with good performance results in solid oxide [64] and molten carbonate [65] fuel cells. The fuel cell performance of the DME is still currently lower than the DMFC due to the more complex anode kinetics involved. Example 6.6 Determination of Anode and Cathode Global Reactions for DME mine the global anode oxidation and cathode reduction reactions for DME. SOLUTION

Deter-

The overall redox reaction is CH3 OCH3 + 3O2 → 3H2 O + 2CO2

At the anode, we take 1 mol of fuel and solve for the carbon dioxide generated as a product of oxidation by balancing on the carbon. Then, we add an appropriate amount of water to the reactants to balance the oxygen on both sides of the reaction. Finally, we add the appropriate number of protons and electrons on the products to balance the total hydrogen on the reactant side: CH3 OCH3 + 3H2 O → 12H+ + 12e− + 2CO2 For the DME fuel cell, the electron transfer number is 12. On the cathode side, the reaction is the same as the PEFC: 4H+ + 4e− + O2 → 2H2 O which can be scaled up to match the anode reaction by multiplying by 3. We can check the accuracy of the result by adding the oxidation and reduction reactions, making sure they add to the global redox reaction. COMMENTS: There are of course many intermediate reactions at the anode and cathode. Despite the high electron transfer number of 12, the elementary charge transfer step(s) at the anode involve only one or two electrons.

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Trioxane Trioxane (C3 H6 O3 ) is solid at room temperature (melting point is 64◦ C), has lower toxicity than methanol, and is derivable from natural gas. Other advantages of trioxane are as follows: 1. High electron transference number of 12 and hence high theoretical energy density 2. Lack of C–C bond 3. Lower anode-to-cathode crossover rate than methanol for the same electrolyte and an ability to control resting crossover loss by keeping in the solid phase until operation [63] 4. Higher boiling and flash points than methanol However, there is no significant trioxane fuel infrastructure, and the fuel must be above 55◦ C to dissolve sufficiently, which means a power-assisted startup is needed. Trioxane tablets or granules could be easily shipped and provide desired molar concentrations of fuel. Trioxane use in fuel cells was studied by Narayanan et al. [66], but the power density was much lower than a comparable DMFC. Dimethoxymethane and Trimethoxymethane Dimethoxymethane (DMM, C3 H8 O2 ) and trimethoxymethane (TMM, C4 H10 O3 ), can be grouped together due to their similar properties. Both are liquids at room temperature and have very low melting points and similar molecular composition and structure. While DMM is an irritant, it is not known to pose any long-term health risks. Initial interest in TMM and DMM arose from several advantages compared to methanol. Both TMM and DMM do not have any carbon–carbon bonds, both have higher energy storage densities compared to methanol, and TMM has a higher flash point and boiling point than methanol. Testing has shown that DMM sustained current densities three to four times that of TMM but less than a modern DMFC. While DMM showed significant promise, the main drawback appears to be lack of infrastructure and performance compared to methanol. Dimethoxymethane does have a potential for use that is unique considering the boiling point lies at 40◦ C at ambient pressure. Therefore, an operating fuel cell could be used to boil liquid DMM solution and create a flow of fuel and vapor without the use of a pump. Ethanol Ethanol (ethyl alcohol or grain alcohol, C2 H5 OH) is a clear, colorless liquid with a characteristic odor and is mildly toxic, although it has a NFPA health rating of 0 since it can be consumed and digested safely in moderate quantities. Ethanol has a number of potential commercial advantages. In some countries such as Brazil, ethanol already has a well-established infrastructure. Ethanol is a renewable energy source derived from the fermentation of sugar cane, corn, or other biodegradable sources. Because of a carbon–carbon bond, the ethanol fuel cell has a performance disadvantage related to the DMFC but has been studied by several researchers [67, 68]. The main disadvantages of ethanol use are the high activation polarization related to the C–C bond and the high relative cost. Besides high activation overpotential, fuel containing the C–C bond often suffer incomplete electro-oxidation and severe CO poisoning. Dimethyl Oxalate and Ethylene Glycol Like trioxane, dimethyl oxalate (DMO, C4 H6 O4 ) offers simplified handling as well as limiting crossover current because it is a solid at room temperature. Dimethyl oxalate also has a high electron transference number of 14

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(which concomitantly means a more complex molecule and generally unfavorable kinetics) but suffers from limited infrastructure and low demonstrated performance compared to methanol, due in part to molecular complexity and C–C bonds. Ethylene glycol (EG, C2 H6 O2 ) is ubiquitously used in the automotive industry as an engine coolant, and hence a distribution infrastructure already exists. Also, EG has a crossover current density roughly half that of methanol [69]. However, PEFC performance with EG is still relatively low, with a fuel cell specific energy density about 20–40% less than that of the same fuel cell utilizing methanol. Additionally, EG has been shown to rapidly degrade PEFC electrolyte material, which obviously limits its potential PEFC applications.

6.5

PEFC DEGRADATION Although begining of the life (BOL) performance is important, fuel cell and system durability and time-dependent performance are just as critical. The lifetime of a fuel cell is expected to compete with existing power systems it would replace. The automotive fuel cell must withstand load cycling and freeze–thaw environmental swings with minimal degradation (3–5%) over a lifetime of at least 5000 h. A stationary fuel cell must withstand over 40,000 h of steady operation with minimal downtime. The fuel cell environment is especially conducive to degradation, since a voltage potential difference exists which can promote undesired reaction, and PEFCs operate at slightly elevated temperature with a corrosive acid electrolyte. There are many phenomena that can result in gradual degradation and performance loss in PEFC systems. These include assorted chemical and mechanical degradation modes [70]. Many different modes of physicochemical degradation are known to exist that can generally be grouped into two categories: reversible and irreversible damage. The state-of-the-art in terms of performance degradation for a PEFC is on the order of 1–10 µV/h. However, this is at steady state in relatively high humidity conditions [71]. The degradation in PEFCs is exacerbated through many mechanisms. In general degradation is accelerated by 1. operation at high-temperature or low-humidity conditions, 2. aggressive load cycling from low to high cell voltages, and 3. large temperature or humidity swings in the environment, also including freezing.

6.5.1

Physical Modes of Degradation Reversible Modes of Physical Degradation Some modes of physical degradation are a result of reversible phenomena, including the following: 1. Diffusion Media Channel Intrusion Figure 6.59 illustrates the phenomenon of DM tenting, or sagging into gas flow channels. This phenomenon occurs mostly with flexible cloth DM. The result is a lack of contact with the catalyst layer under the channel and excessive pressure drop in the affected channel. In large stacks this can cause severe flow maldistribution effects and the gap created can serve as a liquid pooling location under the DM. This is reversible in principle by replacing the DM in the affected fuel cell.

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Land

357

Channel DM Catalyst layer PEM Gap

Figure 6.59 Diffusion Media tenting in flow channels, resulting in poor electrical contact and increased gas-phase pressure drop.

2. Flooding or Dryout These losses, already discussed, are reversible through a variety of methods, including changing flow rate of reactants or coolant and inlet humidification or coolant flow modification. 3. Reactant Starvation If a location in the catalyst layer of the anode or cathode is blocked with liquid or the flow rate to a stack cell is reduced due to maldistribution, poor performance from fuel or oxidizer starvation can result. Prolonged fuel starvation may result in voltage reversal and in some cases carbon corrosion, which is irreversible. 4. Voltage Reversal (Benign) Some fuel cell voltage reversal reactions are benign and thus reversible as soon as conditions in the cell are returned to normal. 5. Physical Intrusion of Unwanted Particulate Matter Dirt, sand, and other foreign matter it in the air can be brought into the fuel cell and block flowchannels. Irreversible Modes of Physical Degradation 1. Diffusion Media Plastic Deformation Under compression from the lands (usually >1.5 MPa), the DM can be plastically deformed. This may not be critical as long as the fuel cell stack remains assembled but may prohibit the reuse of the DM upon stack disassembly. 2. Catalyst Layer Cracking and Delamination Catalyst layers are typically sprayed, deposited, or spread onto the electrolyte from a viscous mixture. This mixture is then baked at an elevated temperature, which drives off volatile compounds in the catalyst mixture used to control mixture viscosity and dispersion. As a result, small fissures, or “mudcracks” are common in catalyst layers, as shown in Figure 6.32, with widths much greater than the average pore size in a continuous portion of the catalyst layer. Over time, and as a result of the electrolyte expansion and contraction with water content variation, these cracks can grow and lead to delamination or catalyst layer degradation. 3. Electrolyte Fracture Electrolyte fracture can result from rapid or severe temperature and or humidity cycling, including frozen conditions. Electrolyte fracture is not always catastrophic but results in increased hydrogen crossover, leading to failure over time. Freeze–thaw cycling can potentially also result in catalyst layer delamination, as shown in Figure 6.60.

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Figure 6.60 Scanning electron micrograph of membrane electrode assembly that had catalyst layer delamination resulting from unrestrained freezing in liquid water. The gaps caused by this delamination can serve as pooling locations for liquid during subsequent operation.

4. Diffusion Media Hydrophobicity Change As a result of regular operational cycling or minute impurities introduced from gaskets and other components of the fuel cell system [72], the wettability of the DM can change over time, altering the water management and increasing flooding. 5. Morphology Changes or Loss in Catalyst Layer or Other Components For all fuel cells, the catalyst layer ECSA is a determining factor in overall power density, and nanosized catalysts and supports are present in a complex three-dimensional electrode structure designed to simultaneously optimize electron, ion, and mass transfer. As a result, any morpholological changes can result in reduced performance. Commonly observed phenomena include catalyst sintering, dissolution and migration, catalyst oxidation, supporting material oxidation (e.g., carbon corrosion for carbon-supported catalysts), and Oswald ripening [71]. These effects result in loss of ECSA and are irreversible. 6. Pinhole Formation As a result of internal stresses, localized hot spots and dryout, or other factors, small pinholes can develop in the electrolyte (see Figure 6.61). This leads to a gradually increasing hydrogen crossover problem and eventual failure. Pinholes often occur at locations near the anode inlet and are believed to be germinated from one of three sources: (a) Dust or other impurities embedded in the electrolyte during manufacturing. This is highly unlikely, since quality control at electrolyte manufacturing plants now prevents this and the problem still exists.

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Figure 6.61 Photograph of pinhole found in PEFC electrolyte from Ballard fuel cell. (Reproduced from Ref. [71].)

(b) Mechanical stresses generated by locations of electrolyte dryout and high local temperature. (c) Local areas of membrane weakness caused by platinum migration from the cathode and subsequent precipitation inside the main electrolyte. These locations serve as nucleation sites for further damage growth. 6.5.2 Chemical Modes of Degradation Reversible Modes of Chemical Degradation 1. Certain Types of Gas-Phase Impurities There are several different species that preferentially absorb on the catalyst surface and can degrade the electrochemical activity of that surface. Platinum oxides on the surface of a catalyst can be cleansed with a quick excursion to low cell voltages (<0.4 V). Another major reversible poison is carbon monoxide (CO). Carbon monoxide poisoning is described in more detail later in this section. Other types of potential environmental pollutants can be detrimental to performance such as dust, aerosols, alcohol vapors, carbon dioxide, hydrocarbons, various sulfur-containing gases, ammonia, halogenated compounds, inert gases, and nitrogen oxides. Some of these pollutants cause reversible damage, and others, especially sulfur-containing compounds such as hydrogen sulfide, can cause irreversible loss of performance. 2. Coolant Conductivity Increase Since the coolant system is in contact with the entire stack, the coolant must be highly nonconductive. Over time, ionic impurities in the coolant stream can degrade the coolant performance, causing shorting within the stack and reducing performance. Coolant flushing or filtering can be used to reverse this effect, and the coolant recirculation system must also be designed to have minimal contact with potential sources of ionic impurities.

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Irreversible Modes of Chemical Degradation 1. Electrolyte Loss Electrolyte material can be lost through a variety of physicochemical mechanisms. For PEFCs, the polymer itself can degrade physically and chemically, particularly from peroxide radical attack [73]. This results in loss of mass and conductivity in the electrolyte and possibly catastrophic pinhole formation. Mechanical stress and cycling have also been linked to accelerated polymer degradation [74]. Over time, the electrolyte in a PEFC can thin considerably as the ionomer is lost. This can result in a temporary increase in performance, since the ohmic losses decrease with a thinner electrolyte. However, over time, the thinning electrolyte is more susceptible to pinhole formation and excessive crossover, leading to failure. This mode of damage is especially amplified in extreme conditions of high temperature and low humidity. In PEFCs, electrolyte degradation can be monitored by measurement of the fluorine content in effluent liquid and vapor and has been found to correlate with membrane degradation. 2. Platinum Dissolution and Migration Platinum migration from the cathode of a PEFC occurs due to the following steps [75]; a. Platinum dissolves into Pt–O in the catalyst layer at high potentials. On the cathode at high potential, a mobile Pt2+ species is created according to the reaction PtO + 2H+ ↔ Pt2+ + H2 O

(6.52)

b. The PtO is mobile in Nafion and can diffuse on the surface of Pt/C, further exposing underlying Pt in clusters. c. Under the voltage gradient between the anode and cathode, PtO migrates away from the catalyst layer through the electrolyte toward the anode. The result is an irreversible loss with fewer active sites in the cathode for the reaction, resulting in a gradually decreasing exchange current density (i0 ) at the cathode. Under load cycling to high cathode potential, the degradation rate is greatly accelerated. This is because of the continuous formation and disruption of mobile oxide film leading to mobile Pt2+ species. The bottom line is that Pt is susceptible to dissolution and migration toward the anode under high potential and load cycling conditions, leading to loss of ECSA. 3. Ionic Impurity Contamination Ionic impurities from metals in the fuel cell system will readily absorb into the fuel cell electrolyte, since it is an ionic conductor. When the ionic impurity gets into the membrane, it can greatly reduce the ionic conductivity and alter water transport in the membrane and catalyst layers, reducing performance from very minute quantities of impurities [76]. Postmortem testing of used membrane electrode assemblies (MEAs) has demonstrated the presence of a surprising array of metallic impurities, such as calcium, iron oxides, copper, magnesium, and various other metals, as shown in Figure 6.62. As a result, most fuel cell systems are designed to avoid contact of the reactant flow stream with any metal connectors or couplings, and special plastics deemed compatible for fuel cell service have been developed for fuel cell systems. 4. Degradation of Hoses and Gaskets Oxidation of components such as metallic current collectors, gaskets, and hose components and fittings can become a major loss in fuel cells over time [77]. The oxidation and decomposition products

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Figure 6.62 Bar chart with cationic impurities found in Nafion 112 electrolyte operated at 0.25 A/cm2 at 75◦ C after 9300 h of operation. (Reproduced with permission from Ref. [76].)

from these materials can permanently change the ionomer conductivity and wettability of components, changing the water management or accelerating membrane degradation. Carbon Monoxide Poisoning In the near term, it is likely that a majority of the hydrogen produced will come from a hydrogen reformation process, in which a carbon-containing fossil fuel (e.g., natural gas or methanol) is partially oxidized into a mixture of mostly hydrogen, carbon dioxide, and water [78]. One of the undesired byproducts of the reformation process is a small fraction of carbon monoxide (CO). Although the amount of CO in the feed stream varies for different reformation processes, even small levels of CO can adversely affect the performance of low-temperature noble metal catalyst fuel cells, such as the PEFC. As a result, a large portion of the total fuel cell reformer system must be devoted to CO removal. Even with bulky and complex CO scrubbing subsystems, nominal CO levels can still be in the 10–50-ppm range, and transient operation during load changes or startup can produce sporadic pulses above the 1000-ppm level. The complexity involved in dynamic control of the reformation subsystem is a barrier in transient automotive and military fuel cell systems, where it would be especially desirable to utilize a conventional liquid fuel with onboard reformation to circumvent hydrogen infrastructure limitations. Although there are alternative theories, the global reaction mechanism of CO poisoning of hydrogen PEFCs with platinum catalyst has been modeled by Springer and co-workers [79]: CO + M ← −−−−−−−→ − (M–CO)

(6.53)

H2 + 2M ← −−−−−−−→ − 2(M–H)

(6.54)

k1 f k1R k2 f k2R

(M–H) −−−−−−−→ H+ + e− + M k3 f

(6.55) +

−

H2 O + (M–CO) −−−−−−−→ M + CO2 + 2H + 2e k4 f

(6.56)

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The forward reactions of Eqs. (6.53) and (6.54) dominate the reverse reactions and respectively represent the parallel processes of CO adsorption and H2 dissociative chemisorption on an active and available platinum catalyst site, M. Equation (6.53) is the CO poisoning step. Here, adsorbed CO takes up active catalyst surface sites, rendering them unavailable for hydrogen dissociative chemisorption of Eq. (6.54) and the desired current-producing hydrogen electrochemical oxidation reaction of Eq. (6.55). In steady state, surface coverage of CO sites with gas streams containing as little as 100 ppm CO can reach 95%. This blockage of available catalyst sites results in reduced fuel cell efficiency (lower cell voltage for identical current). Equation (6.56) is the electrochemical oxidative desorption of CO from the catalyst site and is the rate-limiting step in the overall mechanism. Based on the mechanisms proposed in Eqs. (6.53)–(6.56), an expression relating the time-dependent fractional surface coverage of the CO (θ CO ) species can be shown [79]: ρ

  αCO Fη A dθCO = k1 f yCO (1 − θCO − θH ) − K 1R θCO − k4 f θCO exp dt RT

(6.57)

where the first term on the right-hand side represents the CO adsorption on the catalyst surface (poisoning step), the second term represents the desorption of CO (reverse of poisoning), and the third term represents the electrochemical oxidative desorption rate equation (6.56). Due to the uncertainty in the various kinetic parameters, the fuel cell dynamic performance is very difficult to predict without use of arbitrary fitting parameters. Carbon monoxide poisoning remediation technology is fairly developed, including air bleeding, alternate catalyst selection, and other methods. In air bleeding, a small percentage (usually <5%) of air is mixed with the anode flow to promote chemical and electrochemical oxidation of CO and reduce poison coverage of the anode catalyst [80]. The drawback of this technique is increased pumping requirements and electrochemical potential losses associated with fuel/oxidizer mixing in the anode feed. Additionally, the mixing of moist air and hydrogen poses safety concerns. The use of CO-tolerant catalysts such as Pt–Ru can greatly reduce the performance loss for operation on moderate amounts of CO in the fuel feed stream. In summary, various modes of physical and chemical degradation exist, which limit life times of operating DEFCs. In particular, membrane moisture variation or chemical impurities can rapidly degrade performance and must be controlled.

6.6

MULTIDIMENSIONAL EFFECTS In the study of fuel cells, there is a natural tendency to imagine the profiles of heat, mass, current, and other parameters as uniform across the active area. There is also a natural tendency to think that a perfectly homogeneous distribution of these operational parameters is ideal. In fact, almost nothing is uniform in PEFC stack operation in the channelwise, through-plane, or plate-to-plate directions. From an engineering design perspective, many of these gradients can be intentionally exploited for performance optimization. An excellent example already discussed is that of water management and temperature distribution. In order to provide a fully moist condition throughout the fuel cell without excessive flooding and simultaneously reduce the load on the humidifier system, the temperature distribution can be adjusted through the coolant flow rate to increase steadily from the inlet region to

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the exit region, so that the relative humidity of the flow is approximately uniform and 100% throughout and the water generated is absorbed as vapor reducing flooding. The computational or analytical prediction of the current, species, and temperature distributions in a fuel cell can be generated by extension of the basic concepts of this text into multidimensional models with various levels of complexity and solved using the tools of computational fluid dynamics (CFD). Models of various complexity abound in the literature, and commercial packages now exist from several CFD software developers for this purpose. Water and Species Distribution Along the channel path from inlet to exit, one can anticipate a reduction in the hydrogen and oxygen species concentrations that follow the consumption by the electrochemical reactions. The mole fractions of the reactant species may not be decreasing, however, since humidification or dehumidification of the flow can alter the water mole fraction. Consider a wet anode input with a dry cathode input and cocurrent flow, depicted in Figure 6.63. Conditions of dehumidifying flow can actually increase the reactant mole fraction, even with consumption, as shown in Figure 6.64. As the flow enters, the net drag will be heavily positive, favoring flow of water from the humidified anode inlet toward the dry cathode. The result will be a decreasing water mole fraction, and increasing hydrogen mole fraction along the anode, despite the fact there is hydrogen consumption along the channel. At the point where the water vapor concentration on the anode and cathode are the same, there will be a diffusion flux reversal point. Temperature Distribution Along the fuel cell channel, the temperature distribution is directly controlled by the heat transfer boundary conditions. For small fuel cell stacks, with no active coolant flow, the external boundary conditions control the temperature distribution and at low current can be considered as uniform in temperature. For larger stacks with active cooling, the temperature distribution can be engineered to match the desired humidity profile to control flooding and promote longevity by elimination of dry- and hot-spot locations. In the in-plane direction, temperature variation exists, with more water accumulation under generally colder lands, as discussed. The temperature distribution in the stack can be fairly Dry cathode inlet

Diffusion reversal location -net flux reversal may be different location Electrolyte/electrode assembly

Net water drag toward cathode

Moist anode inlet

Figure 6.63 Schematic of dry cathode–wet anode inlet flow that results in diffusion reversal process in electrolyte. The arrows represent the direction of diffusion flux, not the net mass flux. (Adapted from Ref. [11].)

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Figure 6.64 Water vapor and hydrogen mole fraction distributions for a concurrent flowing serpentine isothermal fuel cell with 100% RH anode inlet, 0% RH cathode inlet at 0.7 V operation. Even though current is being produced and hydrogen consumed, the hydrogen mole fraction along-the-channel is increased near the inlet due to dehumidification of the anode. (Adapted from Ref. [11].)

well predicted using known thermal parameters and voltage current behavior to predict heat generation. Current Distribution The current distribution in a PEFC can be measured experimentally with a variety of techniques, as discussed in Chapter 9. For larger fuel cell active areas, gradients in temperature, reactant concentration, humidity, and liquid water can drastically alter the local current density and should be considered in any advanced analysis. In order to predict the current distribution in a cell on a qualitative basis, one has to keep in mind the major driving forces that control the current at a given voltage: 1. Local relative humidity 2. Local reactant concentration 3. Local liquid water distribution Since the temperature in the PEFC typically varies by at most ∼15◦ C, the effect of temperature distribution on the reaction kinetics will be relatively small compared to the temperature interaction with the liquid water distribution and relative humidity that controls membrane ionic conductivity. The local relative humidity in the anode phase typically controls the local current density of an underhumidified fuel cell because electroosmotic drag exacerbates anode dryout, while water generation at the cathode diminishes any electrolyte dryout in the cathode catalyst layer [11]. That is, if the other parameters are constant, the local current distribution can be predicted with a knowledge of the anode in an underhumidified cell [11]. Anode dryout can be the result of the loss of only a few hundredths of a milligram of water per square centimeter active area in the catalyst layer

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Water flux reversal to anode

Balanced water content inlet

Current

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inlet

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Peak height increased with current, net water imbalance

Dip due to anode dry-out at high i Region I

Multidimensional Effects

Region II

Flooding/concentration losses (may or may not occur) Region III

Location (x/L)

Figure 6.65 Ref. [11].)

Characteristic local current curve for undersaturated inlet conditions. (Adapted from

[10]. Since the catalyst layer is only on the order of 15 µm thick and consists of about 30% ionomer by weight, a very small amount of local drying can significantly decrease the ionic conductivity of the catalyst layer. Figure 6.65 is a sketch of the generic relative current versus location along the flow channel for different combinations of inlet humidity on the anode and cathode with a concurrent serpentine design and is key to understanding local performance for underhumidifed conditions. The generalized performance curve is qualitatively sinusoidal in shape (although not necessarily symmetric or with equal amplitude or wavelength, as shown for convenience). These results were obtained for a uniform coolant temperature boundary condition, so any effects of a nonuniform temperature are not included. Region I begins at the inlet of the fuel cell. If the anode is dryer than the cathode and the current is relatively low, the net flux of water is always neutral or toward the anode, resulting in an increasing performance through region I. The steepness of the slope of this portion is exacerbated with increased moisture imbalance between anode and cathode, increased current density, and other thermodynamic and geometric parameters. In contrast, if the water vapor imbalance initially favors the anode (dryer cathode), diffusion and electro-osmotic drag are both initially toward the cathode, resulting in a drying condition at the anode catalyst layer and electrolyte, reducing performance until a local minimum is reached, which terminates region I. The minimum in performance is exacerbated by increased current density and moisture difference between anode and cathode as well as flow rates and other thermodynamic and geometric parameters. Note that for closely hydrated anode and cathode at low to moderate current density performance in region I can be homogeneous, as illustrated in Figure 6.65. Note that the end of region I is shown as the same current for dry anode and dry cathode conditions, when this is not necessarily the case. In fact, region II for a relatively dry anode inlet is really a continuation of region I and no discrete boundary between the two regions is defined. In region II, the case with relative dry anode feed continues increasing performance to a maximum (if reached), which ends region II. The decrease from the maximum current is

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a result of decreasing reactant availability or flooding and depends on operating conditions, and therefore may not be severe, as shown in Figure 6.65. The dry relative cathode case begins region II at the point of water mass flux reversal from cathode to anode. In this situation, this reversal may not occur with a thick electrolyte if back diffusion never overcomes electro-osmotic drag to the cathode. This flux reversal reduces anode-side dryout performance loss and initiates an increase in performance. For both the dry relative anode and cathode cases, region II concludes with a maximum in performance. Note that the location of the maximum is dependent on the fuel cell and operating conditions. In region III, for convenience, both dry anode and cathode cases are shown to peak at the same location, although this depends on the individual conditions and is not necessarily the case. Following the maximum local current, there is a downward trend resulting from local flooding or gas-phase mass transport losses at the electrode(s). This peak and downward trend will only occur if a reactant starvation condition (via flooding or high utilization) is reached. The generalized performance curve of Figure 6.65 closely follows anode gas channel water vapor content through region II, indicating anode catalyst layer and electrolyte moisture content plays a key role in controlling the distributed performance of an undersaturated inlet PEFC. Cathode conditions are generally locally moist at the catalyst layer and control the location of the maximum performance which initiates region III. The region I trend depends on the side with greatest hydration and local water activity. The amplitude of the peaks is increased with increasing current density and water imbalance between anode and cathode at the inlet. The width of regions I–III depends on current density, flow rate, water imbalance, and membrane and electrode thicknesses as well. In general, under high-humidity conditions with neat hydrogen flow, the current profile follows oxygen distribution. The current distribution is reduced along locations of flooding, which typically occurs near the cathode exit or in cold spots in the fuel cell under landing areas. In this case, excessive liquid water buildup restricts oxygen flow to the catalyst layer, and local current can be greatly reduced. In single-cell and stack situations, it is quite possible that certain locations of the fuel cell are dry, and others are flooded. Example 6.7 Qualitative Prediction of Current Profiles in Simple Fuel Cell System For an isothermal neat hydrogen fuel cell at moderate current density with adequate cathode flow stoichiometry, sketch the current distribution from inlet to exit for the following cases: (a) (b) (c) (d)

Fully moist inlet anode and cathode, concurrent flow Dry anode and cathode inlet, concurrent flow Dry anode and cathode inlet, countercurrent flow Dry cathode and fully moist anode inlet flow, concurrent flow

SOLUTION (a) In this case, the flow is fully moist at both the inlets, so that the current should be dominated by the oxygen mole fraction. The current should decrease from the inlet to the exit in a decaying fashion, since the oxygen consumption will follow the same qualitative shape as the current decays. At some point, the effects of flooding will likely induce severe performance loss, as sketched.

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Current Density

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(b) In this case, both the anode and cathode are dry, and thus the performance should be quite low at the inlet and gradually increase as water is produced along the channel and hydrates the electrolyte. If the flow path is long enough, the performance will peak when the membrane is fully humidified and can eventually decrease due to flooding effects.

Possible flooding Current Density

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(c) In this case, both the anode and cathode are dry but the flow is countercurrent. This is a flow configuration often employed in portable applications, where no humidifier system is used. In this underhumidified case, the performance should be dominated by the anode moisture content. Along the anode flow channel, the moisture content will gradually increase to a peak as moisture is transferred by diffusion from the cathode, then it should decrease toward the exit as the moisture is transferred back to the cathode. The current profile will look follow the water

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uptake trend, although the peak current location will depend on the relative flow rates of the anode and cathode dry flows.

Current Density

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Cathode

(d) In this case, the current distribution will be dominated by anode moisture content, since the overall flow is underhumidified. As the water is transferred from the moist anode to the cathode, the current will decrease to a minimum then increase again after flux reversal. Given a long enough channel length, the performance will eventually decline due to flooding. Possible flooding

Current Density

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COMMENTS: The sketches drawn should be thought of as qualitative tools only, to help in understanding the internal distributions of the various controlling parameters.

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6.7 SUMMARY The goal of this chapter is to present the reader with a summary of the operational issues and design constraints of the PEFC. Within the PEFC scope is the hydrogen-powered PEFC and the alternative fuel PEFC, normally called a DAFC, since the vast majority of the alternative fuels proposed are alcohol based. The DAFCs all have inherently reduced fuel cell performance compared to the H2 PEFC because the anode kinetics are more complex. Additionally, issues of fuel and water crossover and anode catalyst poisoning from intermediate reactions further reduce the performance relative to the hydrogen fuel cells. The reduced performance of DAFCs is deemed tolerable in portable applications, however, where system size and simplicity are valued more than efficiency. Portable DAFC systems can be designed to eliminate the humidification, cooling, and bulky hydrogen storage needed for H2 PEFC systems. Despite the fact that the PEFC is a water generation reactor, some humidification of the reactants is usually necessary to enable high performance and longevity. A dry inlet feed results in poor local performance, hot spots, and internal stresses that can lead to short lifetimes. There are various active and passive humidification methods used to accomplish humidification, including membrane humidification, direct injection, and internal or external recirculation. One of the most difficult engineering challenges in the PEFC is achieving a net water balance without flooding. Like dryout, a flooding condition with liquid water accumulated in the pores of the various media or in the flow channels can reduce performance and exacerbate various degradation mechanisms. From a global perspective, we seek to remove the net water produced from the fuel cell to maintain a steady-state condition in terms of water storage in the fuel cell. This condition is accomplished via Eq. (6.16), derived from a control volume balance on the entire fuel cell assumed at steady state and repeated here: 

λO 2 yO2 ,in,dry

−1



χout,c 2

 −

λO 2 yO2 ,in,dry



χin,c 2

1 − χout,c 1 − χin,c  n˙ slugs,out,a + n˙ slugs,out,c

+ =1 i A 2F

 +

λH 2 yH2 ,in,dry

− 1 χout,a

1 − χout,a

 −

λH 2 yH2 ,in,dry



χin,a

1 − χin,a

whereχ = RH · Psat (T )/P. The condition of a balance can be obtained in practice through tailoring the inlet humidity, flow rates, exit temperature (through coolant flow manipulation), and pressure drop though the fuel cell. Since a condition of exact balance is rarely achieved and an overall balance may not satisfy the desire for maximum performance, the fuel cell is typically operated in a slightly flooded situation, and a periodic growth and rejection cycle of liquid droplet slugs from the fuel cell achieves a quasi-steady balance condition. Even when the fuel cell achieves a global water balance, there can be areas of dryout and flooding inside the fuel cell itself. Water transport inside the fuel cell through the electrolyte is governed by diffusion, electro-osmotic drag, hydraulic permeability (of gas and liquid phases), and temperature gradient effects. Electro-osmotic drag is always toward the cathode, but the diffusion, temperature, and hydraulic permeability gradients can be engineered to achieve a favorable water balance. The liquid permeability direction

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can be tailored by engineering the wettability and pore size distributions of the catalyst layers, microporous layers, and DM on the cathode and anode. This approach of capillary pressure management is also used on the DMFC to control water and methanol crossover. The water flux caused by a temperature gradient and heat flux can be exploited during shutdown to help purge the fuel cell. The overall roles of the various fuel cell components in controlling the liquid- and gas-phase water balance inside the fuel cell were discussed. In particular, the MPL, a thin, highly hydrophobic layer between the DM and catalyst layer, is critical in the overall water management. At the cathode, a MPL helps to push liquid water in the hydrophilic pores of the catalyst layer back toward the anode. The MPL also acts as a barrier to prevent liquid water flow from the DM into the catalyst layer and provides a low saturation condition to permit flow of oxygen to the catalyst layer. At the anode, the MPL acts to restrict water vapor transport away from the catalyst layer and reduce dryout, since water vapor diffusivity into hydrogen is around four times higher than into air. Hydrogen access to the catalyst layer is typically not limiting, and the additional restriction from the MPL is not critical. Although an understanding of capillary flow is important, condensation, evaporation, interfacial and morphological factors also play important roles in flooding, and need to be considered in any comprehensive approach. For DAFCs using a liquid feed, like the DMFC, the water balance and fuel crossover problem are more acute than the hydrogen fuel cell. Dilute liquid solutions, thicker membranes, and capillary pressure management are used to control these two issues. As a result of the high methanol and water crossover in the DMFC, the open-circuit potential is very low, and performance is also low compared to the H2 PEFC. However, the use of diffusion barriers in the anode and capillary pressure management eliminates the need for highly dilute methanol solutions, and these systems may ultimately be more appropriate than their H2 PEFC counterparts for portable applications. Various flow field designs and configurations have been designed and used in PEFCs. There is no “optimal design,” and there are advantages and drawbacks of all different design solutions. Most flow designs are a mixed parallel–serpentine design, made to balance pressure drop and slug holdup considerations. Unintentional crossover should be avoided in the design stage. This bypass phenomenon occurs when flow from one channel short circuits underneath the land and into an adjoining channel because the pressure drop to continue along the flow path is similar or greater than the pressure drop to bypass the channel. Any PEFC channel design needs to consider flooding management, channel drainage by gravity, humidity loss versus reactant availability and electrical contact. Although beginning-of-life (BOL) performance is important, fuel durability and timedependent performance are just as critical. The lifetime of a fuel cell is expected to compete with existing power systems it would replace. The automotive fuel cell must withstand load cycling and freeze–thaw environmental swings with minimal degradation (3–5%) over a lifetime of at least 5000 h. A stationary fuel cell must withstand over 40,000 h of steady operation with minimal downtime. There are many phenomena that can result in gradual degradation and performance loss in PEFC systems. These include assorted chemical and mechanical degradation modes [81]. Many different modes of physicochemical degradation are known to exist that can generally be grouped into categories of reversible and irreversible physical and chemical damage. Almost every component in PEFC systems is susceptible to lifetime degradation. In general, degradation is accelerated by operation at high-temperature

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or low-humidity conditions, aggressive load cycling from low to high cell voltages, and large temperature swings in the environment. The final section of the chapter dealt with multidimensional effects. While this topic is sufficiently detailed that an entire book could be written about it, the goal here was to reinforce the reality that almost nothing inside the PEFC is isotropic, and strong gradients in species, temperature, and current commonly exist under normal operating conditions. Under low-humidity environments, the anode moisture profile tends to control the current distribution profile, since anode dryout is limiting performance. Under higher humidity and flooding conditions, however, the cathode oxygen content and flooding condition controls the current distribution. Gradients is nearly every parameter are normal in PEFC operation, and many can be exploited to improve operating performance.

APPLICATION STUDY: DIRECT LIQUID FUEL CELL FOR PORTABLE APPLICATIONS Perhaps the first real commercial PEFC system to reach mass production will be the portable DMFC. Ultimately, the DMFC system must replace some existing power source. Take the laptop computer system as an example for comparison purposes: 1. Find the expected time of operation, power density, and weight of a typical existing battery system. 2. Using 0.1 W/cm2 active area as a design point and a best estimate to account for flow manifolding (assume 15% of the total volume) estimate the volume of a DMFC stack to provide equivalent power of the battery. 3. Estimate the methanol solution reservoir volume needed to compete with the existing battery system assuming (a) a diluted 2 M methanol solution or (b) a neat methanol solution feeds the anode. 4. What power density must the DMFC achieve to be able to compete favorably with a modern battery? 5. Discuss the trade-offs (in as much engineering detail as possible) between the use of stored hydrogen and methanol for this application. 6. How would you propose to maintain a thermal balance of the stack?

PROBLEMS 6.1 Determine the change in the mass transfer limiting current density for the cathode of a PEFC between an uncompressed and a 20% compressed DM. The fuel cell is operating at 80◦ C on fully humidified cathode air flow at 1 atm pressure. The uncompressed DM is 300 µm thick with a porosity of 70%. Assume there is no flooding on the catalyst layer or in the DM. 6.2 Discuss the various methods of flow humidification and identify the strengths and weaknesses of each approach.

6.3 Do some reading and find out how the relative humidity of a flow of gas can be measured in a fuel cell. Is there a robust, inexpensive sensor that is readily available? 6.4 Calculate the net rate of water vapor uptake into an air cathode flow at the given conditions (see the table on page 372) for a 250-cm2 fuel cell operating at 1.2 A/cm2 . Compare the cathode uptake to the water generation. What drying rate would the anode have to share to obtain a steadystate global balance?

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Cathode Condition

Inlet

Outlet

Cathode/Anode Condition

Inlet

Outlet

RH Temperature Pressure Stoichiometry

0.5 80◦ C 3.2 atm 2.0

1.0 80◦ C 2.7 atm —

RH Temperature Pressure Stoichiometry

0.5/1.0 65◦ C 1.2/1.1 atm 2.5/1.2

1.0/1.0 70◦ C 1/1 atm —

6.5 Derive Eq. (6.16), assuming a transient buildup or dryout of water can occur. 6.6 For the fuel cell in problem 6.4, determine the inlet relative humidity that would achieve a global balance, assuming all uptake occurs in the cathode and there are no water slugs at this balanced condition. 6.7 For the fuel cell in problem 6.4, determine the exit temperature that would achieve a global balance, assuming all uptake occurs in the cathode and there are no water slugs at this balanced condition. If the exit temperature is not changed, what is the total volume of liquid water that must exit a 100-fuel-cell stack in 1 h to maintain a balance at these conditions? 6.8 Calculate the net rate of water vapor uptake into an air cathode flow at the given conditions for a 320 cm2 fuel cell that is operating at 1.0 A/cm2 . If the net transport coefficient of water from the anode to the cathode is -0.2, calculate the net rate of water storage in the fuel cell at this condition. What would happen over time to the fuel cell performance and operating parameters in the accompanying table? Cathode/Anode Condition

Inlet

Outlet

RH Temperature Pressure Stoichiometry

0.5/1.0 80◦ C 3.2/3.2 atm 2.0/1.5

1.0/1.0 80◦ C 2.6/2.8 atm —

6.9 For the fuel cell in problem 6.8, what exit temperature of the fuel cell would be needed to achieve a water balance in this condition, assuming all other parameters remain the same? 6.10 For the fuel cell in problem 6.8, what inlet RH of the fuel cell would be needed to achieve a water balance in this condition, assuming all other parameters remain the same? 6.11 For a 100-cm2 fuel cell at 1 A/cm2 operation, with a net drag coefficient of 0.1, and the other conditions shown in the accompanying table, solve for the cathode flow rate that must be used to achieve a water balance with no liquid water ejection from the fuel cell

6.12 For the fuel cell in problem 6.11 and the conditions shown in the table for problem 6.11, solve for the cathode exit temperature that must be used to achieve a water balance with no liquid water ejection from the fuel cell. What would happen to the net drag coefficient if the anode humidity at the inlet were reduced? 6.13 The problem of unintentional crossover, or the bypass phenomenon, can be reduced in several ways. A few ways we can design a flow channel with reduced crossover to an adjacent channel include increased compression, decreased DM porosity, and increased land width. Discuss the trade-offs associated with these approaches. 6.14 For a net drag coefficient of 4.0, no hydraulic permeation effects, and an electro-osmotic drag coefficient of 3.0, calculate the water crossover and equivalent power lost per day for a 10 M methanol solution at idle in the anode of a 10-cell, 10-cm2 /cell DMFC stack. 6.15 Determine the ideal net water transfer coefficient for a hydrogen fuel cell so that external humidification is not needed. How would you design the electrode and diffusion media structure to achieve this goal? 6.16 Determine the global anode oxidation and cathode reduction reactions for trioxane, formaldehyde, and ethanol. 6.17 Would the best possible diffusion media used in the anode of the DMFC be hydrophobic or hydrophilic? Why? 6.18 Consider a typical DMFC operating system. On the anode side, a 2 M solution of methanol (2 mol of methanol per liter of solution) is circulated into the anode and then pumped back into the fuel tank. Some of the methanol in the solution is being consumed at the anode, and ∼100 mA/cm2 equivalent is being consumed at the cathode via crossover. The water generated at the cathode or transported to the cathode by drag/diffusion is condensed and pumped back into the anode tank, along with all effluent from the anode. Write a symbolic expression to solve for the required mass flow rate of pure methanol back into the anode mix to maintain molarity of the mixture as constant. (Hint: the water produced at the cathode is being added to the mixture, and some of the methanol is being consumed, so the mixture

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Problems will become more diluted with time unless a stream of pure methanol is added to balance the mass loss.) Pure MEOH .

mCH3OH = ?

All water in + generated + left over methanol back to anode

Water, methanol out

Water, methanol in

Anode Dry air in

Cathode

Condenser and pump Dry air to ambient Moist air out

6.19 For an isothermal neat hydrogen fuel cell at moderate current density with adequate cathode flow stoichiometry, sketch the current distribution from inlet to exit for the following cases: Ĺ 50% RH inlet anode, 50% RH inlet cathode, concurrent flow Ĺ 50% RH inlet cathode, 50% RH inlet anode, concurrent flow 6.20 Determine the relationship between the required water at the anode (water stoichiometry) and the fuel stoichiometry for a dimethyl ether (DME) fuel cell in symbols. What are the consequences on performance of so much water required at the anode inlet? What can be done to engineer this situation? 6.21 Assume a 100-cm2 fuel cell anode exit at 100% RH, λa = 1.5 at 1 A/cm2 and a cathode exit of 80%, λc = 2.5 at 1 A/cm2 , 363 K, 1 atm back pressure throughout. What is the total combined relative humidity of the exit flow? That is, if the anode and cathode exit flow were mixed, what is the resulting RH? This concept of total humidity can be useful when evaluating the expected performance and flooding criteria. That is, if total RH > 100%, then some liquid buildup and slug ejection will occur. 6.22 Calculate the percent change in effective diffusivity for a gas flowing through an uncompressed DM and a DM compressed to 10 and 20% strain, assuming the tortuosity remains the same. 6.23 What is the effect of reactant dilution on water vapor uptake? That is, will a 50% mixture of hydrogen and nitrogen at the anode pick up more, less, or the same moisture as a pure hydrogen feed? 6.24 Compare hydraulic permeability to drag and diffusion. Under what cases would each mode dominate water transport?

373

6.25 For a direct methanol anode reaction, 1 mol of water is reacted per mole of methanol. Determine the molarity of a 1 : 1 molar ratio DMFC solution. This is the desired design molarity of the solution at the anode electrode.

Open-Ended Problem 6.26 Can you think of a way to actually monitor the solution molarity? That is, is there a way to make some sort of gauge to measure the molarity of a methanol solution? How would you do this in practice? (Hint: There are several ways to achieve this, think of what property variation there would be between different molarity solutions.)

Computer Problems 6.27 Program the gas-phase water balance for a H2 PEFC in Excel or other computer language or workbook software you are comfortable with. Assume the net drag to the cathode is zero (i.e., electro-osmotic drag = diffusion and hydraulic drag is zero). Is this cell flooding or drying? Hint: This zero-net drag assumption is generally valid (globally, at least) for thin membranes and means that all water generated must be removed by the cathode flow, that is, you can ignore the anode here. Complete the following: (a) Calculate the mass flow rate of water into an air cathode at RH = 50%, 80◦ C, 3.2 atm pressure, and stoichiometry of 2.6 at 1 A/cm2 for a 100-cm2 cell. Check your computed solution with a hand calculation. (b) Calculate the mass flow rate of water out of the same air cathode at RH = 100%, 80◦ C, 3.1 atm exit pressure. Check your computed solution with a hand calculation. (c) One way to balance the water in the cell is to use the heat generated by the cell to tailor the cooling channels and provide a desired outlet temperature. Calculate the exit temperature of the cathode required to balance the water with this cell, assuming the exit RH is 1. (d) Another way to balance the water in the cell is to tailor the exit pressure of the cell. Calculate the exit pressure required to balance the water with this cell, assuming the exit RH is 1. If this is not possible with the given cathode stoichiometry, what cathode stoichiometry will get the job done? (e) Another way to balance the water is to tailor the inlet RH. Calculate the inlet RH required to balance the water with this cell, assuming the exit RH is 1. If this is not possible with the given

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Polymer Electrolyte Fuel Cells cathode stoichiometry, what cathode stoichiometry will get the job done?

6.28 Expand your program in problem 6.27 to include a net drag coefficient and the effects of anode flow. For the same cathode conditions as problem 6.27, (a) and (b), determine the anode/cathode (assume they are the same) exit temperature needed to balance the water generated. The flow of humidified hydrogen into the anode is at RH = 100%, 80◦ C, 3.2 atm pressure, and stoichiometry 1.5 at 1 A/cm2 for a 100-cm2 cell. The anode flow leaves at 3.1 atm and 100% RH at the chosen exit temperature. Plot the required exit temperature as a function of net drag coefficient. 6.29 Apply the program developed in problem 6.27 to a direct methanol fuel cell. There will be no uptake by the

anode, and the cathode must remove all water to prevent flooding. The flow of a 5 M methanol solution into the anode is at 60◦ C, 1 atm pressure, and stoichiometry 1.5 at 0.2 A/cm2 for a 100-cm2 cell. The anode flow leaves at 1 atm. The cathode flow enters at 0% RH and leaves at 100% RH. (a) Plot the required cathode flow rate at 60◦ C to avoid slug formation in the cathode for a net drag coefficient of 3.0. (b) Plot the required cathode flow rate at 80◦ C to avoid slug formation in the cathode for a net drag coefficient of 3.0. (c) Plot the required cathode flow rate at 60◦ C to avoid slug formation in the cathode as a function of net drag coefficient.

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Polymer Electrolyte Fuel Cells 63. T. Haraguchi, Y. Tsutsumi, H. Takagi, N. Tamegai and S. Yamashita, “Performance of Dimethyl Ether Fuel Cells Using a Pt-Ru Catalyst,” Electrical Eng. Jpn., Vol. 150, No. 3, pp. 19–25, 2004. 64. E. P. Murray, S. J. Harris and H. Jen, “Solid Oxide Fuel Cells Utilizing Dimethyl Ether Fuel,” J. Electrochem. Soc., Vol. 149, No. 9, pp. A1127–A1131, 2002. 65. S. Freni, M. Minutoli, N. Mondello and S. Cavallaro, Abstract Volume of the 2000 Fuel Cell Seminar, Washington, DC, 2000. 66. S. R. Narayanan, E. Vamos, S. Surampudi, H. Frank, G. Halpert, G. K. Surya Prakash, M. C. Smart, R. Knieler, G. A. Olah, J. Kosek and C. Cropley, “Direct Electro-Oxidation of Dimethoxymethane, Trimethoxymethane, and Trioxane and Their Application in Fuel Cells,” J. Electrochem. Soc., Vol. 144, No. 12, pp. 4195–4201, 1997. 67. J. Wang, S. Wasmus and R. F. Savinell, “Evaluation of Ethanol, 1-Propanol, and 2-Propanol in a Direct Oxidation Polymer-Electrolyte Fuel Cell: A Real-Time Mass Spectrometry Study,” J. Electrochem. Soc., Vol. 142, No. 12, pp. 4218–4244, 1995. 68. A. S. Aric`o, P. Cret`ı, P. L. Antonucci and V. Antonucci, “Comparison of Ethanol and Methanol Oxidation in a Liquid-Feed Solid Polymer Electrolyte Fuel Cell at High Temperature,” Electrochem. Solid-State Lett., Vol. 1, No. 2, pp. 66–68, 1998. 69. E. Peled, T. Duvdevani, A. Aharon and A. Melman, “New Fuels as Alternatives to Methanol for Direct Oxidation Fuel Cells,” Electrochem. Solid-State Lett., Vol. 4, pp. A38–A41, 2001. 70. A. B. LaConti, M. Hamdan and R. C. McDonald, “Mechanisms of Membrane Degradation,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 647–662. 71. D. P. Wilkinson and J. St-Pierre, “Durability,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 612–626. 72. T. Jinzhu, Y. J. Chao, J. W. Van Zee and W. K. Lee, “Degradation of Elastomeric Gasket Materials in PEM Fuel Cells,” Materials Science and Engineering A, pp. 669–675, 2007. 73. J. Divisek, “Low Temperature Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 99–114. 74. M. Crum and W. Liu, “Effective Testing Matrix for Studying Membrane Durability in PEM Fuel Cells: Part 2. Mechanical Durability and Combined Mechanical and Chemical Durability,” ECS Trans., Vol. 3, No. 1, p. 541, 2006. 75. R. M. Darling and J. P. Meyers, “Kinetic Model of Platinum Dissolution in PEMFCs,” J. Electrochem. Soc., Vol. 150, No. 11, pp. A1523–A1527, 2003. 76. T. Okada, “Effect of Ionic Contaminants,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 627–646. 77. M. Fowler, R. F. Mann, J. C. Amphlett, B. A. Peppley and P. R. Roberge, “Reliability Issues and Voltage Degradation,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 663– 677. 78. J. R. Rostrup-Nielsen and K. A-Petersen, “Steam Reforming, ATR, Partial Oxidation: Catalysts and Reaction Engineering,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 159–176. 79. T. E. Springer, T. Rockward, T. A. Zawodzinski and S. Gottesfeld, “Model for Polymer Electrolyte Fuel Cell Operation on Reformate Feed-Effects of CO, H2 Dilution, and High Fuel Utilization,” J. Electrochem. Soc., Vol. 148, No. 1, pp. A11–A23, 2001.

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References

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80. S. Gottesfeld, “Preventing CO Poisoning in Fuel Cells,” US Patent 4,910,099, March 20, 1990. 81. A. B. LaConti, M. Hamdan and R. C. McDonald, “Mechanisms of Membrane Degradation,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 647–662.

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Fuel Cell Engines Matthew M. Mench

7

Copyright © 2008 by John Wiley & Sons, Inc.

Other Fuel Cells Finally, advances in technology are beginning to offer a way for economies . . . to diversify their supplies of energy and reduce their demand for petroleum, thus loosening the grip of oil and the countries that produce it. . . . The only long-term solution . . . is to reduce the world’s reliance on oil. Achieving this once seemed pie-in-thesky. No longer. Hydrogen fuel cells are at last becoming a viable alternative. . . . One day, these new energy technologies will toss the OPEC cartel in the dustbin of history. It cannot happen soon enough. —“The End of the Oil Age,” editorial, The Economist, October 25, 2003

At this point, the reader should be quite familiar with the basic operation of fuel cells, in particular polymer electrolyte fuel cells (PEFCs). What is surprising for some to realize is that PEFCs have only recently been considered to be the most logical choice for future power. Several other fuel cell systems have been developed over the past century, including proposed direct carbon conversion in solid oxide–based systems. Alkaline fuel cells (AFCs) have been used for space and naval applications since the 1960s. Phosphoric acid fuel cells (PAFCs) were fully developed into commercial systems for stationary power, with hundreds of units sold to the public since the mid-1990s. Molten carbonate and solid oxide systems also continue to be developed and, in stationary applications, offer unique advantages compared to PEFCs. Other fuel cell systems, such as biological fuel cells, may become viable in certain technological niches. The question is often asked, what is the best fuel cell system and when will we see it? The answer is simple: Like any commodity, the value and marketability must be compared to the alternatives available. The best fuel cell for a particular purpose depends on the application and the competing technologies. We will see the fuel cell introduced to the public when it becomes a better alternative to the competing technologies. As long as there are less expensive and more convenient alternatives, fuel cells will not be introduced in large quantities. The purpose of this chapter is to describe the development and operation of the various fuel cell systems besides the PEFC. With background information from Chapters 1–5, the reader should be able to fully appreciate and analyze the different designs, operational advantages, and technical challenges of the other fuel cell varieties discussed.

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Although a brief summary of the history of these systems is given here, detailed historical summaries of the various fuel cell technology development can be found in many resources.

7.1 SOLID OXIDE FUEL CELLS Development History High-temperature solid oxide fuel cells (SOFCs) began with Nernst’s 1899 demonstration of the ionic conductivity of solid-state yttria-stabilized zirconia (YSZ) [1], but significant practical application was not realized for a variety of technical and practical reasons. Modern SOFC development has been revived worldwide, as several companies in the Unites States, Europe, and Asia are competing to bring small and large SOFC power systems to market. Development is on going 1–5-kW units for auxiliary electrical power (not propulsion) by BMW and Delphi [2] and for cogeneration and auxiliary distributed power by Siemens (formerly Siemens-Westinghouse). In 2006, Mitsubishi Heavy Industries demonstrated Japan’s first SOFC-micro gas turbine combined-cycle power generation system. The 75-kW system achieved power generation efficiency above 50%, significantly higher than conventional systems, and plans for a 200-kWe system are underway [3]. Rolls Royce Fuel Cell Systems (RRFCS) has been developing SOFC technology since 1995, focusing on cogeneration hybrid power plant technology using low-cost screen-printing manufacturing techniques [4]. Australian-based Ceramic Fuel Cells Unlimited (CFCL) has developed 1-kWe combined heat and power (CHP) flat-plate SOFC technology called NetGen, with an electrical efficiency of ∼40% and a combined efficiency of ∼80% [5]. Many other companies and research laboratories are also conducting intense research and development, and journal publications and patent literature should be consulted for the latest developments. Despite the high operating temperatures, there is even research and development of compact power systems for portable applications. Lilliputian Systems is developing hand-held SOFC units for portable power applications [6]. In the United States, there has been much SOFC development incubated by the Department of Energy Solid State Energy Conversion Alliance (SECA) program. The 10-year goal of the SECA program is to develop kilowatt-sized SOFC APU units at $400/kW by 2010. By 2005, some systems developed under this program already reached $746/kW [7]. 7.1.1 Operation and Configurations The SOFC and molten carbonate fuel cell (MCFC) represent high-temperature fuel cell systems. The SOFC avoids some of the major disadvantages of the high-temperature MCFC, however, since the electrolyte is a solid ceramic and therefore not prone to corrosion or evaporative loss as observed in liquid electrolyte systems. The current operating temperature of most SOFC systems is around 800–1000◦ C, although new technology has demonstrated 600◦ C operation, where vastly simplified system sealing and metallic materials solutions are feasible. The desire for lower temperature operation of the SOFC is ironically opposite to the PEFC, where higher operating temperature is desired to simplify water management and CO poisoning issues. Reduced temperature operation would enable more rapid startup and use of common metallic compounds for cell interconnects, reduce thermal stresses, reduce

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the rate of some modes of degradation, and increase reliability with lowered manufacturing costs. Despite the technical challenges, the SOFC system is a good potential match for many applications, including stationary cogeneration plants and auxiliary power. The high operating temperature of the SOFC requires long startup time to avoid damage due to nonmatched thermal expansion properties of materials. Another temperaturerelated limitation is that no current generation is possible until a critical temperature is reached in the solid-state electrolyte, where oxygen ionic conductivity of the electrolyte becomes nonnegligible, as shown in Chapter 5. Commonly used electrolyte conductivity is nearly zero until around 650◦ C [8], although low-temperature SOFC operation at 500◦ C using doped ceria (CeO2 ) ceramic electrolytes with anode support materials has shown feasibility [9]. Many other electrolyte and electrolyte structures have potential for even lower temperature operation [10, 11]. In many system designs, a combustor is utilized to preheat the fuel cell during warmup and to burn fuel and oxidizer effluent to provide a source of heat for cogeneration. The poststack combustor can effectively eliminate effluent residual hydrogen and CO, which is especially high during startup when fuel cell performance is low. It is especially important during start-up and shut-down transients that electrolyte, electrode, and current collector materials have matched thermal expansion properties to avoid internal stress concentrations and damage. The solid-state, high-temperature SOFC system eliminates many of the technical challenges of the PEFC while suffering unique limitations. In general, a SOFC system is well suited for applications where a high operating temperature and a longer startup transient are not limitations or where conventional fuel feedstocks are desired. The elevated temperature of operation means that high-quality waste heat is available for cogeneration systems. Besides manufacturing and economic issues beyond the scope of this section, the main technical limitations of the SOFC include thermal management, manufacturing processes, material design, startup, durability, and, in some designs, cell-sealing problems resulting from mismatched thermal expansion of materials. For additional details, an excellent text devoted to the SOFC was written by Minh and Takahashi [8]. The manufacturing methods for the SOFC structure are critical components in the ultimate cost of the system. Methods are diverse and vary depending on the cell design and manufacturer. Methods of SOFC production can include evaporative deposition, extrusion, tape casting, screen printing, plasma spraying, wet powder spraying, sintering, electrophoretic deposition, and vacuum slip casting. For details on these processes, the reader is referred to ref. [12, 13]. Manufacturing of these cells is a critical challenge, as a significant fraction of manufactured cells are not useful due to thermal stress related damage, increasing cost. A schematic of the basic materials and electrochemical reactions of the SOFC is given in Figure 7.1. In the SOFC system, yttria- (Y2 O3 ) stabilized zirconia (ZrO2 ) is most often used as the electrolyte, although many other combinations are continually evaluated [14]. In this solid-state electrolyte, O2− ions are passed from the cathode to the anode via oxygen vacancies in the electrolyte as described in Chapter 5. Other cell components such as interconnects and bipolar plates are typically doped ceramic, cermet, or metallic compounds. The conductivity of the electrolyte, electrodes, and interconnects normally dominates cell losses. Because of a desire to achieve high power density, the individual layers in the SOFC should be made as thin as possible. However, if they are too thin, the brittle materials

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383

H2O + 2eAnode - Nickel on YSZ Electrolyte - Yttria stabilized zirconia O2-

Cathode - Strontium-doped lanthanum manganite Cell-to-cell interconnect - Metals or ceramics

O2 + 4e-

Figure 7.1

2O2-

Schematic of materials and reactions occurring in a SOFC.

will crack and break under their own weight. Therefore, an electrode-, cathode-, or anodesupported design is used, as shown in Figure 7.2. In the case of a cathode-supported design, the main limitation is cathode electrode polarization, since the thick cathode prohibits oxygen diffusion. Also, thermal mismatch between the thin anode can lead to damaging delamination stresses. In the anode-supported design, the stresses generated by the nickel anode, which expands more than other materials under increased temperature, creates vertical cracks in the electrode structure, which can actually facilitate hydrogen diffusion. Since hydrogen diffusion is so much more rapid than oxygen diffusion and an electrolytesupported design results in very high ohmic losses, an anode-supported design is generally favored [15], especially to achieve lower operating temperatures, since the ohmic loss is proportional to the layer thickness [16]. Some designs use an inert porous supporting structure and eliminate the need for a thick electrode or electrolyte altogether. Unlike most other fuel cells, water is produced at the anode of the SOFC (and MCFC). Additionally, instead of being a poison, CO can act as a fuel in the SOFC through the following anodic reaction: CO + H2 O → CO2 + H2

(7.1)

Figure 7.2 Schematic of anode-, cathode-, or electrolyte-supported design and related typical thicknesses. (Adapted from [15].)

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Figure 7.3 SOFC stack with pre-reforming zones before fuel introduction into main reacting cells. (Image courtesy of Siemens Power Generation.)

Thus, CO, a minor species product of fuel reformation and a major poison to PEFCs, can actually be used as a fuel. In practice, this means that use of reformed gas without any CO cleanup is perfectly acceptable directly at the anode. The high temperature, anodic water production, and CO tolerance are some of the distinct advantages of the SOFC because they allow for direct steam reformation of a wide variety of fuel gases, eliminating the need for pure hydrogen feed and associated infrastructure. Reforming is discussed in Chapter 8, but a brief introduction is given here. When a carbon-containing fuel is steam reformed, the carbon is reacted with oxygen and water to form carbon dioxide, hydrogen, and carbon monoxide. This type of reforming is an endothermic process. The ratio of carbon dioxide to carbon monoxide depends on the temperature, pressure, and the amount of steam present. For methane, reformation can occur above 600◦ C, well within the range of SOFC operating temperatures. The reformation process can take place external to the fuel cell using waste heat and product steam for the endothermic process, or internal to the fuel cell. Internal reformation can be accomplished inside the stack in special reformer cells before the incoming anode fuel gas, as shown in Figure 7.3. Direct internal reformation can also be accomplished by injecting the untreated fuel gas directly into the reaction zone. Although this is potentially space and cost saving, it can lead to accelerated degradation of the anode catalysts and material compatibility problems. Since the reformation reaction is endothermic, the local temperature at the inlet of the reformer zone can drastically decrease, causing thermal stresses which result in catastrophic damage. Additionally, undesired minor species such as carbon can foul the electrode surface. Control of the temperature distribution in SOFCs is an important engineering design aspect for several reasons: (1) Since the performance is dominated by the conductivity of the materials, which are directly related to the temperature, the temperature distribution dominates the current distribution, and (2) internal thermal stresses should be minimized to avoid cell damage and promote good sealing.

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High electrolyte temperature is required to ensure adequate ionic conductivity (of O2− ) in the solid-phase ceramic electrolyte1 which reduces activation polarization so much that cell losses are typically dominated by internal cell ohmic resistance through the electrolyte material. Typical SOFC open-circuit cell voltages are around 1 V, very close to the theoretical maximum, and operating current densities vary greatly depending on design. While the theoretical maximum efficiency of the SOFC is less than the H2 PEFC because of increased temperature, activation polarization is extremely low. Operating efficiencies as high as 60% have been attained for a 220-kWe cogeneration system [17], which compare well to gas-turbine based cogeneration systems for stationary power. SOFC Designs Perhaps no other type of fuel cell has more variety of cell and stack designs than the SOFC. The problems of thermal mismatch and dominance of ohmic losses have resulted in very innovative solutions. There are several different basic design classifications for the SOFC system: the planar, sealless tubular, monolithic, and segmented cell-in-series designs. Two of the designs, planar and tubular, are the most promising for continued development. The other designs have been comparatively limited in development to date. Planar Design The planar configuration looks geometrically similar to the planar PEFCs and can be fitted with internal or external manifold systems. The three-layer anode–electrolyte–cathode structure can be an anode-, cathode-, or electrolyte-supported design (see Figure 7.2). Since excessive ionic and concentration losses result from electrolyte- and cathode-supported structures, respectively, many designs utilize an anodesupported structure, although ribbed supports or cathode-supported designs are utilized in some cases. For the planar design, the flow channel material structure is used as support for the electrolyte, and a stacking arrangement is employed. Although this design is relatively simple to manufacture, one of the major limitations is difficulty sealing the flow fields at the edges of the fuel cell. Sealing is a key issue in planar SOFC design because it is difficult to maintain system integrity over the large thermal variation and reducing/oxidizing environment over many startup and shutdown load cycles. Compressive, glass, cermet, glass–ceramic, and hybrid seals have been used with varied success for this purpose. As the stack heats, the volume and sealing surfaces will move significantly, making any sealing difficult, especially for the highly diffusive hydrogen. Planar designs can achieve a much higher power density than the tubular designs (up to 2 W/cm2 ), opening the door to auxiliary power applications [18]. A plot of a typical polarization curve for an anode-supported planar SOFC is given in Figure 7.4. Sealless Tubular Design The second major design is the sealless tubular concept pioneered by Westinghouse (which became Siemens-Westinghouse and is now Siemens) in 1980. A schematic of the general design concept is shown in Figure 7.5. Air is injected axially down the center of the fuel cell, which provides preheating of the air to operation temperatures before exposure to the cathode. The oxidizer is provided at adequate flow rates to 1) ensure negligible concentration polarization at the cathode exit, 2) to maintain desired cell temperature, and 3) to provide adequate oxidizer for effluent combustion with unused fuel. The major advantage of the tubular configuration is that the high-temperature 1 Relationships

for ohmic losses in the YSZ were given in Chapter 5.

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Figure 7.4

Performance of anode-supported planar SOFC at 800◦ C. (Adapted from Ref. [16].)

seals needed for the planar SOFC design are eliminated. Tubular designs have been tested in 100-kWe atmospheric pressure and 250-kWe pressurized demonstration systems with little performance degradation (less than 0.1% per 1000 h) and conversion efficiencies of 46 and 57% (LHV), respectively [19]. A polarization curve at various temperatures from a tubular SOFC is shown in Figure 7.6. A 24-stack bundle and integrated SOFC system layout are shown in Figures 7.7 and 7.3, respectively. In this bundle, rows of tubes are connected in parallel, and columns in series. In contrast to a completely series stack commonly used in PEFCs, this series–parallel arrangement is highly useful for system service durability. In this configuration, individual cells can suffer catastrophic damage, and the stack does not have to go offline, since the current is redistributed through other cells in parallel along the bundle. This allows simplified maintenance and individual tube replacement without suffering sudden catastrophic failure of the stack power, which is a major advantage.

Figure 7.5 ation.)

Schematic of sealless tubular SOFC design. (Image courtesy of Siemens Power Gener-

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Figure 7.6 from [16].)

387

Voltage–current density plots of typical 2.2-cm-diameter tubular SOFC cell. (Adapted

One drawback of this type of tubular design is the more complex and limited range of cell fabrication methods. Another drawback is high internal ohmic losses relative to the planar design, due to the relatively long in-plane path that electrons must travel along the electrodes to and from the cell interconnect. Some of these additional ionic transport losses have been reduced by use of a flattened tubular SOFC design with internal ribs for current flow, called the high-power-density (HPD) design by Siemens [12, 16]. The evolution of the tubular cell design and performance at Siemens is shown in Figures 7.8 and 7.9, respectively. The triangular Delta9 design has 300% higher power density and 60% higher gravimetric power density than the pure tubular design [20]. This design can also experience significant losses due to limited oxygen transport through the porous (∼35% porosity) structural support tube used to provide rigidity to the assembly. The internal tube can also be used as the anode, reducing these losses through the higher diffusivity of hydrogen. Purely tubular cells have a power density at 1000◦ C of about 0.25–0.30 W/cm2 ,

Figure 7.7

SOFC tubular stack bundle. (Image courtesy of Siemens Power Generation.)

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Figure 7.8

Evolution of SOFC design at Siemens. (Image courtesy of Siemens Power Generation.)

in comparison to power densities of planar SOFCs, which can reach about 2 W/cm2 [18]. Flattened cells reduce this gap between tubular and planar designs considerably. In-Plane Design Another design concept for SOFCs is the in-plane fuel cell. This concept is similar to the in-plane stack design proposed for use with DMFCs for portable applications discussed in Chapter 6. The ion path length through the electrolyte is minimzed with this design but is still longer than the planer design, increasing ohmic drop. Mechanical support for the electrolyte comes from a porous fuel-side flat plate. Power output from this design

Figure 7.9 Evolution of SOFC design polarization behavior at Siemens, Statistics at 1000◦ C, 0.65 V operation. (Image courtesy of Siemens Power Generation.)

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Figure 7.10 tion.)

389

Schematic of monolithic SOFC design. (Image courtesy of Siemens Power Genera-

is reported to be greater than 0.5 W/cm2 at 950◦ C, which compares favorably to tubular designs but is less than the best planar designs. Other Designs The monolithic and segmented cell-in-series designs are less developed, although demonstration units have been constructed and operated. A schematic of the monolithic cell design is shown in Figure 7.10. In the early 1980s, the corrugated monolithic design was developed, based on the advantage of high power density compared to other designs. The high power density of the monolithic design is a result of the high active area exposed per volume and the short ionic paths through the electrolyte, electrodes, and interconnects. The primary disadvantage of the monolithic SOFC design, preventing its continued development, is the complex manufacturing process required to build the corrugated system. The Delta9 configuration of Figure 7.8 is close to a corrugated design and combines the assembling advantages of the tabular design with the power density advantages of the corrugated design. The segmented-cell-in-series design has been successfully built and demonstrated in two configurations: the bell-and-spigot and the banded configuration shown schematically in Figure 7.11. The bell-and-spigot configuration uses stacked segments with increased electrolyte thickness for support. Ohmic losses are high because electron motion is along the plane of the electrodes in both designs, requiring short individual segment lengths (∼1–2 cm). The banded configuration avoids some of the high ohmic losses of the bell-andspigot configuration with a thinner electrolyte but suffers increased mass transport losses associated with the porous support structure used. The main advantage of the segmentedcell design is a higher operating efficiency than larger area single-electrode configurations. The primary disadvantages limiting development of the segmented-cell designs include the necessity for many high-temperature gas-tight seals, relatively high internal ohmic losses, and requirement for manufacture of many segments for adequate power output.

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Other Fuel Cells Electrolyte Anode

Cathode

Electrolyte Cathode Interconnect Oxidant

Interconnect Anode

Fuel

Fuel Oxidant Fuel

Oxidant

(a)

(b)

Figure 7.11 Schematic of segmented cell-in-series design: (a) banded and (b) bell-and-spigot configuration. (Image courtesy of Siemens Power Generation.)

Other cell designs, such as radial configurations and more recently microtubular designs, have also been developed and demonstrated [21]. The microtubular designs can achieve lower operating temperature, since it has long been recognized that thinner electrolyte and electrode layers promote operation at lower temperature [22]. Durability Most of the durability issues of the SOFC are related to the brittle nature of the ceramic structures that make up the stack components. Thermal expansion mismatches between the various components lead to high thermal stresses during both manufacture and operation. In fact, a planar fuel cell electrolyte/electrode plate will typically be nonplanar and slighty curved at room temperature because it is designed to be planar at operational temperature. During operation, temperature gradients as large as 100◦ C or larger can persist across the stack location, depending on design, which can lead to failure. In the tube-style bundle, individual tubes that fail can be replaced without massive disruption to the remaining fuel cell stack, as discussed. Because of the series/parallel stack bundle design, individual cells that fail can be tolerated, an important advantage of this approach. The thermal mismatch during operation is not the only concern, however. The manufacturing approach is tremendously important in SOFC operation. A high rate of wasted materials due to breakage is typical during the manufacture and deployment of the fuel cells. Durability of SOFCs is not solely related to thermal mismatch issues. The electrodes suffer a strong poisoning effect from sulfur (in the parts-per-billion range), requiring the use of sulfur-free fuels. Additionally, anode oxidation of nickel catalysts can decrease performance and will do so rapidly if the SOFC is operated below 0.5 V. This can be a problem in stack operation if not every cell is monitored, since individual cells in series

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can easily fall below 0.5 V due to flow maldistribution, degradation, cold temperature, or other effects. Therefore, operation above 0.5 V in all cells is required. As SOFC reduced operating temperature targets are achieved and use of inexpensive metallic interconnects become feasible, accelerated degradation from metallic interaction becomes a problem. Metals utilizing chromium (e.g., stainless steels) have shown limited lifetimes in SOFC and can degrade the cathode catalyst through various physicochemical pathways [23]. As more data are available and new materials are used, there will always be durability issues. Durability extension is a continual improvement process for any system, and SOFCs are no exception. However, compared to PEFCs, longterm durability of SOFCs in large stationary systems is slightly more advanced. 7.1.2 Summary of Advantages and Disadvantages The SOFC has many technical advantages compared to other fuel cell systems. Like all fuel cell systems, however, it is not a perfect fit for all applications and has some technical challenges that must be overcome. Despite the advantages of the high temperature, development of the SOFC system is now based on achieving a lower temperature operation to enable metal components and interconnects and better sealing. The main advantages of the SOFC system are as follows: 1. Non–noble metal catalysts are used, so that the raw material costs are low. 2. High operating temperature and water generation at the anode greatly reduce activation polarization and eliminate the need for expensive catalysts. This also provides a tolerance to a variety of fuel stocks and enables internal reformation of complex fuels. 3. High-quality waste heat combined with a bottoming or cogeneration system enables a potential for high overall system efficiencies (∼80%) utilizing a bottoming or cogeneration cycle [19]. 4. Tolerance to carbon monoxide (CO) is a major poison to Pt-based low-temperature PEFCs. 5. Solid ceramic electrolyte used does not suffer electrolyte vaporization loss or excessive corrosion seen in high-temperature liquid electrolyte systems. The major disadvantages of the SOFC include the following: 1. The system power density is lower than PEFC systems, especially for tubular SOFC designs. 2. The high temperatures involved preclude the use of larger SOFC systems for transient applications. Also, the electrolyte is not conductive until an elevated temperature is reached, so that some kind of preburner heating system is needed for startup. 3. Damage to the components due to thermal stresses in manufacturing and operation is difficult to control, leading to a high rate of damage to the highly brittle thin ceramics involved, even before installation and operation. The manufacturing waste residual is high, leading to increased manufacturing costs. The SOFC has seen tremendous advancement in recent years, especially in terms of cost per kilowatt. High system reliability with acceptable degradation has been observed in

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prototype systems. Additional development will be toward a commercial system to compete in stationary and distributed power markets, where the high efficiency of CHP systems using the high-quality waste heat of the SOFC can be exploited.

7.2

MOLTEN CARBONATE FUEL CELLS Development History The MCFC utilizes a mixture of alkali metal carbonates retained in a solid ceramic porous matrix that become ionically conductive and molten at elevated (>600◦ C) temperatures. MCFCs were first studied for application as a direct coal fuel cell in the 1930s [24]. Development of MCFC systems has focused on large, kilowatt-to-megawatt stationary distributed power applications, due to the fact that these high-temperature systems are really only suited for steady power generation, and the efficiency can be maximized by utilizing the waste heat. Theoretical electrical conversion and cogeneration efficiencies of MCFC units are expected to reach 50 and 85%, respectively. Dutch scientists G. H. J. Broers and J. A. A. Ketelaar developed MCFCs in the 1950s. In the United States, MCFC research at Texas Instruments funded by the U.S. Army began in the 1950s and sought to develop fuel cells for combat operations. Since operation on battlefield fuel was desired, a high-temperature fuel cell was sought that could run on reformed diesel fuel. Testing of several prototype units was conducted, but further development abated. Development in the 1980s continued in various countries, primarily in the United States, Japan, and Europe. Recently, development has accelerated and reached the commercial stage. In the United States, Fuel Cell Energy (FCE) of Danbury, Connecticut, manufactures Direct FuelCell units ranging from 300 to 2.4 MWe. These units are designed to run on a variety of renewable and conventional fuel stocks using direct internal reformation technology. In January 2007, FCE had over 150 million kilowatt-hours of generated power at customer sites [25]. Recently FCE partnered with the Linde Group, a worldwide leader in industrial gases, to sell and market the FCE Direct FuelCell products worldwide. Fuel Cell Energy has other strategic alliances in the United States (Caterpillar), Europe (MTU Friedrichshafen), and South East Asia (Marubeni), and now has a facility in Connecticut capable of building up to two-hundred 200-kWe systems per year [26]. In Asia, Hitachi, Toshiba, and others have designed and built prototype units and have commercial product development plans. Europe and South Korea also have several active research organizations and industry in this area. Reviews of the MCFC development and commercial prospects are given in refs. [27, 28].

7.2.1

Operation and Configurations The MCFC normal operation temperature is 650◦ C, with nearly atmospheric pressure, although elevated pressure systems have been utilized. At temperatures much above 650◦ C, electrolyte loss and corrosion are too rapid. Much below this temperature, performance is poor. Due to the presence of liquid electrolyte and mechanical damage concerns to the brittle ceramic electrolyte retaining matrix, the differential pressure between the anode and cathode must be very low. At the elevated temperature, the Nernst voltage and the maximum thermodynamic efficiency of the MCFC are lower than for PAFC or PEFC stacks. Also, the high temperatures

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Hydrogen Oxidation Reaction (HOR) H2 + CO32H2O + CO2 + 2eFuel gas

Anode Matrix Cathode

CO32Separator Plate

Oxidizer gas O2 + 2CO2 + 4e-

2CO32-

Oxidizer Reduction Reaction (ORR)

Figure 7.12 Schematic of reactions occurring in MCFC. (Adapted from [28].)

require very long startup times on the order of tens of hours. There are also great advantages to the higher temperature systems, including rapid kinetics so that less expensive catalysts can be used. Additionally, the high-quality waste heat from the MCFC can be used in a bottoming cycle or other purposes to increase the overall combined efficiency as in the SOFC. Operating Conditions The MCFC global electrochemical reaction is the same as for other hydrogen air fuel cells, which is the same as a balanced combustion reaction2 : H2 + 12 O2 → H2 O

(7.2)

A schematic of the fuel cell reactions and the main components of the MCFC is given in Figure 7.12. The global anode hydrogen oxidation reaction (HOR) is − H2 + CO2− 3 → H2 O + CO2 + 2e

(7.3)

The global oxidizer reduction reaction (ORR) on the cathode is O2 + 2CO2 + 4e− → 2CO2− 3

(7.4)

Operation on a CO stream is possible as well, as with the SOFC. Thus, CO, a minor species product of fuel reformation and a major poison to PEFCs, can actually be used as a fuel. In practice, this means that use of reformed gas without any CO cleanup is perfectly acceptable at the anode. On-anode reformation is also achievable, as with SOFCs, since water is generated after anode, which is necessary for steam reformation. A wide variety of fuels, including natural gas, coal gas, and biologically produced gases, can be successfully used with the MCFC system [29, 30]. Unique to this fuel cell system, CO2 is consumed in the electrochemical reaction at the cathode, is converted into the carbonate anion, which carries the current through 2 Electrochemical

redox reactions have been called “cold combustion” by some, since the overall reaction is similar, yet it occurs at lower temperature.

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Figure 7.13 [31].)

Structure and material selection of typical MCFC. (Reproduced with permission from

the electrolyte, and is converted back into CO2 an the anode. Since the net exchange of carbonate in the electrolyte is zero, a steady state can be achieved. However, CO2 does need to be supplied to the cathode. This additional complexity of the MCFC can be accomplished by anode gas recycling or use of reformed gas products. The general in-cell configuration and most common cell materials are shown in Figure 7.13. In order to retain the molten carbonate electrolyte, which becomes mobile at the operating temperature, a thin (0.5–1-mm) porous α-LiAlO2 or γ -LiAlO2 matrix is used. The particle size in the matrix must be small and tightly controlled in manufacturing, so that the overall electrolyte plate can be thin to reduce ohmic losses and hold the electrolyte in by capillary forces. The pore sizes in the matrix and electrodes are tightly controlled so that electrolyte leakage into channels and catalyst corrosion are minimized while optimizing the three-phase boundary between electrolyte, catalyst, and reactant. The operating temperature of the MCFC (650◦ C) is actually a nice range. The high temperatures facilitate the use of nickel-based alloys for catalysts, a major advantage in raw material cost compared to the PAFC and PEFCs. However, since the operating temperature of the MCFC is considerably lower than the SOFC (800–1000◦ C), metal separator plates and interconnects can be used. This is a tremendous advantage compared to conventional SOFC systems. Stackwise, both internally and externally manifolded configurations have been used, depending on the manufacturer [31].

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d

Figure 7.14

Relative performance of MCFCs at 1 atm pressure. (Adapted from Ref. [26].)

The performance of the MCFC has improved greatly over the years, at the beginning of life and during its life history. Figure 7.14 shows the historical development in the performance of the MCFC. Improvements in the materials, electrolyte matrix, and other aspects have resulted in steady improvement in the power density. Continued improvement in durability is needed for stationary applications, however. A model of MCFC performance has been developed based on the dominating losses in the system, ohmic resistance, and anode and cathode kinetic losses. The fuel cell performance model from ref. [32] is given in Eqs. (7.5)–(7.8): E cell = E (T, P) − i (RIR − Ra − Rc )

(7.5)

This is similar to our basic model developed in Chapter 4, where the total anodic and cathodic resistances are lumped into two terms, and the ohmic (IR) losses constitute the other resistance: 
23,800 (7.6) RIR = 9.84 × 10−3 exp Ru T The anode polarization is quite low, compared to the cathodic and ohmic losses, but it can be significant at high current: 
27,900 −7 TP−0.5 Ra = 9.50 × 10 exp (7.7) H2 Ru T Finally, the cathodic activation losses are written as 
179,200 0.5 TP−0.75 Rc = 6.91 × 10−15 exp PCO O2 2 Ru T

(7.8)

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Of course, the choice of electrolyte thickness, type, time of service, and other factors not accounted for in the above equations will affect performance significantly. However, the above model can be used for qualitative estimation of MCFC performance variation with temperature and pressure. Reforming As discussed, since the MCFC produces waste heat and steam at the anode like the SOFC and can use CO as fuel, an excellent opportunity exists for internal reformation of the fuel gas. There are two types of internal reformation practiced, indirect internal reformation (IRR) and direct internal reformation (DIR). In IRR, the fuel gas is mixed with water vapor, heated inside the stack with waste heat, and reformed over a catalyst bed into a hydrogen–CO mixture. The reformed mixture then enters the active fuel cell area. In DIR, the fuel gas is reformed directly in the active area flow fields. Although the DIR approach is more compact and can theoretically be used to remove a significant portion of the waste heat from the stack, IRR allows the use of different catalysts specifically for reformation, prolonging system life [32]. Example 7.1 Nernst Voltage Effect of CO2 The MCFC is a little different than other fuel cells in that carbon dioxide is a reactant at the cathode and a product at the cathode. Write a symbolic expression for the expected change in thermodynamic voltage with partial pressure of all reacting species. SOLUTION From the definition of Nernst voltage given in Chapter 3 and the governing anodic and cathodic reactions given, we can show that    1/2 PH2 PO2 PCO2,c RT G + ln E =− 2F 2F PH2 O PCO2,a      1/2 PH2 PO2 PCO2,c RT G + ln E2 − E1 = − 2F 2F PH2 O PCO2,a 2      1/2 PH2 PO2 PCO2,c G RT − − + ln 2F 2F PH2 O PCO2,a

1 1/2 PH2 (PO2 ) PCO2,c /(PH2 O PCO2,a ) 2 RT

ln E2 − E1 = 2F PH2 (PO2 )1/2 PCO2,c /(PH2 O PCO2,a ) 1 where the subscripts a and c on the partial pressure of the CO2 represent anode and cathode, respectively. COMMENTS: In this fuel cell, the CO2 pressure on the anode and cathode enter the Nernst equation. The effect of a concentration difference is only a few millivolts, though, and the MCFC cannot withstand high pressure differentials between the anode and cathode due to the liquid electrolyte and material strength limits of the electrolyte matrix. Durability The lifetime durability of MCFCs has been greatly improved during the most recent period of development. The MCFC system still suffers from a variety of durability

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issues, as discussed below [31, 32]: 1. Electrolyte Loss Loss of the electrolyte will cause openings in the electrolyte matrix, resulting in gas crossover. Electrolyte loss can come from vaporization of the liquid electrolyte or reaction with the matrix, catalyst, or support materials. Electrolyte vaporization was thought to be a lifetime limiting issue, but stack testing has shown the evaporative losses to be much less than equilibrium thermodynamics would predict. 2. Nickel Shorting The lithiated porous nickel oxide cathode catalyst is slightly soluble in the electrolyte, which can result in dissolution of the catalyst in the electrolyte. This reduces the cathode activity but also can lead to a nickel metal bridge between the anode and cathode. As the nickel dissolves into Ni2+ ion, it migrates under the voltage gradient to the anode and is eventually reduced with dissolved hydrogen, precipitating in the electrolyte [33]. Over time, this bridge works back to the cathode, causing shorting. This issue is more serious in high-pressure systems. Approaches to mitigate this serious problem include thicker electrolyte bridges, the use of alloying agents to the NiO cathode to reduce solubility, and the use of lithium–sodium carbonate mixtures (rather than the Li–K mixture normally used) to reduce NiO solubility, or introduction of a ferrite layer [34]. 3. Separator Plate Corrosion The stainless steel separator plate used can suffer severe corrosion in the high-temperature environment at the anode and the cathode. Corrosion with the electrolyte reduces contact efficiency and also consumes electrolyte. This problem can be mitigated with a nickel or alternative metal coating on the anode [35] and reduction of the separator plate surface area on the cathode. 4. γ -Li–Al2 O3 Matrix Phase Transformation The γ -Li–Al2 O3 used for the electrolyte matrix can undergo phase transformation to α-Li–Al2 O3 over time. This results in particle growth in the matrix, which reduces capillary suction and results in lost electrolyte. Switching to an α-Li–Al2 O3 matrix material as the initial structure may avoid this problem. However, sintering and other changes with this phase have also been observed [36]. There are of course other degradation modes, but they tend to be more minor. There has been a resurgent interst in these systems, and progress has reduced the decay rate to nearly acceptable levels. Measured voltage decay rates in MCFC stacks manufactured by several companies show losses approaching the lifetime goal of 0.25% voltage loss per 1000 h, or 4% over the 40,000-h lifetime between overhaul for stationary applications [32]. 7.2.2 Summary of Advantages and Disadvantages The main advantages of the MCFC system include the following: 1. Fuel Flexibility The MCFC can internally reform a wide variety of fuel sources and use carbon monoxide as a fuel, a major poison in PEFC applications. This alleviates the need for a hydrogen infrastructure with this system. 2. Inexpensive Catalysts and Metal Materials High-temperature operation eliminates the need for expensive noble metal catalysts found in PAFC and PEFC applications. Non–noble metal catalysts are used, typically nickel–chromium or

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nickel–aluminum on the anode and lithiated nickel oxide on the cathode. Since the temperature is not too high, metal interconnects and current collectors can still be used eliminating a major limitation of SOFC systems. 3. Quality Waste Heat The high-temperature waste heat can be used to power a steam turbine in a bottoming cycle or for cogeneration of heat to increase overall efficiency. There are significant drawbacks of the MCFC, however, including the following: 1. Long Startup Time The high temperature requires tens of hours for startup to avoid damage. This eliminates the MCFC for all but continuous-power applications. 2. Low Power Density This is not a major issue in stationary and distributed power applications, but the system size is still relatively large compared to other fuel cell and competing technology systems. 3. Durability System longevity and durability still need to be improved. Systems with liquid electrolyte all suffer from evaporative loss, and compared to the SOFC, the MCFC has a highly corrosive electrolyte that, coupled with the high operating temperature, accelerates corrosion and limits longevity of cell components, especially the cathode catalyst. The cathode catalyst (nickel oxide) has a significant dissolution rate into molten carbonate electrolyte, causing nickel sintering. 4. Carbon Dioxide Injection Carbon dioxide must be injected into the cathode stream. This can be accomplished with recycling from the anode effluent or injection of combustion product but complicates the system design and dilutes the oxygen mole fraction at the cathode, lowering cell voltage. 5. Electrolyte and Matrix Maintenance The liquid electrolyte interface between the electrodes is maintained by a complex force balance involving gas-phase and electrolyte liquid capillary pressure between the anode and cathode and refractory electrolyte matrix. Significant spillage of the electrolyte into the cathode can lead to catalyst dissolution, and the vapor pressure of the electrolyte is nonnegligible, leading to loss of electrolyte through reactant flows. Additionally, it is yet uncertain if the MCFC systems will be cost competitive with other technologies. This issue ultimately relegated PAFCs to the premium power niche. The MCFC is poised to become the second major commercially available fuel cell system, after PAFCs discussed in the following section. Certainly, hundreds of kilowatts- and megawattssized units will be in operation in the coming years from several manufacturers. A MCFC plant is quiet with low emissions and the potential to reach 50% electrical conversion efficiency and over 80% overall combined efficiency. Whether or not truly deep market penetration into tens of thousands of units will occur will come down to the cost, durability, and convenience comparisons with other technologies.

7.3

PHOSPHORIC ACID FUEL CELLS Development History Phosphoric acid fuel cells were developed from the 1970s through the 1990s by several companies in the United States, including ONSI, a division of International Fuel Cells (IFC), which eventually became United Technologies Corporation

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Figure 7.15 Photograph of 100-kWe transit bus with PAFC system and methanol reformer. (Reproduced with permission from Ref. [37].)

Fuel Cells (UTC Fuel Cells). Worldwide, Fuji Electric Company and Mitsubishi Electric Company in Japan developed PAFC systems for residential and stationary power applications. The PAFC demonstration units have been developed for a wide variety of backup power and even transportation applications. In the 1990s Georgetown University helped operate a PAFC bus fueled by reformed methanol. The original stack was produced with a Fuji Electric fuel cell stack, and a second system was installed with an IFC 100-kWe PAFC stack, shown in Figure 7.15. This bus was operated successfully for a number of years and then sent to the University of California–Davis. However, large relative system size and rapid development of the PEFC have since limited development of the PAFC to stationary power applications [37]. In April 1992, the first commercially available fuel cell power unit, a 200-kWe PC25 PAFC system developed by ONSI, was delivered and installed [38]. Since the prototype 200-kWe PAFC unit, there have been three generations of PC25 units, with continual reduction in size and weight and increased durability. The first-generation PC25A weighed in at 30,800 kg and almost 80 m3 in total system volume, for a gravimetric and volumetric power density of 6.5 W/kg and 2.5 W/L, respectively. The third-generation PC25C, built only three years later in 1995, weighed 17,700 kg with a system volume of only only 51 m3 , for a gravimetric and volumetric power density of 11.3 W/kg and 3.92 W/L, respectively. Although the fuel stack materials, design, and operation itself were improved, much of the reduction in size and weight was achieved through total system improvement. Significant

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Figure 7.16 PC25C 200-kWe PAFC power plant and accesories. (Reproduced with permission from Ref. [38].)

advances in durability and lifetime were also achieved during operation of these units. In 2002, operation of over 245 units all over the world had accumulated 5 million hours of operation, with durability between major system overhauls exceeding 40,000 h [38]. Worldwide, over 500 PAFC systems had been installed by 2004 [39]. Shown in Figure 7.16, like many fuel cell power plants, the fuel cell itself is actually a smaller fraction of the overall size and weight of the system compared to the ancillary components. In the case of the 200-kWe PC25 PAFC, the stack constitutes only about 25% of the system volume and cost [40], which is a reasonable estimate for most nonportable fuel cell systems. Ancillary systems provide the following: 1. Fuel Management: The PC25 reforms natural gas to hydrogen fuel. 2. Heat Management: The fuel cell stack must be cooled to avoid electrolyte loss. To increase the overall efficiency, the waste heat can be used as cogenerated power through a hot-water heat exchanger system. 3. Water Management: The stack product water is rejected to the atmosphere and used for steam reforming of the natural gas. 4. Flow and Power Management: The air and hydrogen flow into the stack must be controlled, and the direct current (DC) produced must be conditioned to produce the voltage and current levels and phases desired. 5. Sensing and Control: The entire system is operated and controlled as a turnkey, with no direct operator input in normal operation [41]. The total electrical efficiency of the PC25 200-kWe unit is shown in Figure 7.17. A polarization curve from a cell in an early PC25 unit is given in Figure 7.18. Modern PAFCs can be higher than this, as shown in Figure 7.19. For operation in the electric mode

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Figure 7.17 Measured electrical and overall (combined heat and power) efficiency for United Technologies Fuel Cell, PC25C 200 kWe PAFC power plant. (Reproduced with permission from Ref. [38].)

only, around 40% chemical-to-electrical conversion is realized, which is better than many combustion systems for submegawatt power application. When the waste heat recovery to the hot water is included (the system puts out about 200–225 kW of recoverable heat), the system efficiency reaches 80%, an outstanding figure that compares very well with combustion-based technologies. Overall combined efficiency can now reach 87% in the cogeneration mode [42]. Overall, the PC25 unit represents the first real fuel cell product to be commercially sold. The system size, weight, and reliability have been continuously improved, and

Figure 7.18 Polarization curve from 200-kWe PC25 PAFC system operating at atmospheric pressure. (Adapted from Ref. [43].)

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Figure 7.19 Polarization curve from 200 kWe PC25 PAFC system operating at 180◦ C and atmospheric pressure. Pt-CO/C supported cathode catalyst, and SiC:ZrSiO4 electrolyte matrix. (Adapted from Ref. [43].)

operation in all environments around the world has been technically quite successful. However, the overall system cost remains at $3000–4000 per kWe, which is about three times higher than needed for deep stationary power market penetration [45]. The reliable off-grid power and quiet, low emission output have found a niche in premium power market venues such as banks, hospitals, or government buildings, however. In these applications, a combustion-based generator may be undesired or comparably unattractive, and the PAFC cost is acceptable. In the case of the Police Barracks in Central Park, New York, the cost of bringing in additional electrical capacity to the barracks ($1.2 million) was greater than the PC25 system ($800,000) [46]. A gas turbine generator would have been less expensive but would have been much louder in the middle of the park. In special applications such as these, the PAFC and its reliable power (>95% service reliability has been observed) are ideal. An added benefit is the heat cogeneration, which can be used for a variety of purposes, including space heating, water heating, or even absorption cycle air conditioning. Future research and development of these systems will revolve around achieving a product more cost-competitive with other stationary power systems. 7.3.1

Operation and Configurations The PAFC is an acid-based electrolyte technology that is in many ways quite similar to the PEFC, and much of the technology learned during early PAFC development is now being applied (or relearned!) to PEFC systems. The PAFC operates at an elevated temperature compared to the PEFC, at 160–210◦ C. The higher temperature PAFC was chosen for development for terrestrial applications after the failure of the (AFC) to demonstrate suitable performance with CO2 . The operating pressure of PAFCs ranges from 1 to 9 atm, and the flow stoichiometries are similar to other fuel cells. Higher operating pressures require larger parasitic losses and ancillary component costs, so most installed systems now operate at near atmospheric pressure. The observed performance increase observed for an increase in

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Hydrogen oxidation reaction (HOR) 2H+ + 2e– H2 Fuel gas

Anode matrix cathode Separator plate

Oxidizer gas 1 – H2O 2H+ + — 2 O2 + 2e Oxidizer reduction reaction (ORR)

Figure 7.20

Illustration of PAFC electrode and components.

pressure when the cell operates at 190◦ C and 323 mA/cm2 has been correlated as [47]: V (mV) = 146 log

P2 P1

(7.9)

As discussed in Chapter 4, this is higher than the Nernst voltage increase due to increased cathode exchange current density. Both systems have an acid-based electrolyte (PEFC is sulfuric acid based), although the PAFC is a liquid electrolyte solution system and the PEFC electrolyte exists as a partially bound solution in a solid polymer matrix. Between the PEFC and PAFC, the anode HOR and cathode ORR are the same. A schematic of the materials and electrochemical reactions in the PAFC system is shown in Figure 7.20. Both systems use a noble metal catalyst or alloy with noble metals on the electrodes, and both suffer from poor ORR kinetics relative to alkaline-based systems. Ironically, since operation of the PEFC at 80◦ C results in catalyst poisoning from CO as well as water management issues that the PAFC avoids, developers seek higher temperature PEFC membranes that can operate at 120–200◦ C like the PAFC but maintain the high power density advantage of the PEFC. Similar to a MCFC, in the PAFC, the electrolyte is stored between the electrodes within a thin ∼50% porosity, 50–200-µm-thick porous matrix. The purpose for the silicon carbide (SiC) porous matrix used in PAFCs is to retain the acid electrolyte by capillary forces. If there were no matrix, the acid could simply drain into the flow channels or bulge according to gravimetric forces. It is critical that the bubble pressure of the matrix exceed 35 kPa, or electrolyte blow-through and excessive crossover from internal pressure differentials would occur. The maximum pressure differential between the anode and cathode is limited to around 20 kPa to avoid this problem. Like all components, the electrode structure has evolved over time, and now a carbonsupported heterogeneous catalyst of platinum or platinum alloys with other metals such as chromium, vanadium, or cobalt is commonly used [40]. Similar to PEFC electrodes, precious metal catalyst loading of around 0.25 on the anode to 0.5 mg/cm2 are used. Although platinum is the base catalyst material, it is not a major contributor to the cost

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of the system and no longer impedes market implementation, since other components dominate PAFC system cost [40]. The electrode is sprayed or cast onto a porous electrode substrate which is similar in some ways to the DM used in polymer electrolytes and AFCs. The purposes of this porous substrate are multiple: 1. To enable transport of reactants, products, electrons, and heat to and from the electrode, 2. to act as electrolyte reservoirs for phosphoric acid, and 3. to serve as the flow channels. In the PEFC, only the first purpose is relevant. The eventual depletion of electrolyte from the PAFC matrix by evaporation results in gas crossover losses and low bulk ionic conductivity that must be avoided or the system will reach end of life. Therefore, a resevior of electrolyte is needed to replace lost electrolyte in service. It is difficult to refill the electrolyte in the PAFC system while in operation, so a lifetime of acid should be available at the beginning of life. In older designs, the electrolyte storage matrix would be thicker or include an internal reservoir to accommodate additional electrolyte. However, this has the detrimental effect of increasing system bulk and ohmic losses through the electrolyte. In order to reduce the size of the SiC matrix needed for prolonged operation as well as simplify stack design, some of the storage of the electrolyte has been moved out of the electrolyte matrix and into the porous and wettable carbon paper substrate material. Electrolyte storage in the carbon paper substrate is accomplished in hydrophilic, small pores. In order to promote gas flux, however, there is typically some wet proofing of the overall substrate with PTFE. The catalyst also shares a dual hydrophobic–hydrophilic nature. The dual hydrophobic–hydrophilic nature of the substrate and catalyst layer is similar to that in PEFCs, except that in the PEFCs the hydrophilic pores in the catalyst layer and DM are filled with water, not electrolyte, which is not desired. In the PAFC, the storage of electrolyte, which is in liquid form at operating conditions in the substrate greatly extends operation life. As discussed in Chapter 5, the pore size and hydrophobicity control the capillary pressure in the liquid. In a hydrophylic media, the smaller pore sizes have a liquid suction pressure, drawing liquid in. In the PAFC, the SiC matrix has uniformly small pores and is more hydrophilic than the catalyst layer or substrate reservoir, so that losses in electrolyte are readily replaced by suction from stored electrolyte these locations. The pressure and pore size distribution set up the electrolyte–catalyst–reactant interface area and thus are critical factors to control the performance of the electrode. The uniformity and control of the pore size in the matrix are extremely important to prevent local drainage spots with severe crossover. Control of the pore size distribution and hydrophobicity of the catalyst layer, substrate, and storage matrix are critical to ensure long life and maximized triple-phase boundary area for reaction in the catalyst layer. There have been many internal configurations of the PAFC stack plates, the most recent involving the use of carbon paper substrate as an electrolyte reservoir and a flow distributor, as discussed. The flow field design in a PAFC is similar to a PEFC, but there is no special provision for flooding, since this is not an issue with the medium-temperature PAFC. Typically, the flow fields are aligned in plane and perpendicular to one another (cross-flow), and external manifolding is used, as shown in Figures 7.21 and 7.22. By

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Figure 7.21 Illustration of PAFC stack flow field assembly with stored electrolyte. (Reproduced with permission from Ref. [26].)

shaping the carbon paper in parallel channels, there is no need to separately machine a bipolar plate with flow fields, and system size and cost savings are realized. The parallel and straight nature of the flow fields cannot be easily fed fuel in a stack using internal manifolding, and an external manifold system like that illustrated in Figure 7.22 is commonly used. This leads to sealing problems along the sides of the porous substrate not used for gas flow, where the edge pores must be closed by dipping or sealing the substrate edges. The entire assembly is then completed with a flat, thin separation plate that serves to isolate the reactants and electrolyte and transport current between cells in series.

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Figure 7.22 [26].)

PAFC stack external manifolding concept. (Reproduced with permission from Ref.

The main advantage of the PAFC is that the higher temperature eliminates or reduces two major problems with the PEFC, CO poisoning sensitivity and water management. The PAFC cannot accomplish internal reformation like the MCFC or SOFC, but because of the elevated temperature of 200◦ C compared to 80◦ C for the PEFC, the anode in the PAFC can tolerate a 1–2% CO in the feed stream. This allows operation on reformed natural gas and other fuel feedstocks with minimal CO filtering, greatly reducing reformer size and control requirements. Due to the high-temperature operation and electrolyte behavior, water management in the PAFC is not a major concern. The electrolyte is a highly concentrated acid solution that is conductive without water and has a very low vapor pressure at high concentration. The electrolyte concentration varies between 90 and 100% during operation depending on the flow rate, current density, and operating temperature. During operation, water is generated at the cathode, which is readily evaporated into the flow stream or absorbed into the electrolyte. If the water is absorbed into the electrolyte, dilution increases the vapor pressure and drives off the water at a faster rate. Therefore, water management in the electrolyte is self-regulating. The generated water leaves the system as steam, which can be used for the steam reformation process in the fuel-processing subsystem or to provide thermal energy for cogeneration application. Another major advantage of the electrolyte system is that control over freeze damage can be accomplished by dilution of the electrolyte to lower concentrations, which can reduce the freeze point of the electrolyte to below −40◦ C [45] before shipping. Once in operation, the PAFC will self-regulate the acid concentration when the operating temperature reaches a high normal value through the vapor pressure dependency discussed. Compared to the SOFC, the PAFC does not suffer the major material compatibility or manufacturing difficulties. Neither the SOFC nor the PAFC is a rapid-startup system, but operation at 200◦ C

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does not present the major thermal stress and seal leakage issues the SOFC suffers from. Provision for removal of the waste heat is accomplished through cooling pipes embedded between every 5–10 cells in the stack. Electrode and Electrolyte System Phosphoric acid, in high concentrations (90–100%), was chosen as the electrolyte in PAFC systems because of its low vapor pressure in high concentrations, which permits long-term operation with a fixed electrolyte system. Below 160◦ C, phosphoric acid is a poor ionic conductor, and problems of carbon monoxide poisoning that plague PEFCs become problematic. Therefore, operation between 160 and below 210◦ C is typical. Above this temperature severe electrolyte loss becomes a limiting factor. The electrolyte inventory in a PAFC is critical to maintain performance over time and protect downstream piping from severe corrosion from high-acid effluent. Therefore, there must be an electrolyte reservoir to allow changes in the electrolyte volume with time. Electrolyte volume can be retained if the cell temperature or cathode flow stoichiometry is decreased, and more water remains in the electrolyte, diluting the solution. The electrolyte inventory can be lost over time due to three reasons: 1. Evaporation of Electrolyte The vapor pressure of phosphoric acid is extremely low (a few ppm at 150–200◦ C [45]) but finite. Over time, electrolyte loss is substantial. This loss can be mitigated by reduced-temperature operation to reduce the vapor pressure, a higher initial inventory of acid, or an acid condensation zone near the exit. In this approach, an uncatalyzed cold zone near the fuel cell exit is used to collect condensed phosphoric acid and return it to the matrix inventory [48]. 2. Reaction with Poisons or Fuel Cell Components Obviously, the catalysts and other materials used in the PAFC must be compatible with H3 PO4 electrolyte. However, the activity of a material is related to the surface area, and when the normally inert SiC electrolyte matrix particles were reduced from 5 to 0.5 µm to decrease electrolyte thickness and stack power density, acid consumption from an H3 PO4 –Si reaction is observed. The size of the SiC particles used in the electrolyte matrix is now around 1 µm [48]. Consumption by poisons can be eliminated with filtering of the reactants. 3. Uptake by Fuel Cell Components The separator plates used in PAFC operation have a closed porosity of around 15%. During operation, the pores become open, drawing acid in by capillary action. By the end of lifetime, significant electrolyte can be stored in the separator plate. Additionally, electrochemical pumping occurs, in which the acid anion accumulates at the anode during high-current operation. This increases the pressure at the anode and can result in loss of performance due to electrolyte excursion into the electrode or channel. Additionally, the electrolyte pumping can result in cell-to-cell motion through the separator plate. Over time, the cathode side of the stack can become depleted of electrolyte first, resulting in excessive crossover and performance decay. Example 7.2 Loss of PAFC Electrolyte by Vaporization Over Time Given a 0.5-m2 2 active-area PAFC operating at 150 mA/cm and an anode stoichiometry of 1.4, determine the amount of electrolyte lost to the anode flow over 40,000 h operation. Assume the equilibrium concentration of H3 PO4 in vapor form is 3 ppm at the operating temperature of 200◦ C. The anode flow is pure hydrogen.

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SOLUTION We must solve for the total vapor uptake in the flow, assuming it reaches equilibrium fully saturated conditions at the exit. The relationships are the same as for moist air mixtures, only now it is the “relative humidity” of H3 PO4,v with which we are concerned. From Chapter 3, the definition of mole fraction is yH3 PO4,v =

n˙ v n˙ v = ⇒ n˙ v ≈ yH3 PO4,v n˙ others n˙ total n˙ others + n˙ v

(small n˙ v )

where n˙ others is the molar flow rate of everything but the acid vapor. Since there is no water generated at the anode and the input is dry, this is equivalent to the total molar flow rate of hydrogen out of the fuel cell: n˙ H2 ,out = (λa − 1)

(0.150 A/cm2 )(0.5 m2 )(10,000 cm2 /m2 ) iA = (0.4) nF (2 e− eq/mol H2 )(96,485 C/eq)

= 1.55 × 10−3 mol H2 /s The vapor equilibrium is 3 ppm, a mole fraction of 3.0 × 10−6 . Therefore n˙ v ≈ (3.0 × 10−6 mol H3 PO4 /mol H2 )(1.55 × 10−3 mol H2 /s) (40,000 h) (3,600 s/h) = 0.669 mol Since the molecular weight of H3 PO4 is 98 g/mol, this is equivalent to losing 65 g of acid just from the hydrogen side during the 40,000-h lifetime of operation. COMMENTS: The cathode would also absorb some electrolyte vapor as well and, since the flow rate and stoichiometry are higher on the cathode, would absorb more. On the cathode, the solution is slightly more complicated since water vapor generated from reaction will also be vaporized into the flow. From this calculation, one can see how even a small decrease in the vapor pressure can greatly extend the operational lifetime of the stack.

Durability Durability of the PAFC system has been demonstrated to be in excess of 40,000 hours between major overhauls of the system and stack components [38]. However, several durability issues degrade performance with time and must be addressed with system engineering design and material solutions. Many improvements were made in this regard between the subsequent generations of PAFC development and have eliminated modes of edge corrosion, damage during startup and shutdown cycles, or increased carbon and catalyst support integrity. However, issues that shorten lifeimte in the PAFC system remain and in many cases are remarkably similar to those observed in the PEFC system. Many of the lessons learned in PAFC design and operation can be applied to PEFC system operation, since many of the degradation modes are similar. Continuing durability issues for the PAFC include the following [38]: 1. 2. 3. 4. 5.

Electrolyte acid loss Electrode stability and impurities Carbon support corrosion Anode starvation Load cycling

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Of these, acid loss is perhaps the most insidious problem, as discussed. Simply reducing the operating temperature 25–30◦ C can double the life of the stack by reducing electrolyte vaporization and slowing other degradation modes [45]. This constant loss prevents the potential elimination of the electrolyte reservoir storage in the substrate and prohibits further major improvements in power density. Impurities in the fuel and oxidizer stream can gradually degrade performance, as in all fuel cells [40]. Hydrogen sulfide (H2 S) can enter the anode stream through fuel impurities or be present in the air as impurity from local industrial processes. At levels greater than 50 ppm, the stack-level damage to the anode catalyst from H2 S can be permanent. Chlorides, ammonia, and dust constitute other potential poisons. Carbon support corrosion and platinum dissolution at the cathode can occur at high potentials, and as a result, operation or idling the fuel cell at voltages above 0.8 V is not normally permitted. During startup, an auxiliary load cuts cell voltage below 0.8 V to prevent damage. Heat treatment of the carbon support structure and use of graphitized carbon can reduce this loss, which is an approach that also is successful in PEFCs. Carbon corrosion is also observed in PEFCs during startup and shutdown and if there are locations of anode starvation. This mode of irreversible loss is exacerbated in PAFCs, since the operating temperature is higher. One fundamental disadvantage of higher temperature operation is that all of the undesired reactions (e.g., corrosion of supports, piping, current collectors, platinum dissolution) are accelerated by the increased temperature. Of course, the increased temperature also hastens the kinetics of the desired HOR and ORR, too. This is a common trade-off in fuel cell systems: At high temperatures, the kinetics are more facile, but the undesired reactions are also accelerated. At low temperature, the degradation reactions are slowed, but so are the kinetics of the desired reaction. Fuel starvation can very rapidly degrade cell performance. If any portion of the anode is starved of hydrogen, the electrode potential will rise to oxygen evolution, and irreversible oxidation of the carbon support, substrate, and separator plate will ensue. To eliminate this, the anode flow field often has several passes, so that the hydrogen concentration is not reduced to low values in any locations [45]. 7.3.2 Summary of Advantages and Disadvantages The PAFC has some definite technical advantages. In many ways, the research thrusts in PEFC technology are based on achieving the same midrange temperature of operation as the PAFC while avoiding the drawbacks. The main advantages of the PAFC system are as follows: 1. Ease of Water Management The water level in the electrolyte is self-regulating by changing vapor pressure, and the temperature is high enough that liquid water flooding is not an issue. 2. Ability to Operate on 1–2% CO in Feed Stream The CO sticking coefficient on platinum is greatly reduced at 200◦ C, so that the PAFC can operate on a wide variety of fuel feeds with a simple steam reformer subsystem and minimal CO cleanup. 3. Demonstrated High Reliability and Developed System The PAFC system is the first fuel cell to reach the consumer production stage and has millions of operation hours accumulated with hundreds of 200-kWe units. This system has demonstrated high service reliability of over 95% as well as combined thermal efficiency of over 80% in the cogeneration mode.

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The major disadvantages of the PAFC are mainly in comparison to the PEFC, whose development has been greatly accelerated at the expense of the PAFC: 1. The system power density is not appropriate for automotive applications. The PAFC is a bulky, heavy system compared to the PEFC. Area specific power (0.2– 0.3 W/cm2 ) is less than half that of a PEFC [49]. 2. The required use of platinum catalyst with nearly the same loading as PEFCs despite the increasal operating temperature. 3. The relatively long warmup time until the electrolyte is conductive at ∼160◦ C (although this is much less than of a problem the MCFC or SOFC). 4. Although the PAFC has been successfully demonstrated in buses, much higher power densities can be achieved with PEFC systems. 5. The ultimate cost of PAFC units is $3000–4000 per kWe, which is three to four times higher than needed for ubiquitous stationary power market application [45]. Although the PAFC has many advantages compared to the PEFC or the SOFC and a demonstrated history of reliable, high-efficiency performance, development of these systems has slowed tremendously as a result of the failure to achieve a competitive market price. Most of this research has been supplanted by SOFC and PEFC development. Some attempts at achieving a high-temperature PEFC system might actually be considered a new generation of PAFCs, however, combining phosphoric acid–based membranes with a PEFC system for high-temperature operation. In these systems, beginning with Wainright et al. [50], a polybenzimidazole (PBI) membrane structure is impregnated with phosphoric acid and can be operated at 200◦ C. There have been many such papers on this approach [e.g., 51–55]. Performance is relatively high, but durability of these systems remains a major question. Ultimately, the main disadvantages of the PAFC are low system power density and cost. The PAFC is too bulky to be used for mobile applications and too expensive to be used in many commercial stationary power applications. Until these issues can be overcome, the PAFC will remain primarily an option for premium stationary power applications only.

7.4

ALKALINE FUEL CELLS The AFC has been developed for space, naval, and transportation applications. The AFC global electrochemical reaction is the same as for other hydrogen air fuel cells, which is the same as a balanced combustion reaction3 : H2 + 12 O2 → H2 O

(7.10)

The global anode HOR is slightly different than the PEFC and PAFC: H2 + 2OH− → 2H2 O + 2e−

3 Electrochemical

(7.11)

redox reactions have been called “cold combustion” by some, since the overall reaction is similar, yet it occurs at lower temperature.

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H2 + 2OH-

2H2O + 2e-

DM - Teflonized

Anode

Electrolyte Matrix

OHCathode

DM - Teflonized

O2 + 2H2O + 4eFigure 7.23

411

4OH-

Current collector/ flowfield land

Charge transfer processes at electrodes in AFC.

The global ORR on the cathode is also slightly different than the PEFC and PAFC: O2 + 2H2 O + 4e− → 4OH−

(7.12)

The AFC and PAFC are both liquid electrolyte solutions. The AFC, however, is based on an alkaline electrolyte solution of potassium hydroxide (KOH) in water. Other alkaline solutions can be used, notably sodium hydroxide (NaOH), but KOH is an inexpensive, easily handled solution that is used in other areas such as agriculture, so a distribution network already exists. The KOH solution molarity is typically between 30 and 80%, depending on the operating temperature. A higher molarity reduces the vapor pressure of the solution, and thus high-temperature systems require a high electrolyte concentration. As shown in Figure 7.23, hydrogen oxidation occurs at the anode via reaction with the hydroxide ion (OH− ) in the electrolyte to generate water (in the PEFC and PAFC, water is generated at the cathode). At the cathode, a balanced rate of hydroxide is formed via reaction with water, electrons, and oxygen. This leads to a water management challenge on the AFC, discussed in detail later in this section. The electrolyte solution conductivity and vapor pressure are strong functions of water content. At high current density, the water consumption at the cathode tends to dry the cathode and can even cause solidification of the electrolyte. In low-temperature AFCs, a flooding problem exists on the anode where water is generated. This ends up being less of a concern than for PEFCs where electrode flooding of the cathode is common, since the HOR is a facile reaction and hydrogen is highly diffusive so that mass transport is not generally limited. 7.4.1 Operation and Configurations Operating Conditions Unlike most other fuel cell systems that operate within a limited range governed by material or kinetic parameters, the AFC has been developed and operated with a variety of catalysts over a very broad range of temperature, pressure, and electrolyte solution concentration. Table 7.1 shows some of the operational parameters for a selection of AFC systems built and tested throughout the years. Although the electrolyte solution must have sufficient water for conductivity, like the PEFC electrolyte, the water generated by the reaction can be used for this, and external humidification is not needed. The original AFCs developed by Francis Bacon had very admirable performance compared to any modern fuel cell (0.8 V at 1 A/cm2 ). The anode and cathode pressure and

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System and Year Bacon cell/1950s Apollo, 1960s Space Shuttle orbiter, 1980s Siemens, 1986 Russian photon system, 1993

Catalyst Temperature Pressure Electrolyte Anode– (MPa) Configuration Cathode (◦ C)

Performance

200 230 93

4.50 0.34 0.41

Recirculating Static Static

Ni–NiO 0.8 V at 1 A/cm2 Ni–NiO 1.5 kWe/109 kg Pt/Pd–Au/Pt 12 kWe/93 kg

80 100

0.22 1.20

Recirculating static

Ni–Ag Pt–Pt

0.8 V at 0.4 A/cm2 Efficiency 65–75%

Source: Data from [56].

temperature were 4.5 MPa and 200◦ C, respectively, and the high temperature of Bacon’s AFC enabled the use of non–noble metal nickel catalysts. The Gemini space program in the United States utilized a PEFC, but the Apollo program (Figure 7.24) and early Space Shuttles used AFCs to generate auxiliary power and potable water [56]. Future Space Shuttle systems will apparently utilize PEFCs for auxiliary power [57]. In the Apollo system, the sintered nickel electrodes were augmented with up to 40 mg/cm2 platinum (cost was not an issue for the Apollo program) to increase performance, despite reduced operation pressure. The AFCs have also been developed for military applications, including the Swedish and German navies, Russian aerospace applications, and power generation by Siemens [58].

Figure 7.24 Cluster of three 1.5-kWe (maximum 2.3-kWe) AFC units used on NASA Apollo program. (Reproduced with permission from Ref. [58].)

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For automotive use, an array of thirty-two 5-kWe AFCs were constructed by Union Carbide and used for propulsion in a General Motors six-passenger van in 1967 [56]. Additionally, a 6-kWe hydrogen/air AFC was installed by K. Kordesch in a lead–acid dual-cell hybrid, and actually ran on public roads for three years with a six-bottle array of compressed hydrogen on the roof [56], using air that was run through a soda lime bed to remove CO2 . Modern AFCs now operate at nearly the same conditions as PEFCs, at slightly elevated pressures (∼ 2 atm) and around 100◦ C. One of the major limitations of the AFC system is the inability to tolerate CO2 , normally found in air in levels of around 380 ppm (0.0383%) [59]. In industrialized areas or locations with combustion activity, the local CO2 concentration can be even greater. The CO2 in the air or in impure hydrogen reacts with the potassium hydroxide in the electrolyte to form solid carbonate crystals through the following reaction [60]: CO2 + 2KOH(aq) → K2 CO3(s) + H2 O

(7.13)

The carbonate particle formation reduces ionic conductivity and can block pores of the electrode, leading to reduced performance. Carbon dioxide intolerance can be managed in three ways: (1) operation on pure oxygen and hydrogen, (2) use of CO2 scrubbers to eliminate CO2 from the input stream, or (3) use of a recirculating electrolyte (discussed below) to remove the carbonate from the electrolyte and avoid buildup. Operation on pure reactants is really only feasible for aerospace applications where pure oxygen and hydrogen are available as fuel for liquid rocket systems. However, the AFC can be coupled with an electrolyzer system to create a reversible fuel cell, discussed in Chapter 1. Use of CO2 scrubbers to eliminate the CO2 from the air stream is not 100% efficient, and if using hydrogen from reformer-based systems, scrubbing is also needed for the hydrogen feed stream. The resulting equipment is expensive and adds to the bulk of the total system. A recirculating electrolyte can be used to increase the CO2 tolerance and lifetime of AFC systems somewhat and is discussed later in this section. Electrolyte System The AFC can be categorized into two main configurations, static electrolyte and mobile electrolyte systems. A schematic of the mobile electrolyte system is shown in Figure 7.25. In this system, the electrolyte is pumped from the stack into an electrolyte reservoir. The mobile electrolyte is constrained within the porous electrode structure either by asbestos or other porous separation layer between the electrode and the mobile electrolyte or by careful control of the differential pressure in the anode and cathode and the surface tension in the porous electrode structure as in the MCFC and PAFC liquid electrolyte systems. The use of a mobile electrolyte offers the following major advantages: 1. Heat Management The electrolyte can be used as a coolant to remove heat from the stack, eliminating the need for a separate coolant system. The electrolyte is passed through a radiator upon leaving the stack. 2. Water Management The product water from the anode can be removed from the system through an evaporator, reducing the parasitic flow requirements on the anode and maintaining a proper water balance. 3. Electrolyte Poison Management The electrolyte is easily poisoned by small amounts of CO2 . Recirculation of the electrolyte can be used to filter and

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Figure 7.25 Mobile recirculating electrolyte system in AFCs. Heat transfer, water removal, and impurity removal occur through the flushed electrolyte. (Reproduced with permission from Ref. [58].)

remove carbonate particles that form as a result of CO2 impurity. Alternatively, the electrolyte can be completely flushed and replaced on a regular basis, given the inexpensive nature of the KOH solution. 4. Electrolyte Gradient Management During operation, the electrolyte solution becomes concentrated (and possibly solidified) at the cathode and diluted at the anode since water is generated at the anode and consumed at the cathode. This affects the conductivity and vapor pressure of the electrolyte solution. Some of this gradient is offset by water diffusion from the anode to the cathode. With a flowing electrolyte, convective flow of the electrolyte minimizes these gradients.

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The major disadvantages of the recirculating electrolyte include the following: 1. The additional hardware and high-temperature pumps that are required to handle the elevated temperature fluid, transfer heat, clean impurities, and remove vapor add to the bulk and reduce the reliability of the system. 2. Since all the electrolyte between individual plates is connected in the AFC system, there is a potential for internal short circuits that rob power. This is managed by maximizing the electrolyte path length between individual cells, by combining cells in a mixed series–parallel arrangement to reduce the maximum voltage potential. 3. The recirculating electrolyte is affected by changes in orientation and gravity unlike a capillary-pressure based static system. In zero-gravity situations, such as the Space Shuttle, the choice of static electrolytes is partially due to the capillary pressure control of these systems. A schematic of the static electrolyte system is shown in Figure 7.26. In this configuration, an asbestos or other porous medium is soaked with the electrolyte solution and maintained between the sintered metal or metal porous mesh electrodes. The advantages of this approach are basically the opposite of the recirculating electrolyte system disadvantages: The static system is more compact and simplified and does not suffer from internal shorting of the electrolyte. However, the static system is almost certainly unsuitable for operation on anything besides completely pure reactants, since CO2 poisoning cannot be remediated and damage will quickly accrue. Two other disadvantages of the static electrolyte are heat and water management. A separate coolant fluid must be used in the static system to remove water heat, and the water generated at the anode must be removed using excess flow stiochiometry at the anode, which is parasitic. A majority of terrestrial AFC applications use circulating electrolyte systems because operation on pure oxygen and hydrogen is not feasible, while space applications demanding less bulk, more reliability, and zero-gravity operation use static electrolyte systems. Stack Configuration The individual cells in bipolar plate stacks such as the PEFC are typically connected in series, with current collection across the entire electrode surface along the interface between the bipolar plate landings and the DM. The flow fields in AFCs are similar to those used in other fuel cells, and various parallel and serpentine configurations are used to optimize mass, heat, and reactant/product transport. A subset of stacks are designed using monopolar plates. Monopolar plates are used for many AFC applications [61]. In this design, there is a PTFE sheet between the electrode and the flow field to prevent the liquid electrolyte from passing through the electrode into the channel, which can be by static forces or by weeping, which is caused by electro-osmotic pressure-induced motion resulting from current flow. The PTFE coating also prevents electrical conduction between the land–DM interface, and the current cannot pass from the anode of one cell to the cathode of the adjacent cell through the flow field plate. Therefore, the individual cells do not need to be connected completely in series, as in the bipolar plate design stack. Instead, they are connected in a series–parallel arrangement to optimize power, compactness, and durability. A monopolar arrangement allows the unique advantage of isolating single cells in the event of replacement or damage as also realized

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Figure 7.26 Static electrolyte system in AFCs. Heat transfer, water removal, and impurity removal occur through the anode and cathode flows. (Reproduced with permission from Ref. [58].)

in SOFC bundle arrangements. In a series arrangement, if one cell is damaged, the entire stack fails. Current collection from the electrode in the monopolar design occurs from a metal current collector that frames and contacts the outside of the electrochemical active area. Obviously, excellent current conduction along the electrode surface is needed to avoid maldistribution of current and dead zones in the middle of the active area. As a result, this approach is typically used only with metal mesh electrodes and small-area (<400-cm2 ) AFCs [62]. Electrode Materials The AFCs developed by F. Bacon utilized nonnoble sintered nickel metal catalysts. The high electrical conductivity of these porous electrodes permits use of current collection from monopolar stack plates [62]. The sintered metal is often applied in two separate layers, with large pores on the channel side, so that control of the liquid electrolyte–gas phase interface can be achieved by capillary and gas-phase pressure forces.

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The use of Raney metals, which are physical mixtures of an active metal such as nickel or silver with an inactive one such as aluminum, is another approach [26]. The aluminum and active metal powder in Raney metals are not alloyed, and subsequent treatment with a strong alkali solution dissolves the aluminum, leaving a porous active metal structure with high electrical conductivity. The lower temperature modern AFCs mostly use noble metals rather than nickel, although other spinels or perscovites can be used at the cathode with the alkaline electrolyte [63]. Modern electrodes are similar to PEFC electrode structures with a porous carbon cloth DM, consisting of a carbon support material with fine metal catalysts, interdispersed with PTFE for hydrophobicity and pressed onto a nickel mesh to improve in-plane conductivity. As discussed, to prevent electrolyte weeping loss into the channels, a thin layer of PTFE is used to coat the electrode, and a monopolar design must be used. This is not a problem, however, considering the nickel mesh used on the electrode surface permits the high in-plane conductivity required to enable efficient current collection around the electrode current-conducting frame. 7.4.2 Summary of Advantages and Disadvantages Alkaline fuel cells are an older fuel cell technology, first seriously developed and applied in aerospace and naval applications, where cost was not much of a concern and pure fuel and oxidizer were available. For a variety of reasons, development of this technology has almost ceased, but it may be revived in the future if a solution to the disadvantages of the system are found. The basic advantages of the AFC system include the following: 1. The highest demonstrated operating efficiencies of any fuel cell system due to the reduced polarization during the ORR compared to acid-based electrolytes. 2. Use of a low-cost electrolyte, potassium hydroxide (KOH). 3. Flexibility in the choice of operating conditions and use of nickel-based electrode structures in high-temperature AFCs. 4. Inexpensive raw materials of the stack. The main limitations which have hindered development of the AFC to date include the following: 1. An intolerance to CO2 , which forces the use of CO2 removal equipment, pure oxygen and hydrogen, or a recirculating electrolyte system that severely reduces system energy density. 2. The need to manage water and electrolyte removal from the anode and electrolyte solution, which complicates system design and control. Development of AFC systems was undertaken by several major companies and research organizations for over 40 years, with interest waning since the middle 1990s. Alkaline fuel cells represent a low-cost, high-efficiency system that does not necessarily need noble metal catalysts. Siemens developed AFC technology for over 20 years and made substantial progress, only to ultimately abandon research efforts in favor of alternative technology [64].

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Ultimately, because of the high efficiency on pure oxygen and hydrogen and the need to run on pure reactants, the AFC is best suited for niche use in reversible fuel cell systems or aerospace applications. However, the intrinsic advantage of reduced ORR losses with an alkaline electrolyte will always remain attractive. A breakthrough in CO2 tolerance, a CO2 -tolerant alkaline electrolyte with similarly good ORR kinetics, or cost-effective CO2 filtration would likely spur renewed interest. Some CO2 tolerance is now possible [65], so there may be a future for this technology. Development of alkaline-based polymer electrolyte fuel cells is also a promising future technology.

7.5

BIOLOGICAL AND OTHER FUEL CELLS Just when it seems all of the possible combinations of fuel cells have been examined, there are more. In this section, a very brief description of some of the fuel cell concepts with future potential is given as a brief introduction. Biological fuel cells, or biofuel cells, use biological processes to convert organic fuel directly into electrons. A microbial biofuel cell uses living microorganisms for the electrochemical reaction. Since the organisms are living, the system is very sensitive to environmental changes which can quickly kill off the microorganisms. Enzymatic biofuel cells utilize redox enzymes as biocatalysts for the redox reactions. Bioprocessing of water products can also be used to directly generate hydrogen for conventional fuel cells. The energy density of these bio-based systems is several orders of magnitude lower than conventional fuel cell systems, however. Excellent reviews and summaries of biofuel cells are given in [66–68]. Metal air batteries are sometimes referred to as fuel cells. Really, they are hybrid systems that operate on flowing air like fuel cells but oxidation of stored metal like a battery. Usually, an alkaline electrolyte is used in these system because of the favorable ORR kinetics. Because the fuel is stored as a solid and the oxygen is not stored onboard, instead absorbing from the ambient air during discharge, the system can achieve a higher specific charge and energy density compared to full-battery systems. Essentially, this behaves as a battery with the oxidizer stored in the ambient air. It is an energy storage system that does not obtain a true equilibrium because the fuel is gradually depleting during discharge, and therefore these are not really fuel cells. Reviews of zinc–air and seawater aluminum–air systems can be found in [69, 70].

7.6

SUMMARY The world of fuel cells comes in many varieties. Although PEFCs are featured in Chapter 6, they are by no means the only option. Several other fuel cell systems can potentially reach commercial production following current development trajectories. In a generic sense, the advantages and disadvantages of each fuel cell fall along the lines of temperature and electrolyte classification. High-temperature fuel cells suffer from reduced maximum thermodynamic efficiency and slow startup times but can use non–noble metal catalysts and reform a wide variety of carbon-based fuel streams, while low-temperature fuel cells can have rapid startup but have higher raw material costs and a need for pure hydrogen streams. All liquid electrolyte systems suffer from vaporization losses and enhanced corrosion.

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Individually, the first real development thrust was focused on the AFC for space applications. The AFC has a broad temperature and pressure operation range and the highest operating efficiency of the various fuel cell combinations due to the reduced ORR polarization. However, its low power density and inability to handle CO2 in air without a scrubber or recirculating electrolyte configuration have limited its usefulness. The PAFC was the next system to be seriously developed following the AFC and is the first mass-produced fuel cell system to reach the consumer market in premium power applications. Through several generations of design, stationary 200-kWe PAFC systems showed reliable (>95%) service and high combined efficiency (>80%). Ultimately, the total system cost has limited development of this technology. Molten carbonate and solid oxide fuel cells are the high-temperature fuel cell technologies available. Both systems have the potential for direct internal reformation of carbonbased fuel sources and used as part of a CHP or cogeneration system for achieving high overall conversion efficiency. Issues with the liquid electrolyte loss and accelerated catalyst and separator plate corrosion in the MCFC must be resolved, and SOFC systems will continue to seek less expensive and more reliable manufacturing methods that increase the stack component robustness. It is a desire of SOFC design to reach lower operating temperatures approaching that of the MCFC (650◦ C), so that metallic parts can be used. This is being approached with anode-supported designs, novel electrolyte materials, and ultrathin electrolyte structures. There are also many other fuel cell technologies that are not yet mainstream but may become mainstream in the future. Metal–air battery systems are really a hybrid between a battery with stored fuel and a fuel cell with flowing oxidizer. Biological fuel cells represent laboratory-based nascent technologies with very low power density. However, the potential advantages of these systems for power neutral waste remediation is worthy of future development. It is a common misconception that no fuel cell system has been marketed as a product. Many have, and more are coming. The high-temperature systems even eliminate the need for a hydrogen infrastructure, so that implementation of stationary power applications can occur right away. Given the high efficiency, low emission, and relatively silent operation of PAFC, SOFC, and MCFC systems, it seems highly likely that at least one of these technologies will be come mainstream for stationary power applications in the coming decades.

APPLICATION STUDY: SYSTEM DESIGN The ancillary components in many fuel cell systems consume 50–75% of the cost and bulk of the system, are responsible for many of the degradation issues, and can consume 20–30% of the gross power output of the system. In this assignment, choose a fuel cell system (e.g., a molten carbonate fuel cell for stationary power applications) and draw a process flow diagram of the system. Try to include all of the components necessary for operation, including pumps, blowers, preheaters, and power conditioning. An example of a process flow diagram for a 3-MWe molten carbonate fuel cell operating on landfill gas is given below. On a separate page, list the function of each component you show. Make sure you have not left anything out. Will the flow be able to come into and leave the stack? What will happen to the unused fuel? Will the power be properly conditioned to suit the application?

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3 MWe direct carbonate fuel cell on LEG.

PROBLEMS Solid Oxide Fuel Cell 7.1 Describe some markets where the SOFC is appropriate and discuss the potential advantages of this technology compared to the competing technologies. What are the hurdles that still must be overcome before the SOFC can enter this market? 7.2 Describe the advantages and disadvantages of the solid-phase electrolyte used in the SOFC. 7.3 There is great potential for increasing overall system efficiency of the SOFC by use of cogeneration or a bottoming cycle to utilize the exhaust gas and waste heat. If the high-temperature hydrogen-rich exhaust gas from the SOFC anode were burned in a combustor and used to power a steam turbine, additional electricity could be generated. Write an expression for the maximum theoretical cogeneration efficiency of a fuel cell–heat engine combination. For maximum system efficiency, what conditions are optimal? 7.4 Compare the oxygen diffusivity in air at 353 and 1273 K. How dilute would an oxygen stream at 1273 K have to be to have the same diffusion flux as one at 373 K? Assume

the 373 K stream has a mole fraction of oxygen of 0.21 and diffusion is to the cathode at limiting current conditions. What would the mole fraction of the equivalent stream at 373 K have to be? 7.5 What are the practical consequences of a leaky (e.g., hydrogen leaks) SOFC fuel cell stack? Think in terms of performance, efficiency, and safety. How could you resolve the leaky SOFC stack issue if the high-temperature seals in a planar stack cannot be made to perfectly seal the system.

Molten Carbonate Fuel Cell 7.6 Describe some markets where the MCFC is appropriate and discuss the potential advantages of this technology compared to the competing technologies. What are the hurdles that still must be overcome before the MCFC can enter this market? 7.7 Use the MCFC model of Eqs. (7.5)–(7.8) to investigate the performance of a MCFC as a function of temperature. At 600, 650, and 700◦ C, what fraction of the polarization comes from ohmic, anodic, and cathodic activation losses. Which loss is most sensitive to temperature?

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References 7.8 Use the MCFC model of Eqs. (7.5)–(7.8) to investigate the performance of a MCFC as a function of gas mole fraction. At 650◦ C, what is the effect of doubling the oxygen partial pressure on the anode? What is the effect of doubling the hydrogen partial pressure on the anode? What role does CO2 play on the anode and cathode? 7.9 The Nernst equation for the MCFC shows that the ratio of cathode to anode CO2 partial pressure can have an effect on voltage. Given that you cannot have a differential pressure between the anode and cathode, what would be the effect of doubling the CO2 mole fraction in the cathode? Is there a drawback to this. (Hint: What happens to the oxygen mole fraction?) 7.10 What is the Nernst Open-Circuit Voltage for a MCFC operating at 650◦ C with equal mole fraction of CO2 on the anode and cathode and dry air and hydrogen at 1 atm are used as the reactants.

Phosphoric Acid Fuel Cell 7.11 Describe some markets where the PAFC is appropriate and discuss the potential advantages of this technology compared to the competing technologies. What are the hurdles that still must be overcome before the PAFC can enter this market? 7.12 Given a 0.5-m2 -active-area PAFC 250-cell stack operating at 150 mA/cm2 , a cathode stoichiometry of 2.0, and an anode stoichiometry of 1.3, (a) plot the amount of electrolyte lost to the anode and cathode flow over 40,000 h operation as a function of H3 PO4 ppm vapor pressure and (b) use another resource to find the vapor pressure of H3 PO4 as a function of temperature from 160 to 200◦ C and discuss the difference in onboard stored H3 PO4 that can be achieved from reducing operating temperature from 200 to 175◦ C. 7.13 Methanol can be steam reformed at a relatively low temperature of reformation of 200◦ C. Can methanol be internally reformed in the PAFC? What would have to be done to the anode flow to allow this? Discuss the potential problems with this approach.

421

7.14 The SiC matrix that holds the PAFC electrolyte has very small, uniform pores. Describe why the pore size is smallest in the matrix compared to the porous flow field or catalyst layer, and what is the consequence of a nonuniformity in the SiC particle size? 7.15 In all electrolytes, there is some solubility and diffusion of reactant gas into the material that results in crossover losses. Is some limited crossover due to this effect as major an issue for the PAFC as the PEFC? Why or why not? 7.16 What is the difference in the Nernst Open-Circuit Voltage for a PEFC operating at 80◦ C, a PAFC operating at 200◦ C, and a SOFC operating at 1000◦ C. Assume all systems operate on air and hydrogen at 1 atm. How do the high-temperature systems make up for this difference?

Alkaline Fuel Cell 7.17 Describe some markets where the AFC is appropriate and discuss the potential advantages of this technology compared to the competing technologies. What are the hurdles that still must be overcome before the AFC can enter this market? 7.18 Do some reading and discuss the major approaches available for CO2 scrubbing from atmospheric air. Is the major impediment to application of this to AFCs efficiency of conversion, cost of the approach, bulk, or something else? 7.19 If a given AFC operates at 0.8V, 1 A/cm2 , compared to the PEFC, at 1 A/cm2 , 0.65 V, what is the savings in terms of waste energy dissipated as heat for a 100-kWe AFC system compared to a PEFC system.

Biological and Other Fuel Cells 7.20 Describe some markets where a microbial fuel cell is appropriate and discuss the potential advantages of this technology compared to the competing technologies. What are the hurdles that still must be overcome before this technology can enter this market? 7.21 Write a one-page summary of microbial fuel cells. Describe the anodic and cathodic reactions and electrolyte used.

REFERENCES ¨ 1. W. Nernst, “Uber die elektrolytische Leitung fester K¨orper bei sehr hohen Temperaturen,” Z. Elektrochem., No. 6. pp. 41–43, 1899. 2. P. Holtappels and U. Stimming, “Solid Oxide Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003 pp. 335–354.

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Other Fuel Cells 3. Press Release, No. 1128, Mitsubishi Heavy Industries, Tokyo, Japan, July 4, 2006. 4. “Fact Sheet: Solid-Oxide Fuel Cell System for Stationary Power Generation”, Rolls-Royce, Fuel Cell Systems Limited, Leicestershire, England October, 2006. 5. Net∼Gen Product Brochure No. 0905, Ceramic Fuel Cells. 6. Advanced Technology Program Project Brief 00-00-5290, National Institute of Standards and Technology. Gaithersburg, Md, 2004. 7. SECA Product Brochure, U.S. Department of Energy, Washington, DC, August 2006. 8. N. Minh and T. Takahashi, Science and Technology of Ceramic Fuel Cells, Elsevier, New York, 1995. 9. R. Doshi, V. L. Richards, J. D. Carter, X. Wang, and M. Krumpelt, “Development of Solid Oxide Fuel Cells That Operate at 500◦ C, ” J. Electrochem. Soc., Vol. 146, pp. 1273–1278, 1999. 10. O. Yamamoto, “Low Temperature Electrolytes and Catalysts,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1002–1014. 11. T. Ishihara, “Novel Electrolytes Operating at 400–600◦ C,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1109–1122. 12. D. St¨over, H. P. Buchkremer, and J. P. P. Huijsmans, “MEA/Cell Preparation Methods: Europe/USA,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1015– 1031. 13. M. Suzuki, “MEA/Cell Preparation Methods: Japan/Asia,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1032–1036. 14. T. Kawada and J. Mizusaki, “Current Electrolytes and Catalysts,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 987–1001. 15. A. V. Vikrant, “Introduction to Solid Oxide Fuel Cells (SOFC): Science and Technology,” Presented at the NETL 2001 Solid Oxide Fuel Cell Training Course, July 10–11, 2001. Morgantown, West Virginia. 16. S. C. Singhal, “Advances in Solid Oxide Fuel Cell Technology,” Solid State Ionics, Vol. 135, Issues 1–4, No. 1 pp. 305–313, 2000. 17. R. F. Service, “New Tigers in the Fuel Cell Tank,” Science, Vol. 288, pp. 1955–1957, 2000. 18. S. C. Singhal, “Solid Oxide Fuel Cells for Stationary, Mobile, and Military Applications,” Solid State Ionics, Vol. 152/153, pp. 405–410, 2002. 19. K. Eguchi, “Internal Reforming,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1057–1069. 20. P. Zafred, “Solid Oxide Fuel Cell Technology Overview,” Paper presented at Pennsylvania State University, University Park, PA, November 2006. 21. K. Kendall, “New Microtube Concepts,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1089–1097. 22. S. de Souza, S. J. Visco, and L. C. De Jonghe, “Thin-Film Solid Oxide Fuel Cell with High Performance at Low-Temperature,” Solid State Ionics, Vol. 98, Issues 1–2, No. 1, pp. 57–61, 1999.

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23. Y. Matsuzaki and I. Yasuda, “Dependence of SOFC Cathode Degradation by ChromiumContaining Alloy on Compositions of Electrodes,” J. Electrochem. Soc., Vol. 148, No. 2, pp. A126–A131, 2001. 24. E. Baur and J. Tobler, “Brennstoff Ketten,” Z. Elektrochem. Vol. 39. pp. 169–180, 1933. 25. Fuel Cell Energy, www.fce.com. 26. J. Larminie and A. Dicks, Fuel Cells Explained, 2nd ed. Wiley, West Sussex, England, 2003. 27. H. Yokokawa and N. Sakai, “History of High Temperature Fuel Cell Development,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 219–266. 28. A. L. Dicks and A. Siddle, “Assesment of Commercial Prospects of Molten Carbonate Fuel Cells,” ETSU Report No. F/03/00168/REP, AEA Technology, Harwell, UK, 1999. 29. M. Farooque and H. Ghezel-Ayagh, “System Design,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003 pp. 942–968. 30. G. Steinfeld and R. Sanderson, “Landfill Gas Cleanup for Carbonate Fuel Cell Power Generation,” Natural Renewable Energy Lab (NREL) DOE-NETL Final Report, Golden, Colorodo, February 1998. 31. Y. Fujita, “Durability,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 969–982. 32. Y. Mugikura, “Stack Material and Stack Design,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 907–920. 33. C. E. Baumgartner, R. H. Arendt, C. D. Iacovangelo, and B. R. Karas, “Molten Carbonate Fuel Cell Cathode Materials Study,” J. Electrochem. Soc., Vol. 131, pp. 2217–2221, 1984. 34. E. Bergaglio, P. Capobianco, S. Dellepiane, G. Durante, M. Scagliotti, and C. Valli, “MCFC Cathode Dissolution: An Alternative Approach to Face the Problem,” J. Power Sources, Vol. 160, pp. 796–799, 2006. 35. S. Randstr¨om, C. Lagergren, and P. Capobianco, “Corrosion of Anode Current Collectors in Molten Carbonate Fuel Cells,” J. Power Sources, Vol. 160, pp. 782–788, 2006. 36. L. Zhou, H. Lin, and B. Yi, “Sintering Behavior of Porous α-Lithium Aluminate Matrices in Molten Carbonate Fuel Cells at High Temperature,” J. Power Sources, Vol. 164, pp. 24–32, 2007. 37. J. M. King, H. R. Kunz, “Phosphoric Acid Electrolyte Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 287–300. 38. J. M. King and B. McDonald, “Experience with 200 kW PC25 Fuel Cell Power Plant,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 832–843. 39. N. Sammes, R. Bove, and K. Stahl, “Phosphoric Acid Fuel Cells: Fundamentals and Applications,” Curr. Opin. Solid State Mater. Sci., Vol. 8, No. 5, pp. 372–378, 2004. 40. D. A. Landsman and F. J. Luczak, “Catalyst Studies and Coating Technologies,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 811–831. 41. T. Brenscheidt, K. Janowitz, H.-J. Salge, H. Wendt, and F. Brammer, “Performance of ONSI PC25 PAFC Cogeneration Plant,” Int. J. Hydrogen Energy, Vol. 23, No. 1, pp. 53–56, 1998. 42. PC25 Data Sheet, UTC Power Corporation. South Windsor, CT, 2005. 43. A. J. Appleby, “FUEL Cell Technology: Status and Future Prospects,” Energy, Vol. 21, No. 7/8, pp. 521–653, 1996.

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Other Fuel Cells 44. M. Neergat and A. K. Shukla, “A High-Performance Phosphoric Acid Fuel Cell,” J. Power Sources, Vol. 102, No. 1/2, pp. 317–321, 2001. 45. R. D. Breault, “Stack Materials and Stack Design,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds.,Wiley, New York, 2003, pp. 797–810. 46. P. Sharke, Associate Editor Police Power, Mechanical Engineering Power, The American Society of Mechanical Engineers, New York, NY, May 2000. 47. T. G. Benjamin, E.H. Camara, and L. G. Marianowski, Handbook of Fuel Cell Performance, prepared for the U.S. Department of Energy under contract number EC-77-C-03-1545, Institute of Gas Technology, Des Plaines, IL, 1980. 48. R. D. Breault, “Method for Reducing Electrolyte Loss from an Electrochemical Cell,” U.S. Patent 4, 414291, November. 8, 1983. 49. Fuel Cell Handbook, 5th ed., EG&G Services Parsons, Science Applications International Corporation, National Technical Information Service, US Dept. of Commerce, Springfield, VA, 2000. 50. J. S. Wainright, J.-T. Wang, D. Weng, R. F. Savinell, and M. Litt, “Acid-Doped Polybenzimidazoles: A New Polymer Electrolyte,” J. Electrochem. Soc., Vol. 142, pp. L121–L123, 1995. 51. O. E. Kongstein, T. Berning, B. Børresen, F. Seland, and R. Tunold, “Polymer Electrolyte Fuel Cells Based on Phosphoric acid Doped Polybenzimidazole (PBI) Membranes,” Energy, Vol. 32, No. 4, pp. 418–422, 2007. 52. J.-T. Wang, R. F. Savinell, J. Wainright, M. Litt, and H. Yu, “A H2 /O2 Fuel Cell Using Acid Doped Polybenzimidazole as Polymer Electrolyte,” Electrochim. Acta, Vol. 41, pp. 193–197, 1996. 53. Z. Qi and S. Buelte, “Effect of Open Circuit Voltage on Performance and Degradation of High Temperature PBI–H3 PO4 Fuel Cells,” J. Power Sources, Vol. 161, No. 2, pp. 1126–1132, 2006. 54. L. Xiao, H. Zhang, T. Jana, E. Scanlon, R. Chen, E.-W. Choe, L. S. Ramanathan, S. Yu, and B. C. Benicewicz, “Synthesis and Characterization of Pyridine-Based Polybenzimidazoles for High Temperature Polymer Electrolyte Membrane Fuel Cell Applications,” Vol. 5, pp. 287–295, 2005. 55. J.-T. Wang, J. S. Wainright, R. F. Savinell, and M. Litt, “A Direct Methanol Fuel Cell Using Acid-Doped Polybenzimidazole as Polymer Electrolyte,” J. Appl. Electrochem, Vol. 26, p. 751, 1996. 56. M. Warshay and P. R. Prokopius, “The Fuel Cell in Space: Yesterday, Today, and Tomorrow,” J. Power Sources, Vol. 29, pp. 193–200, 1990. 57. M. Warshay, P. R. Prokopius, M. Le, and G. Voecks, “NASA Fuel Cell Upgrade Program for the Space Shuttle Orbiter,” Proc. Intersoc. Energy Conversion Eng. Conf., Vol. 1, pp. 1717–1723, 1996. 58. M. Cifrain and K. Kordesch, “Hydrogen/Oxygen (Air) Fuel Cells with Alkaline Electrolytes,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 267–280. 59. http://www.cmdl.noaa.gov/ccgg/trends/. National Oceanic and Atmospheric Administration. 60. A. Tewari, V. Sambhy, M. Urquidi Macdonald, and A. Sen, “Quantification of Carbon Dioxide Poisoning in Air Breathing Alkaline Fuel Cells,” J. Power Sources, Vol. 153, pp. 1–10, 2006. 61. E. G¨ulzow, M. Schulze, and U. Gerke, “Bipolar Concept for Alkaline Fuel Cells,” J. Power Sources, Vol. 156, pp. 1–7, 2006. 62. K. Kordesch and V. Hacker, “Stack Materials and Design,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 766–773.

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63. K. Kordesch and M. Cifrain, “A Comparison Between the Alkaline Fuel Cell (AFC) and the Polymer Electrolyte Membrane (PEM) Fuel Cell,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 789–793. 64. K. Strasser, “System Design and Applications,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 4, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 775–788. 65. E. G¨ulzow, N. Wagner, and M. Schulze, “Preparation of Gas Diffusion Electrodes with Silver Catalysts for Alkaline Fuel Cells,” Fuel Cells, Vol. 3, pp. 67–72, 2003. 66. S. Calabrese Barton, J. Gallaway, and P. Atanassov, “Enzymatic Biofuel Cells for Implantable and Microscale Devices,” Chem. Rev., Vol. 104, No. 10, pp. 4867–4886, 2004. 67. E. Katz, A. N. Shipway, and I. Willner, “Biochemical Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 354–381. 68. B. E. Logan, and J. M. Regan, “Microbial Fuel Cells—Challenges and Applications,” Environ. Sci. Technol., Vol. 40, No. 17, pp. 5172–5180, 2006. 69. O. Haas, F. Holzer, K. M¨uller, and S. M¨uller, “Metal/Air Batteries: the Zinc Air Case,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 382–408. 70. J. P. Iudice de Souza and W. Wielstich, “Seawater Aluminum/Air Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 1, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 409–415.

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Fuel Cell Engines Matthew M. Mench

8

Copyright © 2008 by John Wiley & Sons, Inc.

Hydrogen Storage, Generation, and Delivery People say that hydrogen cars would be pollution-free. Lightbulbs are pollution-free, but power plants are not. —University of Calgary engineering professor David Keith

The politics of the so-called hydrogen economy are fascinating, and it will be interesting to see how the future of energy generation, storage, and delivery develops. Some people see the hydrogen economy as an economic or practical impossibility and instead advocate an electron-based economy [1], where electrons are transmitted from distributed power plants to generate hydrogen or recharge battery devices locally, eliminating some of the economic and engineering difficulties inherent with hydrogen. Others advocate the use of clean-burning coal or natural gas, energy sources that are available in the near term in sufficient quantities to help offset crude-oil usage. The purpose of this chapter is not to debate the particular economic or political merits or limitations of the myriad possibilities but to present the reader with a basic background on the methods of hydrogen storage, generation, and delivery. Regarding future energy supply, this much is clear; over time, worldwide fossil fuel reserves will eventually peak, causing oil prices to rise to the point where other energy sources become economically viable. This, coupled with environmental and world-security concerns, will eventually force a change in the way energy is stored, delivered, and generated. It is likely that hydrogen derived from noncarbon or carbon-neutral sources will eventually play an important role in this future society.

8.1

MODES OF STORAGE In fuel cell applications where the power source is mobile, such as automotive or portable usage, a hydrogen carrying fuel reservoir is needed. For stationary applications, where the fuel cell can be attached to a natural gas or hydrogen pipeline, storage is not as critical. Consider a portable electronic application. Even if the fuel cell is optimized to the point where the stack itself is quite small, there is a need for a highly dense fuel storage reservoir or the total system will be unacceptably large. Similarly, in automotive applications, there needs to be a hydrogen fuel tank capable of achieving approximately the same total driving range as the gasoline tank it replaces with at least comparable volumetric and gravimetric 426

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Modes of Storage

427

Table 8.1 Selected Thermodynamic Properties of Fuels Property/Fuel Boiling Point (K) Heat of combustion (MJ/kg) based on LHV Density (at STP) (kg/m3 ) Flammability limits in air (%)

Hydrogen H2

Gasoline, C8 H18 ∗

Ethanol C2 H5 OH

Methanol CH3 OH

20 120.97

398 44.43

352 28.87

338 19.94

0.09

703

789

792

4–75

1–6.5

3.3–19

6–36

∗ Note

that gasoline is actually a very complex blends of fuels, detergents, and other agents that vary among region, season, and manufacturer. It is common, however, to estimate the thermodynamic properties of gasoline with octane.

energy densities. This turns out to be a difficult challenge. Gasoline is a high-energycontent, high-density liquid that can be stored at atmospheric pressure. Hydrogen also has a molar high-energy content but a very low density as a gas phase. Some of the properties of hydrogen compared to gasoline and some other alcohol fuels are shown in Table 8.1 for comparative purposes. The U.S. Department of Energy (DOE) goals for hydrogen storage are as follows [2]: Ĺ By 2010, develop and verify on-board hydrogen storage systems achieving 2 kWh/kg (6 wt. %), 1.5 kWh/L, and $4/kWh. Ĺ By 2015, develop and verify on-board hydrogen storage systems achieving 3 kWh/kg (9 wt. %), 2.7 kWh/L, and $2/kWh. Example 8.1 How Much Hydrogen Is Needed? Consider that a gasoline tank on a common automobile is about 15 gal. Estimating the gasoline as octane (C8 H18 ), determine approximately how many kilograms of hydrogen are needed to replace the gasoline in the conventional automobile on an energy basis. You can consider the hydrogen fuel cell to be approximately twice as efficient at energy conversion compared to the gasoline engine. SOLUTION We first convert the 15 gal of gasoline into kilograms and look up the values of octane density from online sources or reference books: (15 gal)(0.003785411784 m3 /gal)(917 kg/m3 ) = 52 kg The heat of combustion of octane can be solved from the balanced chemical reaction, found in thermodynamic reference books, or from an energy balance of the chemical reaction: C8 H18 + 12.5 (O2 + 3.76N2 ) −→ 8CO2 + 9H2 O + 47N2

   Hc = n i h¯ i − n i h¯ i = −5512 kJ/mol P

R

This value is negative because it is an exothermic reaction. This is equivalent to 48.3 MJ/kg (MWoctane = 114 kg/kmol). Therefore, the typical gasoline tank contains (52 kg) (48.3 MJ/kg) = 2.5135 × 103 MJ

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Hydrogen Storage, Generation, and Delivery

Assuming the average fuel cell efficiency is about double that of gasoline, we only need about half of the initial chemical energy, or 1.25 × 103 MJ. The heat of combustion of hydrogen is 120.97 MJ/kg. Therefore, we would need 1.257 × 103 MJ = 10.4 kg H2 120.97 MJ/kg This seems like a very favorable comparison to gasoline, in that the mass of gasoline was 52 kg. However, when you consider the density difference, the hydrogen storage problem is obvious. At room temperature and pressure, the density of hydrogen is 0.08988 kg/m3 , over 10,000 times less than gasoline. COMMENTS: Assuming a typical driving range of 350 miles on a tank of gasoline, a 15-gal hydrogen tank at room temperature and pressure would only have a driving range of about 0.05 miles! Obviously, the challenge is finding a way to store enough hydrogen so the tank is not prohibitively large or heavy. From Example 8.1, we learned that, depending on the fuel cell efficiency, about 5–10 kg of hydrogen storage is needed to replace gasoline in conventional automotive applications. A similar calculation could be made for portable electronic applications. The required hydrogen storage can be technically achieved by several methods: 1. 2. 3. 4. 5.

Compressed gas Cryogenic liquid Hydride storage Carbon storage Liquid fuel storage

The advantages and difficulties of each approach will be discussed in the following sections. Compressed Gas Compressed hydrogen is perhaps the most well-developed approach to providing hydrogen storage. Pressurized gas storage vessels are common in everyday life (e.g., medical oxygen, helium balloons, welding equipment). The storage pressures of these vessels are normally below 17 MPa. While the technology and safety for these storage vessels are well developed, vehicular applications require much higher gas pressures up to 71 MPa (700 bars, or ∼10,000 psig), while maintaining a low storage vessel mass and high inherent safety. With a 71-MPa storage vessel, 1.3 kWh/kg mass storage density and 0.8 kWh/L volumetric storage density have been achieved [3]. This compares to 2010 DOE goals of 2.0 kWh/kg and 1.5 kWh/L, respectively More advances can be made, although relative to other competing technologies, compressed storage is fairly well developed. Figure 8.1 is a picture of a wound-fiber pressure vessel developed for this purpose. Modern high-pressure gas-phase storage vessels are constructed of plastic or thin metallic inner liners wrapped in high-strength load-bearing woven fiber embedded in a composite matrix material [4]. These so-called composite vessels are significantly lighter and more robust than their fully metallic predecesors. The desired profile of a gasoline tank in an automotive application is typically flattened, and although a purely cylindrical profile is ideal to hold pressurized gas, the shape is

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8.1

Figure 8.1 Ref. [4].)

Modes of Storage

429

Photograph of 10,000-psig hydrogen storage tank. (Reproduced with permission from

inefficient to fit in a normal automobile. For this reason, noncylindrical and conformed shape vessels are also desirable. Some relevant design data for composite high-pressure hydrogen storage vessels are given in Table 8.2. It can be seen that a 1-m-long, 30-cmdiameter vessel at 700 bars (∼71 MPa) pressure stores only 2 kg of hydrogen, so that three to four of these would be needed in a typical automobile to achieve a normal cruising range. At such high pressures, non–ideal gas effects are present, as discussed in Chapter 3. Thus, the scaling relationships between storage pressures are nonlinear, and the weight specific energy storage of the highest pressure vessels actually decreases. Another major drawback of the high-pressure storage concept is the work required to compress the gas and time to deliver the compressed gas into the fuel tank. The minimum thermodynamic work of compression of gas for an internally reversible compressor (gas) or pump (liquid) per unit mass is [5] 2 dP (8.1) w int.rev. = − ρ 1

Table 8.2 Selected Properties of Composite Compressed Hydrogen Vessels of 200, 400, and 700 bars Pressure Property Internal volume (L) Vessel diameter (m) Vessel length (m) Vessel weight (kg) Stored energy (kWh) Stored H2 (kg) Vessel-to-hydrogen weight ratio Weight specific energy storage (kWh/kg) Volume specific storage (kWh/L) Source: Adapted from [4].

200-Bar Vessel

400-Bar Vessel

700-Bar Vessel

50 0.3 1.0 25 24 0.7 35.7 0.96 0.48

50 0.3 1.0 45 43 1.3 34.7 0.96 0.86

50 0.3 1.0 85 66 2.0 42.5 0.78 1.32

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For a liquid pump, the density (ρ) is almost constant, and the minimum work per unit mass can be evaluated as w int.rev. =

P1 − P2 ρ

(8.2)

For gas-phase compression, the work to achieve the same increase in pressure compared to the liquid pump is much higher, since the density is not constant. Since significant non–ideal gas effects are present when compression is to 71 MPa, a simple integration with the ideal gas assumption is an underestimate but serves as a qualitative comparison. For an isothermal compression of an ideal gas, we can show that   P1 Ru T (8.3) ln w int.rev. = MW P2 For a nonisothermal polytropic compression [where (P/ρ)n = constant] of an ideal gas, we can show that

 P2 (n−1)/n n Ru T1 −1 (8.4) w int.rev. = n−1 P1 The work required to compress the gas to the high pressures adds to the overall cost and complexity of the compressed hydrogen energy solution and can exceed 20% of the specific energy content of the compressed hydrogen itself. This greatly reduces the overall well-to-wheel efficiency of the fuel cell system. Another challenge with compressed hydrogen storage is the delivery of the hydrogen to the fuel tank. Delivery of gas from a high-pressure to low-pressure source cannot be accomplished rapidly or the temperature will quickly rise as it is compressed in the lowpressure side, causing safety concerns and reducing storage capability. Additionally, the safety of compressed hydrogen is always a question. The public perception of hydrogen as a dangerous fuel is at least partially a result of the Hindenberg disaster of 1937, in which the hydrogen-filled German zeppelin ignited while docking in Lakehurst Naval Air Station in Manchester, New Jersey (Figure 8.2). After ignition from a spark, lightning, or lighting (several theories abound), the flame quickly spread, resulting in the death of tens of passengers and crewmen. Although hydrogen was widely believed to be the cause, it is now believed that the hydrogen fuel was not completely to blame, and the ignitable surface coating on the craft also played a major role [6]. Hydrogen does have a very wide flammability limit of 4–77%, meaning that an air–hydrogen mixture is ignitable from 4 to 77 mol %. However, since the diffusivity of hydrogen in air is so high and it is so light, it quickly disperses upward into the atmosphere making continual combustion more difficult to sustain. Finally, the high-pressure hydrogen storage tank is a concern not only due to flammability but also perhaps even more from the stored energy of compression, which can cause major damage if suddenly released in the event of an accident. In summary, the main advantages of compressed hydrogen are as follows: 1. Reasonably advanced and developed technology that can be implemented in the near term. 2. Favorable comparison to current cryogenic storage systems in terms of parasitic energy requirements for preparation.

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Figure 8.2 The Hindenberg disaster symbolizes the danger of the use of hydrogen to many, although it is now believed the paint on the skin of the vessel played a major role in the flame propagation.

The main disadvantages include the following: 1. Low volumetric and gravimetric storage density compared to gasoline storage and lower than desired gravimetric and volumetric energy densities, even at 70 MPa pressure. 2. Energy-intensive hydrogen compression process. 3. Safety concerns of high-pressure cylinders and hydrogen flammability. 4. Slow refill of hydrogen tank from a high-pressure source. Ultimately, improvements in other hydrogen storage alternatives may eliminate highpressure storage as the main storage mode, considering the disadvantages noted. For the near term or until other technologies develop, however, compressed storage remains a viable option and the storage solution used in most automotive fuel cell systems. Cryogenic Liquid When cooled to about 20 K, hydrogen condenses into a liquid. Liquid hydrogen has been used for various industrial processes since the 1940s, but application to automotive use would require a completely new infrastructure. Figure 8.3 shows a comparison of the volumetric energy content of liquid versus gas-phase hydrogen storage, not

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Figure 8.3 Comparison of energy content in liquid hydrogen (LH2 ) and gas-phase hydrogen stored at different pressures. (Reproduced with permission from Ref. [7].)

including the storage cylinder volume. Obviously, cryogenic storage offers big advantages compared to compressed hydrogen in terms of storage volume and reduced storage pressure. Additionally, due to the lower pressures, it is possible to conform the shapes of the storage vessel to the available space in automotive applications, increasing storage efficiency. Another potential advantage of cryogenic fuel compared to compressed hydrogen is faster refill capability, although the technical and safety concerns of public handling of a cryogenic liquid at the fuel pump are nontrivial. There are significant limitations to the liquid hydrogen approach. Considering the cryogenic nature of the fluid and extremely low temperature, advanced thermally insulated vessel technology must be used to reduce hydrogen boil-off rates. Boil-off is a result of heat leakage into the storage vessel, which increases the temperature of the liquid pool until the boiling point is reached. Additional input energy is absorbed as latent heat of vaporization. The increased internal pressure of the sealed storage vessel as gasification occurs can delay the boil-off somewhat, but these vessels are generally not designed with very high pressure capability. Therefore, when boil-off occurs, the excess hydrogen must be vented or consumed to avoid overpressurization of the storage vessel. Venting hydrogen to the environment poses safety and environmental concerns and results in loss of stored fuel, which is a major inefficiency and practical annoyance. No one wants to leave their car in the garage, go on vacation, and have an empty fuel tank on return. This also precludes prefueling of vehicle rental or other fleets in storage. Another primary limitation of the cryogenic approach is the high energy loss required to prepare liquid fuel (up to 30% of the total specific energy content [7]). Estimates of future production costs of various fuel alternatives predict that liquid hydrogen production will be significantly more expensive than compressed hydrogen production, methanol, or

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conventional oil resources [8]. This greatly reduces the overall well-to-wheel efficiency for this option. Also, public refilling stations for liquid (and likely gas-phase) hydrogen will need to be automated, so that human interaction and possible contact with the cryogenic fuel are eliminated. In summary, the main advantages of cryogenic storage are as follows: 1. 2. 3. 4. 5.

A relatively developed technology with demonstrated storage capability. A high gravimetric and volumetric storage density. Relatively quick refill capability. Efficient transport from liquid hydrogen generation stations. Some limited existing industrial infrastructure.

The main disadvantages include the following: 1. Use of a cryogenic fuel that will gain heat from the surroundings, causing boil-off losses and necessitating highly advanced insulation. 2. The high energy loss over time and cost required to prepare liquid fuel. 3. Safety concerns to the public for delivery of cryogenic fuel. Both pressurized storage and liquid hydrogen storage are commonly utilized in prototype automotive units. Ultimately, however, neither cryogenic or high-pressure hydrogen storage satisfies all the needs of the consumer, and alternate approaches or further advances in the technology are needed. Hydride Storage Metal and chemical hydrides also offer a potential solution to the hydrogen storage issue. In hydride storage, the hydrogen is stored as part of the solid material matrix and released by chemical reaction or heat addition. Storage of hydrogen in this manner offers the potential for safe, controllable and convenient storage. In general, hydride storage comes in two varieties1: (1) chemical hydrides and (2) metal hydrides. Both approaches have the potential to resolve hydrogen storage issues in mobile fuel cell applications but must achieve a higher gravimetric storage density or lower cost to compete with other technologies. Another factor that must be considered with hydrides is the rate of availability and release of hydrogen. Unlike compressed hydrogen storage, matching the hydrogen release rate to the required fuel cell flow rate is not a trivial matter, and proper heat transfer and flow systems must be employed. Chemical Hydrides Chemical hydrides are manufactured hydrogen-containing materials that are chemically reacted with water, releasing heat and hydrogen gas. The hydrogen release process occurs upon a hydrolysis reaction with water. For example, the sodium borohydride reaction is [9] NaBH4 + 2H2 O → NaBO2 + 4H2 + heat

(8.5)

Usually the chemical hydride reacts in a water solution, and some of the hydrogen released is from the water itself. After hydrogen release, the reaction product can typically be 1 Liquid-hydrogen-carrying

fuels are also sometimes referred to as liquid hydrides.

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Gas Pump NaBO2 spent fuel in

rehydrided Chemical Plant

fuel out NaBH4 + H2O

spent fuel recovery NaBO2

Figure 8.4 Schematic of chemical hydride recycle process.

recycled and reused (see Figure 8.4). Other potential chemical hydrides include calcium hydride (CaH2 ), lithium aluminum hydride (LiAlH4 ), and magnesium hydride (MgH2 ). The hydrogen release rate must match that required by the fuel cell, so there must be an ability to control the hydrogen production reaction. The chemical hydride reaction rate can be controlled by temperature via heat transfer from recycled waste heat, solution concentration, or flow rates. Rapid production of hydrogen is not typically limiting, however [10], and the technical challenge lies in achieving the proper control of the heat transfer and flow system response. Advantages of the chemical hydride reaction approach are the ability to rapidly and controllably generate hydrogen, storage and transportation of hydrogen in solid form with high hydrogen storage density, and ability to recycle and recharge the spent fuel. However, the disadvantages of this approach are the expense of the hydride regeneration reaction and added complexity of the hydrogen production control needed, compared to compressed gas cylinders. Metal Hydrides Metal hydrides have been in use for many years. Perhaps the most well-known application is the rechargeable nickel metal hydride (NiMH) batteries that are used in hybrid electric vehicle and laptop computer applications. These applications use metal hydrides for electricity generation and not hydrogen storage, however. The key feature of the metal hydride is that the hydrogen bond between the metal and hydrogen can be reversibly controlled by thermodynamic (temperature and pressure) conditions, and therefore the hydrogen can be liberated from the metal matrix at desired rates needed for stack operation through controlled heat addition. Similarly, the discharged metal hydride can be reversibly recharged with hydrogen by refilling the storage vessel in a controlled temperature and pressure environment. The generic thermodynamic equilibrium reaction for the metal hydride process is [9] M + 0.5 × H2 ↔ MHx + heat

(8.6)

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Hydrogen out

H2 recycle Flow control PEFC

Hydride storage tank

PEFC

Waste heat Coolant bypass

Coolant flow loop

Radiator

Coolant pump M y Hx + heat

H2 + M

Figure 8.5 Schematic of metal hydride fueling/refueling flow diagram in a fuel cell car.

Note that this is an expression of thermodynamic equilibrium, and the proportion of hydride metal and hydrogen is thus a reversible reaction. In chemical hydrides, the hydrogen generation is accomplished through an irreversible chemical reaction of the fuel, and the spent fuel cannot be simply recharged in situ. The solid metal hydride itself is usually in the form of small solid particles or powder. This is a result of a process known as decrepitation, where the volume change of the metals during charging and discharging results in crushing of the initial metal particles. Before use for storage, the hydride elements must undego an activation procedure to ensure maximum storage capacity is reached. This process involves removal of impurities and particle decrepitation to maximize the surface area for the reaction, which is a key factor in storage potential. In the metal hydrides investigated for hydrogen storage, the hydrogen storage step [forward reaction in Eq. (8.6)] is exothermic. Therefore, storage at a refueling station requires cooling of the tank during charging. During discharge, the hydrogen liberation is endothermic, so that external heat must be used to maintain the temperature and pressure level in the storage vessel. This can be accomplished by recycled waste heat from the fuel cell but requires a more complex heat and flow control system compared to compressed gas storage (see Figure 8.5). Equilibrium charging and discharging of the metal hydride is governed by thermodynamics, and a common metric of comparison of the various metal hydrides is an isothermal pressure–composition loop. A generic isothermal metal hydride charging and discharging cycle diagram is shown in Figure 8.6. This hydrogen storage plot represents the central figure of merit for metal hydrides, defining the storage fraction and pressure at a given temperature. The vertical axis is gas-phase hydrogen pressure, which can greatly vary for different hydrides. For automotive storage applications, a range of 0.3–3 MPa is possible [9]. Along the horizontal axis is the hydrogen–metal (H–M) mole ratio. The maximum value of the H–M ratio achievable to date is less than 2.0, with most observed values closer to 1.0. This low value greatly reduces the gravimetric storage density of these materials. Typical weight storage percentages for these materials are around 2–3% for normally achievable operating pressure and temperature. Also note from this plot that there is

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Log pressure

c08

Pa Pa /Pd sis Hystere P

d

Charge/ discharge Pressure plateau H/M mole ratio

(H/M max)

Figure 8.6 Schematic of generic isothermal metal hydride charging and discharging cycle. (Reproduced with permission from Refs. [9] and [11].)

generally a hysteresis between the absorption and desorption pressures (Pa and Pd , respectively). In order to achieve suitable operation in fuel cell vehicles, the absorption and desorption pressures must be sufficiently low at reasonable temperatures for the charging and discharging process. Materials that desorb with suitably fast kinetics at pressures and temperatures below 1 MPa and 100◦ C are sought for automotive fuel cell applications. The desorption temperature is particularly important since the waste heat from a PEFC must be used in the process and is not normally available at temperatures above 90◦ C. The pressure must be sufficiently low to avoid bulky storage containers and overlap with the problems of compressed hydrogen storage. A bevy of elemental metals, solid solutions, intermetallic compounds, and other metal mixtures have potential for hydrogen storage and the possibilities continue to evolve. Therefore, a comprehensive listing is not given here. Instead, a brief summary of some of the more fundamental trends is given here. Most elemental metals do not possess suitable desorption temperatures or pressures for fuel cell storage needs, requiring temperatures greater than 200◦ C. Therefore, intermetallic compounds are chosen where the hydriding properties of each metal can be mixed to achieve the desired temperature and pressure desorption and absorption characteristics. The approach has led to the successful development of several classes of intermetallic compounds that have desirable thermodynamics of absorption and desorption. Compounds AB, AB2 , and AB5 are common, where A is a strongly hydriding element and B is a weakly hydriding element. For example, TiFe, ZrMn2 , and LaNi5 represent AB, AB2 , and AB5 compounds, respectively. More complex intermetallic compounds of the same general formulations have been developed as well according to ABx = AB(x−a) Ca

(8.7)

Where a + x equals 2 or 5 for the AB2 or AB5 compounds, respectively. An example of this for an AB5 compound is LaNi4.8 Sn0.2 . Although the potential to mix and match hydrides in this manner opens up a nearly infinite degree of combinations, the required automotive storage density levels of 6 wt. % have not yet been achieved.

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Besides gravimetric storage density limitations, the control of the heat transfer during storage and hydrogen evolution, several other technical challenges must be addressed [9]: 1. Cycle Durability The charge/discharge capacity of the hydride must maintain high values for many cycles. This is mainly a function of the chemical stability of the metallic compounds and the presence of poisons in the absorption hydrogen source stream. 2. Purity of Absorption Hydrogen Source Stream The storage capacity of the hydrides are very sensitive to even minute levels of gas-phase impurities. Gas-phase impurities can retard kinetics, reduce storage capacity, or cause irreversible corrosion of the storage alloy matrix. Although the raw materials and processing costs for most of the hydriding metals are relatively high, they can potentially be recycled after use to recover some costs, similar to the planned recycling of platinum and other materials from PEFCs. Despite the high potential for safe, reversible, and low-pressure hydrogen storage, metal hydrides have not met the needs of automotive hydrogen storage due to low gravimetric energy densities and other economic and technical challenges, but new materials hold promise for eventually achieving this solution. Example 8.2 How Much Would the Metal Hydride Gas Tank Weigh? From Example 8.1, we found that an automotive fuel cell system needs about 7.5 kg of hydrogen to replace a gasoline fuel tank in automotive systems. Considering an AB2 metal compound (ZrMn2 ), with a hydrogen storage capacity of 1.77 wt. % as shown in ref. [9], determine the minimum weight of a ZrMn2 hydride storage tank needed. SOLUTION 7.5 kg = 960 kg 0.0177 That is over a ton of metal powder, greater than 2100 lb! Some smaller cars actually weigh less than this. In comparison, 15 gal of gasoline weighs 52 kg, or almost 20 times less. COMMENTS: This represents the minimum weight of the metal hydride, since some significant bulk will also be required to contain the hydride powder. If the DOE goal of 6 wt. % storage were met, the hydride powder would still weigh 150 kg, or roughly 330 lb. Even if these goals are achieved, there is still room for improvement. Carbon Storage Much has been made of the potential for hydrogen storage on specialized carbon nanoconfigurations (activated carbon, exfoliated graphite, fullerenes, nanotubes, nanofibers, and nanohorns) or other special configurations. Very high gravimetric storage densities have been reported, even approaching 50% for these configurations [12]. However, initial reports were erroneous due to experimental difficulties in quantification of the actual stored hydrogen content. Storage of a few weight percent of hydrogen on carbon structures has been observed in low-temperature (77 K) or high-pressure (>10 MPa) environments. In October 2006, the DOE ceased research funding of single-walled nanotubes (SWNTs) for hydrogen storage due to the inability for these materials to reach 6% storage by material weight at room temperature [13]. However, research on metal-doped carbon nanotubes or

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other alternatives is still ongoing [14, 15]. Ultimately, the goal is to achieve >6% weight storage at room temperature and pressure. The keys to achieving high storage seem to be increasing the surface area of carbon and tailoring the bond energy between the carbon and hydrogen. As a rough rule of thumb, the hydrogen storage percentage increases 1% with each 500 m2 /g of carbon surface area [16]. Several different carbon-based storage approaches have shown at least qualitative agreement with this trend. Using this as an approximation, a surface area of at least 3000 m2 /g will be needed to satisfy the storage requirements of 6%. Being able to achieve this at low pressure and ambient temperature will require significantly more development and understanding of the nature of bonding between the hydrogen and substrate. Several other approaches to hydrogen storage on carbon have potential but are not yet developed, including boron-doped carbon nanostructures, which show some increased storage capacity at room temperature [17]. Additionally, carbide-derived carbons (CDCs), produced by high-temperature chlorination of carbides, have high potential to achieve high storage capacity since the average pore size, size distribution, and total pore volume can be controlled with great sensitivity to achieve the high surface area needed for hydrogen storage [18]. Metal organic frameworks (MOFs), which are highly ordered and linked carbon networks, also have a potential for low-cost hydrogen storage [19]. The MOFs have demonstrated 7.5 wt. % at 77 K under high pressures (∼7 MPa) and a desirable surface area greater than 5000 m2 /g [20]. Liquid Fuel Storage The use of a nonhydrogen liquid fuel, such as methanol, as a hydrogen carrier is a common approach to reduce fuel storage volume in portable applications using PEFCs, as discussed in Chapter 6. For these applications, the reduced performance of the fuel cell when using the alternative fuel is acceptable because of the reduced overall system complexity and size. For larger power applications, the use of a nonhydrogen liquid fuel is also an option. Due to the low power density associated with DAFC application, however, DAFCs are not viable for large applications. The generation and transportation of a variety of liquid fuels such as methanol, ammonia, or synthetic liquid fuels as hydrogen carriers remain important options, discussed in Section 8.3. For high-temperature solid oxide or molten carbonate systems, the liquid fuel can be internally reformed, as discussed in Chapter 7. This unique capability reduces the burden of fuel storage in these systems, although SOFCs and MCFCs are generally not considered for mobile applications. In stationary systems, however, this capability allows for operation directly from the natural gas grid.

8.2

MODES OF GENERATION Hydrogen generation can be achieved by a variety of chemical, electrochemical, biological, and other methods. In 2005, about 90% of hydrogen worldwide was generated from chemical reformation of carbon-based fuels. Much of the remaining hydrogen was generated via electrolysis. Biological production of hydrogen holds great promise for an environmentally friendly solution but is not yet practiced in large volumes comparable to the other available approaches. Each approach has merits and limitations, and the choice of what is “best” depends on the economics of the location involved.

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8.2.1 Chemical Hydrogen Production Chemical generation of hydrogen from liquid- or gas-phase carbon-based fuels is known as fuel reformation. While there are many manifestations of reformation, a generic schematic of the process is shown in Figure 8.7. Some carbon-containing fuel, such as natural gas or methanol, enters the reformer and the carbon is oxidized to produce hydrogen, carbon dioxide, and other species. In principle, any carbon-containing species can be reformed to produce hydrogen. Reformation is well developed and convenient but produces carbon dioxide, a greenhouse gas, and carbon monoxide, a major poison for low-temperature PEFCs. Although this approach produces carbon dioxide and carbon monoxide, since hydrogen fuel cells can potentially be more efficient than direct use of the reformed fuel in a conventional process, less overall fuel is used so there can still be a net benefit to the environment. Carbon sequestration from large reformation plants can also be used to further minimize the impact of the carbon emissions to the environment. Because of the undesired CO byproduct, the hydrogen produced for PEFCs generally needs to be further processed to reduce CO levels. One way to achieve this is through a water–gas shift (WGS) reaction: CO + H2 O → CO2 + H2 + heat

(8.8)

This is an exothermic process that liberates 41 kJ/mol of CO and can usually reduce the CO levels in the stream to around 1%, which is still too high for PEFC operation but is suitable for PAFC operation. A WGS reactor is often used downstream of or in parallel with the fuel reformer to reduce CO levels. Another methods to remove the CO is the preferential oxidation reaction: CO + 12 O2 → CO2 + heat

(8.9)

In this case, air or oxygen is introduced to the fuel stream to promote oxidation of CO to CO2 . This reaction can be used to reduce the CO content to the 10–100-ppm level, which is still harmful for PEFC operation. Further cleanup can be accomplished through selective membrane filtering and catalyst absorption beds. Obviously, the CO cleanup required for PEFC operation is extensive and represents a major drawback of the reformation approach for supplying hydrogen for PEFCs. Besides water management and heat rejection, increased

Carbon containing fuel (e.g., CH4, CH3OH)

Reformer

H2 + CO2 + CO + N2 + H2O

Oxidizer (air/H 2 O)

Figure 8.7 Generic fuel reformation process.

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CO tolerance is one of the primary reasons that higher temperature membranes are sought for PEFCs. For high-temperature molten carbonate and solid oxide fuel cells, no gas cleanup is necessary since the CO can be used as a fuel. Alkaline fuel cells are not suitable for reformed gas since they are intolerant to CO2 . Despite the environmental drawbacks, the reformation process is generally more cost effective and compact than other hydrogen generation technologies. Electrolysis is inefficient and consumes excess electrical and freshwater resources. Considering the world also faces shortages of electrical capacity and freshwater, rapid large-scale conversion to electrolysis for hydrogen generation is unlikely. Biological production requires very large hydrogen generation facilities, additional development of the technology, and a biological waste transportation infrastructure. Therefore, in the near term, fuel reformation remains the most likely source for large-scale hydrogen generation. Another advantage of reformation is that the fuel can be transported to the generation location as a liquid, solid, or gas, so that existing and cost-effective delivery infrastructure can be used. For example, in locations where natural gas is plentiful and a distribution infrastructure exits, direct reformation of natural gas can be used to generate hydrogen locally, avoiding the need for a separate hydrogen infrastructure. There are also new technologies for the generation of liquid fuels from reformed gas, or even the direct generation of hydrogen from coal resources, which are plentiful in many parts of the world. There are also many sources of liquid fuel that are generated from a variety of processes. For example, methanol can be made from nearly any carbon-containing fuel stock or from biological processes. The methanol is then relatively easily reformed to hydrogen. There are many different approaches and technologies for fuel reformation. The three most widely utilized methods are: 1. Steam reformation 2. Partial oxidation 3. Autothermal reformation Steam Reformation In steam reformation, water and fuel are mixed over a catalyzed bed to produce hydrogen, carbon dioxide, and other minor species in an endothermic reaction. Compared to partial oxidation or autothermal reformation, steam reformation produces the highest hydrogen mole fraction effluent stream, approaching 80% H2 on a dry basis:  y H2 Cx H y + (2x) H2 O + heat → xCO2 + 2x + (8.10) 2 Minor species, such as CO, result from subsequent dissociation reactions governed by thermodynamics. Of the various fuels involved, methanol is the simplest liquid-based fuel to reform due to the lack of carbon–carbon bond and low reformation temperature of only around 200◦ C [21]. This temperature can easily be coupled to low-temperature systems. The PAFC is almost perfectly thermally matched to the methanol reformation temperature, so that waste heat from the fuel cell can be used to drive the process. For PEFCs, some additional input heat is needed for methanol and other fuel reformation. For hightemperature fuel cells, methanol (and other fuel) reformation can be accomplished internally or externally, as discussed in Chapter 7. The reformation temperature of other fuels can be several hundreds of degrees higher than that of methanol, depending on the complexity and strength of the chemical bonds as well as the catalyst used to promote the reaction.

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The relative ease of methanol reformation and difficulty of hydrogen storage and transport have led to substantial development of on-board reformation systems for automotive applications. However, interest has waned due to the need for rapid transient response to load demands, CO poising, and the added bulk and cost of equipment needed. Essentially, the automotive fuel cell is already difficult enough to achieve without the reformer sub system. In portable applications, research has been conducted on ultrasmall methanol reformers for applications that have shown greater energy density than the lithium ion batteries they would replace [e.g., 22]. Since liquid methanol is ultimately more transportable than hydrogen, this would be useful for military and other portable applications as long as the fuel cell size can be reduced to make up for the added bulk of the reformer. Partial Oxidation Partial oxidation is an exothermic reformation method where air (or oxygen) is mixed with the fuel stream and the fuel is partially oxidized to produce a hydrogen-rich stream: Cx H y + 12 x (O2 + 3.76N2 ) → xCO + 12 y H2 + (1.88x) N2 + heat

(8.11)

The CO fraction from this reaction is obviously much higher than catalyzed steam reformation. Subsequent or simultaneous reaction in a water gas shift reactor can be used to convert the CO into CO2 . Because this reaction is exothermic, the reaction temperatures are much higher (>1000◦ C) and the use of a catalyzed bed is not typically needed. The exothermic heat release for this reaction can be used for other purposes, such as preheating a cold fuel cell or providing space heating in residential units. Although the lack of a catalyst bed and exothermicity of the reaction is an advantage, the use of air introduces nitrogen to the fuel stream and reduces the ultimate hydrogen fraction available from the process. Autothemal Reformation The exothermic nature of the partial oxidation reaction, combined with the higher hydrogen mole fraction of the endothermic steam reformation process, can be combined in an energy neutral configuration, known as an autothermal reformer (ATR). Typically, a partial oxidation reformer is used to generate heat and a high-temperature hydrogen, CO, and nitrogen stream (if air and not pure oxygen is used). Subsequently, the remaining fuel stream enters a catalyzed steam reformer/water gas shift reactor. The partial oxidation reaction is controlled to release the heat needed to drive the steam reformer, so that there is no net heat input to the system required. The hydrogen mole fraction produced by ATR lies somewhere in between the partial oxidation and steam reformation approaches at around 40–50%. 8.2.2 Electrochemical Hydrogen Production Electrolysis of water has been used for over a century to produce hydrogen and oxygen. The concept of a reversible fuel cell for space applications is based on a combined electrolytic–galvanic fuel cell. Like fuel cells, several different types of electrolyzers and catalysts have been developed, including atmospheric and high-pressure acid-based polymer electrolyzers, alkaline solution systems, and solid oxide–based systems. A major advantage of electrolysis is that hydrogen generation can be carbon-free, provided the source of the required electricity is from nuclear or renewable sources, such as hydraulic, solar, or wind power. Another advantage of electrolysis is that the hydrogen

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and oxygen produced are extremely high purity, which is especially advantageous for low-temperature applications where minute impurities can drastically reduce performance. Although discussed here as a hydrogen generation device, electrolysis also produces highpurity oxygen, which could be used in a fuel cell or as a valuable product for other applications. Another advantage of liquid water electrolysis is that high product pressure up to 20 MPa is possible without mechanical compression, which greatly reduces the energy required if the produced hydrogen is used to fill a compressed gas tank or charge a pressurized carbon or metal hydride fuel tank. Electrolysis is an established method for small-scale local generation of high-purity hydrogen and oxygen. Small, local electrolysis devices could be used for portable generation capabilities to circumvent hydrogen infrastracture limitations. For large-scale generation, electrolysis is less desirable due to several drawbacks: 1. Electrolysis is an inefficient process. Conversion efficiencies of only 65–75% based on the lower heating value are possible [23]. As a result, electrolysis tends to be more expensive than natural gas reformation unless a source of inexpensive electricity is available. 2. Electrolysis requires a source of freshwater, which, globally, is also a scarce resource. 3. Although production can be carbon free if the electricity is derived from renewables or a nuclear reaction, it requires an inexpensive source of electricity. Many power grids in the world do not have the excess capacity to supply the additional power required, and additional electricity infrastructure would be needed.

8.2.3

Biological Hydrogen Production Biological hydrogen production is a method to produce hydrogen, or hydrogen-containing fuels, using biological processes. These processes are generally controlled by fermentive or photosynthetic organisms and thus utilize natural processes to generate hydrogen. Because these processes can be used to decompose organic waste products, they offer an environmentally remediate pathway to simultaneously produce hydrogen and remediate waste. A wide variety of organic waste can be used as fuel for these processes, including human waste, farm waste (including animal and fruit/vegetable waste), and miscellaneous garbage. The main limitation of this approach is the time scale and size associated with these processes. Compared to hydrogen generation from high-energy-density fuel sources such as natural gas, the size of the bioplant required would be enormous to achieve a comparable generation rate. In some cases, however, the hydrogen generated may be secondary to the economic benefits of the energy-neutral waste remediation that occurs. According to [24], biological hydrogen production can be grouped into four main categories: 1. Biophotosynthesis of water using algae and cyanobacteria: In this approach, an adapted version of photosynthesis is used to generate oxygen and hydrogen from water.

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Hydrogen Delivery

2. Photodecomposition of organic compounds by photosynthetic bacteria: In this method, various microbial organisms utilize energy from light to break down organic material into hydrogen and other products. 3. Fermentative hydrogen production from organic compounds: A fermentative process is utilized in this method (as opposed to a photosynthetic process) to break down the organic matter into hydrogen and other species. 4. Hybrid systems using photosynthetic and fermentative bacteria. Biological hydrogen production involves carbon, unlike renewables or nuclear energy. 8.2.4 Other Hydrogen Generation Technologies Besides the technologies discussed for hydrogen generation, many others exist. Not all liquid hydrogen–rich fuels include carbon. Ammonia (NH3 ) is a widely distributed chemical used for fertilizer and in many industrial processes. At low pressure and room temperature, the liquid storage density of hydrogen in ammonia is 1.7 times that of cryogenic liquid hydrogen. Over a catalyst bed at around 400◦ C, ammonia dissociates according to [25] 2NH3 + heat → N2 + 3H2

(8.12)

High-temperature thermochemical cycles have also been investigated for hydrogen generation, and some have shown increased efficiency compared to electrolysis [e.g., 26, 27]. These generally require high-temperature catalyst bed flow reactors and are thus suitable for nuclear or solar power–based hydrogen generation. Metals can also be combusted in water to generate hydrogen and heat simultaneously. An example is the aluminum–water reaction: Al + 32 H2 O → 12 Al2 O3 + 32 H2 + heat

(8.13)

In principle, other energetic metals such as magnesium could also be used in a similar fashion. Since the reaction is also exothermic, the heat generated could potentially be used to cogenerate electricity. Many other methods for hydrogen generation exist, but they are too numerous to give in exhaustive detail here. In particular, methods for generation of liquid hydrocarbons from a variety of organic stocks exist, and these can be further refined into hydrogen through conventional reforming or cracking processes. Methods for coal to hydrogen and synthetic fuel production exist that will become more attractive as conventional petroleum resources become increasingly scarce and more expensive.

8.3 HYDROGEN DELIVERY Another vast challenge in the hydrogen infrastructure is the mode of hydrogen delivery, both to the fueling station and into the vehicle or storage device. For portable applications, small hydrogen generation devices or replaceable alcohol cartridges for DAFCs are the most likely sources of fuel. However, for large transportation applications, there must be a hydrogen-specific delivery infrastructure. Even if the fuel cell itself is more efficient than the gasoline engine it replaces, the delivery infrastructure efficiency must also be favorable, or the net well-to-wheel efficiency of the fuel cell system may actually be worse

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than the gasoline engine it is to replace. From a consumer perspective, the delivery inefficiencies add to the cost, which must also be competitive with the existing petroleum infrastructure. Other special concerns are safety and the environment. Hydrogen is an extremely small molecule with very high diffusivity, and is difficult to contain without leakage. One study has estimated the hydrogen leakage rate from existing hydrogen transport, generation, and storage technologies to be as high as 10% [28], or up to 20% for commercial transportation [29]. Hydrogen leakage is a potential risk for fire or explosion due to its broad flammability range of 4–77%, especially in enclosed environments, where it can accumulate in high concentrations if not properly ventilated. Because of this concern, hydrogen fuel cell testing facilities have extensive recirculation and venting equipment to avoid potential problems. Besides the flammability concern, hydrogen simply vented to the atmosphere also poses a potential problem. When released to the atmosphere, hydrogen generates stratospheric water from oxidation at high altitudes. The effect of this hydrogen emission is predicted to increase the size and duration of the ozone hole over the Artic and Antarctic polar regions [30], although this prediction has been disputed as overestimating the leakage rates. Gas versus Liquid Truck Delivery For delivery from future pipeline or generation stations, some hydrogen transport by truck will be needed. The vast majority of pure hydrogen is presently shipped as cryogenic liquid, and a small fraction is shipped as compressed gas over short distances [23]. The reason for this can be understood by considering that a compressed hydrogen gas delivery truck carries around 530 kg of hydrogen in the gas phase (or about 60–70 hydrogen PEFC car fuel tanks), or 3370 kg (about 425 tanks) in the liquid phase. Gas-bottle hydrogen delivery is limited to small laboratory volumes and short travel distances. Pipeline Delivery Where long distances are involved, hydrogen delivery by pipeline can be the most efficient means for transporting the fuel, similar to the way petroleum or natural gas is shipped throughout the world. Pipeline delivery of hydrogen can take place by three methods: 1. Gas-phase hydrogen pipelines 2. Cryogenic liquid hydrogen pipelines 3. Hydrogen carrier pipelines Interestingly, pure gas-phase hydrogen pipelines have existed for over 75 years, with over 1000 km of total pipeline in operation at various locations all over the world, at near atmospheric up to 30 MPa pressure [23]. Gas-phase pipelines exist worldwide for natural gas, so that design principles and experience for optimized design are readily available. One study estimated the parasitic losses in a 12-MPa, 2000-km pipeline with 480 TWh/year throughput at 8% of the throughput energy, which is much less than the energy lost shipping the same hydrogen by truck [23]. Compared to a hydrogen gas pipeline, transport of cryogenic liquid hydrogen has the advantage of decreased pumping losses for a fluid compared to a gas and greatly increased energy density, but has the disadvantage of greater initial infrastructure cost to provide an insulated pipeline to prevent boil-off and the use of expensive cryogenic pump

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Hydrogen Delivery

445

Heavy insulation

Superconducting metal to carry electrons

Cryogenic hydrogen flow (~20 K)

Figure 8.8 Schematic of the cryogenic hydrogen/superconductor annular hydrogen/electron transport system.

equipment. Nevertheless, short subkilometer-long liquid hydrogen pipelines have been utilized for specialty applications, such as fueling of liquid rocket engines for the Space Shuttle. Another interesting concept for delivering hydrogen fuel and electricity demands is known as the SuperGrid [31]. In a SuperGrid combined electron/hydrogen pipeline (see Figure 8.8), cryogenic hydrogen would flow around a superconducting metal to deliver vast amounts of current with high efficiency. Because transmission losses through superconducting metals are so low (AC resistance in superconductors is about 0.5% of copper at the same temperature), the distributed energy sources could be located far away from populated areas. Another option for hydrogen transport is to ship it by hydrogen carrier species. Chemical or metal hydrides or carbon–based storage could become feasible if storage densities are high enough. In terms of pipeline delivery, the transport of gaseous hydrogen is ultimately less efficient than natural gas, due to the low energy density of hydrogen. Shipping liquid hydrogen through pipelines is also inherently less efficient than other liquid carbon–based fuels, due to the low relative energy density and need for complex, highly insulated cryogenic pipelines and pumps. For these reasons, in certain situations, it will be more economical to deliver the fuel in pipelines as a liquid hydrogen–carrying fuel. Examples include transport via ammonia (NH3 ), natural gas (CH4 ), or a liquid fuel such as methanol. The higher energy density, lower pumping requirements, and room temperature of these fuels in comparison to pure hydrogen are the main advantages of this alternative, although the complete elimination of carbon from the fuel cycle would not be possible. For fuel cells with local or internal reformation, the existing natural gas pipeline distribution can be used for this purpose. Many stationary fuel cell systems operate directly from reformed natural gas delivered in this manner. Fueling Fueling of hydrogen storage tanks is not a trivial concern. Hydrogen refueling should be rapid, safe, and inexpensive technology. For portable electronic applications,

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alcohol-based fuel cartridges, similar to replaceable ink cartridges, have been designed for use in new product designs. For compressed and liquid hydrogen storage refilling, robotic refueling is probably necessary to eliminate safety concerns with public handling of high pressure or cryogenic fuels and hydrogen leakage. The potential flammability hazard of handling of hydrogen is perhaps overemphasized, considering the public deals with a highly flammable fuel in gasoline. However, given the wide flammability limits of hydrogen, additional safety concerns must be addressed, including elimination of static potential accumulation and discharge with grounding cables. For chemical hydride refueling, the spent fuel residual can be recycled and recharged at a separate location or disposed. Therefore, a chemical hydride recycling and distribution network for these materials would need to be established. As discussed, metal hydrides and carbon-based hydrogen storage are designed to be recharged from a gas-phase hydrogen source in situ in a controlled temperature and pressure environment.

8.4

OVERALL HYDROGEN INFRASTRUCTURE DEVELOPMENT The development of the overall hydrogen infrastructure is a complex topic that will evolve as a mixture of political, economic, and environmental realities and combines hydrogen generation, storage, and delivery issues. What is the best possible hydrogen infrastructure? The answer depends on the location, technological developments, and demand. Right now, tens of millions of cubic meters of hydrogen is generated per year [32], mostly at the location of use. The remainder is either shipped by truck as compressed or liquefied fuel or shipped in small localized pipelines. In the future, the preferred hydrogen generation, storage, and delivery mode will depend on the progress of the competing technologies, but a general pathway to a hydrogen economy is generally considered to occur in several stages, shown as a near- and long-term infrastructure in Figure 8.9. In the near term, the hydrogen production and availability will follow from the same infrastructure already in place, with most generation from carbonbased fuels. As fuel cell vehicles go beyond the prototype and into initial production stages, localized generation will provide fuel for small centralized fleets of fuel cell vehicles, such as public transportation buses and taxicabs. The advantages of the initial fuel cell infrastructure development with fleet vehicles are as follows: 1. Fleet vehicles drive a repeatable drive cycle and return to the same location each day, so that only a single fuel station is needed to service the vehicles. The additional capacity from these fleet stations can also be used as the initial public fueling stations. 2. Only a small initial group of trained mechanics will be needed to maintain the vehicles. 3. Fleet vehicle purchases can be government subsidized to jump start the demand required to spur manufacturers to produce the larger numbers needed to achieve higher manufacturing efficiency. 4. The controlled driving cycles allow manufacturers to gain quality performance and operation feedback that will enable further system improvement.

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447

Fleet vehicles

Liquid H2 truck delivery

Local, small-scale reformation or electrolysis to fuel fleet vehicles

(a)

Renewable resources

CO, CO2 sequestor

H2 pipeline delivery to fueling stations Delivery to rural areas

Gas pump

Small-scale local generation off the pipeline infrastructure

(b) Figure 8.9 Schematic of potential hydrogen infrastructure development route over time: (a) nearterm local generation and limited distribution; (b) Long-term distributed generation and pipeline networks.

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As the demand for hydrogen evolves into the private sector in the long term, larger distributed generation networks will grow near population centers and branch out into rural areas over time. For locations off the grid where network connectivity is not cost effective, there will continue to be localized generation stations for small quantities, or home-based electrolysis units.

8.5

SUMMARY The hydrogen economy is at a very nascent stage, and many competing technologies exist for hydrogen storage, generation, and delivery. Ultimately, the success or failure of the hydrogen economy will rest with the cost of competing fuels and the local cost advantages of different fuel stocks and generation techniques. For portable fuel cells, liquid alcohol fuels such as methanol are most often used because of the high storage density of hydrogen. For distributed and high-temperature fuel cells, the existing natural gas or other fuel infrastructure can be used until a hydrogen infrastructure exists. For mobile fuel cell applications, however, to compete with conventional gasoline automobiles, around 7.5 kg of hydrogen storage is needed, which presents significant difficulties. For hydrogen storage, six main technologies exist: (1) compressed gas, (2) cryogenic liquid, (3) metal hydrides, (4) chemical hydrides, (5) carbon-based storage, and (6) liquid hydrogen carrier fuels (also called liquid hydrides). Each has limitations and advantages, but none is yet established to fulfill all the needs of mobile applications. Compressed gas is an established technology, but high-pressure (70-MPa) storage is needed to approach driving range goals. This high pressure is slow to refill and energy intensive to compress in addition to the safety concerns. Cryogenic liquid hydrogen storage is less energy intensive for delivery and has relatively higher density but is more energy intensive to produce than compressed hydrogen and will boil off over time in storage. Metal hydrides hold much promise but have not yet met the desired storage fraction of 6% by weight at room temperature and pressure. Chemical hydrides are not yet economically competitive and would require new generation and recovery infrastructure. Hydrogen storage in single-walled carbon nanotubes have not shown the storage capability initially reported, but variations, including metal-doped structures, differently organized carbon nanostructures, and carbidederived carbons, show some promise. Liquid fuels include hydrogen-carrying liquids such as methanol, ethanol, or propane. These are used extensively for portable applications where low efficiency is tolerable in light of compact storage. In mobile applications, however, hydrogen must be used for higher system efficiency, but on-board reformation is generally too complex, and pure hydrogen storage is preferred. Hydrogen generation can be accomplished through chemical, electrochemical, biological, and other means. Around 90% of hydrogen generation is presently accomplished through a chemical reformation process of carbon-based fuels, and this should continue into the near future as it is a well-established technology. In the future, carbon sequestration could be used with fuel reformation to reduce the environmental impact. Electrochemically, electrolysis is a well-established technique to separate hydrogen and oxygen from water and is useful for local small-scale or back-up generation. However, it is less efficient than other methods and requires a source of inexpensive and excess capacity electricity and freshwater. Biological-based hydrogen generation processes offer an opportunity to recover hydrogen from products normally considered waste. Biological methods to produce methanol or other

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alcohols can also be exploited to produce hydrogen-rich fuel stocks. Other new technologies for hydrogen generation will almost certainty continue to be developed, considering the vastly different fuel stocks and other local factors. Hydrogen delivery consists of transport from generation stations and delivery into the fuel cell storage container. Delivery in the short term will likely continue to be from smallscale local reforming stations and by truck as a cryogenic fuel. Introduction of a distributed hydrogen infrastructure would likely initially spread from fleet vehicle applications, with long-term distributed generation networks eventually connected by pipeline infrastructures.

APPLICATION STUDY: A GROWING HYDROGEN AND ELECTRON INFRASTRUCTURE In 2004, The United States produced over 17 million cubic meters of hydrogen for various industrial processes [33], a minor fraction of which were fuel cells. Assuming that over the next 50 years 100 million hydrogen-powered cars averaging 15,000 miles per year will be on the road, how much additional capacity to produce hydrogen will be needed? If the hydrogen required is produced by electrolysis, how much additional electrical capacity must be added to the existing infrastructure? Can an argument for fuel reformation as a better alternative be made? Note that you will have to use your knowledge to make some reasonable assumptions about the efficiency and size of fuel cell stacks for automotive applications. Next, analyze the possibility of delivering this hydrogen by compressed gas or as cryogenic liquid. You can assume a normal hydrogen delivery truck carries 530 kg in the gas phase or 3370 kg in the liquid phase and will travel an average of 100 km per day. Do these choices make sense? What would you recommend for the mode of delivery of this much fuel in the future?

PROBLEMS 8.1 Estimate the maximum rate of hydrogen availability that would be required to supply a 100-kWe maximum output PEFC stack for an automotive application in grams in per second. Assume an anode stoichiometry of 1.2.

8.5 Make a plot of the weight of a metal hydride hydrogen storage vessel used to power a fuel cell to provide a laptop computer with 53 Wh of energy versus the hydrogen storage weight percent.

8.2 Determine the minimum gravimetric storage fraction that would be required for a cell phone application to provide 4800 mAh of energy with a 28-g hydrogen fuel storage container.

8.6 Consider hydrogen and oxygen production by electrolysis. Is it possible to have a water-powered car using onboard electrolysis with the oxygen and hydrogen generated to power a fuel cell? What would be the main drawbacks of this approach?

8.3 Determine the gravimetric storage fraction required to achieve 7 kg storage for an automotive application in the same volume profile as two 25-gal gasoline tanks. Assume the walls of the gasoline tank are negligibly thin.

8.7 What fraction of compression work would be saved by using high-pressure electrolysis at 20 MPa followed by regular compression to fill a compressed hydrogen tank to 70 MPa, compared to only compression from 0.1 MPa?

8.4 Determine the weight of a magnesium hydride fuel storage system with 6 kg of hydrogen in a 2 wt. % storage media. Compare this to the weight of a car. Is this reasonable? What storage in weight percent would be reasonable?

8.8 Determine the temperature increase in a hydrogen storage tank that is adiabatically compressed from 0.1 to 70 MPa. Discuss why this effect limits the rate of hydrogen filling the storage tank.

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8.9 Would isothermal or nonisothermal compression with continually increasing temperature be desirable to achieve high-efficiency gas compression? Would you want an insulated or cooled compressor? 8.10 Determine the fraction of throughput energy required to compress hydrogen gas from 0.1 to 70 MPa assuming an isothermal, ideal gas compression process. How would nonideal gas effects affect the result? 8.11 What is the fraction of throughput energy lost to compress liquid hydrogen from 0.1 to 30 MPa for pipeline delivery? How does this compare to the fraction of throughput energy lost to compress gas-phase hydrogen from 0.1 to 30 MPa for pipeline delivery? 8.12 Consider the use of on-board methanol or ethanol storage for automotive PEFC applications. The methanol or ethanol would be reformed on-board and sent to the fuel cell. What minimum storage tank volume and weight would be needed to replace a conventional 15-gal gasoline tank in terms of energy for each of these fuels? How does this compare to a metal hydride hydrogen storage tank that stored 4 wt. % hydrogen? 8.13 Consider a hydrogen production plant using electrolysis for hydrogen production. If the electrolysis is 65% efficient and the automotive PEFC is 90% efficient in transmitting the PEFC power to propulsion, draw a plot of the net process efficiency versus output cell voltage for the 200-cell fuel cell stack. Compared to an internal combastion engine efficiency of 25%, what is the lowest stack voltage where the net efficiency of the hydrogen–air fuel cell is still higher than the conventional automobile? 8.14 The estimated throughput loss of shipping pressurized hydrogen a distance of 2000 km by pipeline is 8% output

for 480-TWh/year flow. What fraction of throughput energy would be lost if this hydrogen was instead shipped by truck at 120 km/L of gasoline. You can assume a normal hydrogen delivery truck carries 530 kg in the gas phase, or 3370 kg in the liquid phase. 8.15 The expected hydrogen storage density in carbon is directly proportional to surface area. Create a plot of diameter of carbon spheres versus surface area if the carbon is a packed bed of perfect spheres. Can a surface area of 3000 m2 /g be achieved with spherical particles? Would nonspherical geometries be better for hydrogen storage? 8.16 Aluminum combustion in water has been considered as a carbon-free source of hydrogen. The enthalpy of formation of aluminum oxide is −1675.7 kJ/mol: Al + 32 H2 O → 12 Al2 O3 + 32 H2 + heat Since the reaction is also very exothermic, the heat could potentially be used to run a steam turbine and generate electricity. For this problem, determine the kilograms of hydrogen per kilogram of aluminum used and try to determine the cost of hydrogen production per kilojoule of hydrogen produced (use the LHV) using online sources. Assume it takes about 7 kWh of energy to manufacture a pound of aluminum. Is this a potentially competitive way to produce hydrogen (ignoring the technical challenges)? 8.17 Compare flammability and health safety risks that hydrogen, methanol, gasoline, and ethanol pose. You can find this information in material safety data sheets available online from various manufacturers. Is there a “safe” fuel?

REFERENCES 1. U. Bossel, “The Hydrogen ‘Illusion’—Why Electrons are a Better Energy Carrier,” Cogeneration and On-Site Power Production, pp. 55–59, March/April 2004. 2. U.S. Department of Energy, “Hydrogen Storage Sub-Program Overview,” FY 2005 Progress Report, Sunita Satyapal, Department of Energy, Washington, DC, 2005, pp. 459–462. 3. W. Dubno and B. Geving, “Low Cost, High Efficiency, High Pressure Hydrogen Storage,” DOE 2006 Annual Progress Report, Part IV. E Hydrogen Storage/Compressed/Liquid Tanks,” Department of Energy, Washington, DC, 2006, pp. 521–524. 4. R. Funck, “High Pressure Storage,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 83–88. 5. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 3rd ed., Wiley, New York, 1995.

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6. A. Bain, The Freedom Element: Living with Hydrogen, Blue Note Books, CoCoa Beach, FL, 2004. 7. J. Wolf, “Liquid Hydrogen Technology for Vehicles,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 89–100. 8. R. Edinger, G. Isenberg, and B. H¨ohlein, “Methanol from Fossil and Renewable Sources,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 39–48. 9. G. Sandrock, “Hydride Storage,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 101–112. 10. S. Suda, “Aqueous Borohydride Solutions,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 115–120. 11. G. Sandrock, “A Panoramic Overview of Hydrogen Storage Alloys from a Gas Reaction Point of View,” J. Alloys Compounds, Vols. 293–295, pp. 877–888, 1999. 12. A. Chambers, C. Park, T. T. K. Baker, and N. Rodriguez, “Hydrogen Storage in Graphite Nanofibers,” J. Phys. Chem. B, Vol. 102B, pp. 4253–4256, 1998. 13. U.S. Department of Energy, “Go/No-Go Decision: Pure, Undoped Single Walled Carbon Nanotubes for Vehicular Hydrogen Storage,” U.S. Department of Energy (DOE) Hydrogen Program announcement, DOE, Washington, DC, October, 2006. 14. J. L. C. Rowsell and O. M. Yaghi, “Effects of Functionalization, Catenation, and Variation of the Metal Oxide and Organic Linking Units on the Low-Pressure Hydrogen Adsorption Properties of Metal-Organic Frameworks,” J. Am. Chem. Soc., Vol. 128, pp. 1304–1315, 2006. 15. A. G. Wong-Foy, A. J. Matzger, and O. M. Yaghi, “Exceptional H2 Saturation Uptake in Microporous Metal-Organic Frameworks,” J. Am. Chem. Soc., Vol. 128, pp. 3494–3495, 2006. 16. C. Ahn, R. H. Grubbs, and R. C. Bowman, Jr., “Enhanced Hydrogen Dipole Physisorption,” Hydrogen Program Annual Progress Report, pp. 452–454, United States Department of Energy, Washington, D.C., 2006. 17. P. Eklund, T. C. M. Chung, H. C. Foley, and V. H. Crispy, “Advanced Boron and Metal-Loaded High Porosity Carbons,” DOE Hydrogen Program Annual Progress Report, Department of Energy, Washington, DC, 2006, pp. 476–478. 18. Y. Gogotsi, R. K. Dash, G. Yushin, T. Yildirim, G. Laudisio, and J. E. Fischer, “Tailoring of Nanoscale Porosity in Carbide-Derived Carbons for Hydrogen Storage,” J. Am. Chem. Soc., Vol. 127, pp. 16006–16007, 2005. 19. J. L. C. Rowsell, A. R. Millward, K. S. Park, and O. M. Yaghi, “Hydrogen Sorption in Functionalized Metal-Organic Frameworks,” J. Am. Chem. Soc., Vol. 126, pp. 5666–5667, 2004. 20. O. M. Yaghi, “Hydrogen Storage in MOFs,” DOE Hydrogen Program Annual Progress Report, Department of Energy, Washington, DC, 2006, pp. 515–517. 21. B. A. Peppley, J. C. Amphlett, and R. F. Mann, “Catalyst Development and Kinetics for Methanol Fuel Processing,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 132–148. 22. D. R. Palo, J. D. Holladay, R. T. Rozmiarek, C. E. Guzman-Leong, Y. Wang, J. Hu, Y.-H. Chin, R. A. Dagle, and E. G. Baker, “Development of a Soldier-Portable Fuel Cell Power System: Part I: A Bread-Board Methanol Fuel Processor,” J. Power Sources, Vol. 108, pp. 28–34, 2002. 23. R. Wurster and J. Shindler, “Solar and Wind Energy Coupled with Electrolysis and Fuel Cells,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 62–77.

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Hydrogen Storage, Generation, and Delivery 24. D. Das and T. N. Veziro˘glu, “Hydrogen Production by Biological Processes: A Survey of Literature,” Int. J. Hydrogen Energy, Vol. 26, pp. 13–28, 2001. 25. V. Hacker and K. Kordesch, “Ammonia Crackers,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 121–127. 26. J. H. Norman, K. J. Mysels, R. Sharp, and D. Williamson, “Studies of the Sulfur-Iodine Thermochemical Water-Splitting Cycle,” Int. J. Hydrogen Energy, Vol. 7, pp. 545–556, 1982. 27. C. R. Perkins and A. W. Weimer, “Likely Near-Term Solar-Thermal Water Splitting Technologies,” Int. J. Hydrogen Energy, Vol. 29, pp. 1587–1599, 2004. 28. M. A. Zittel, in Proceedings of the Eleventh World Hydrogen Energy Conference, T. N. Veziroglu, C.-J. Winter, J. P. Baselt, and G. Kreysa, Eds., Sch¨on & Wetzel, Frankfurt, Germany, 1996. 29. S. A. Sherif, N. Zeytinoglu, and T. N. Veziroglu, “Liquid Hydrogen: Potential, Problems, and a Proposed Research Program,” Int. J. Hydrogen Energy, Vol. 22, pp. 683–688, 1997. 30. T. K. Tromp, R.-L. Shia, M. Allen, J. M. Eiler, and Y. L. Yung, “Potential Environmental Impact of a Hydrogen Economy on the Stratosphere,” Science, Vol. 300, pp. 1470–1472, 2003. 31. P. M. Grant, C. Starr, and T. J. Overbye, “A Power Grid for the Hydrogen Economy,” Sci. Am., July 2006. 32. J. M. Ogden, “Alternative Fuels and Prospects—Overview,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 1–24. 33. “Facts and Figures”, Chem. Eng. News, Vol. 83, No. 28, p. 41, 2005.

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Fuel Cell Engines Matthew M. Mench

Copyright © 2008 by John Wiley & Sons, Inc.

Experimental Diagnostics and Diagnosis There have already been two oil crises; we are obligated to prevent a third one. The fuel cell offers a realistic opportunity to supplement the “petroleum monoculture” over the long term. All over the world, the auto industry is working in high gear on the fuel cell. We intend to be the market leader in this field. —J¨urgen Schrempp, Chairman of the Board of Management, DaimlerChrysler, November 2000

At this point the reader should be very familiar with the polarization curve and the basic analytical approaches used to model the various polarization losses. Each of the analytical models for these losses requires some material, transport, or other parameters to solve. In a textbook problem, these values are simply given. In practice, however, while some basic transport parameters are well established, there is often a need to experimentally measure many of these parameters as new materials or diagnostic techniques become available. For design optimization, it is especially useful to delineate the losses which affect our polarization curve as a function of operating conditions, including the following: 1. Reactant Crossover The equivalent crossover current density or molar flow rate of crossover is desired. 2. Kinetic Losses on Anode and Cathode The exchange current density, electrochemically active surface area (ECSA), and catalyst utilization are desired. 3. Ohmic Losses The ionic and electrical transport losses are desired. 4. Mass Transport Losses The gas-phase transport and flooding losses (PEFC) and the other transport-based limitations affecting the voltage are desired. Additionally, we seek diagnostic tools to understand how the fuel cell performance varies with the location in an individual fuel cell and between fuel cells in a stack. Spatial and cell-to-cell variations in current, temperature, reactant concentration, and other parameters occur, especially at moderate to high currents and during load transients, and tools are needed which can measure or directly observe these effects. In an operating stack, the number of sensors are limited due to various cost and size constraints, but laboratory diagnostics are very sophisticated. To understand distributed effects such as flooding in PEFCs or temperature distribution in SOFCs, direct visualization tools and sensors are 453

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Experimental Diagnostics and Diagnosis

necessary to understand the various phenomena and optimize performance and durability. Taken together, the various diagnostic tools available are used to develop predictive models, optimize material selection and design, and identify the source of performance anomalies. Finally, besides beginning-of-lifetime performance, tools are needed to diagnose the source of physicochemical degradation modes which limit operational lifetime. Both in situ (in cell) and ex situ (outside of a fuel cell) techniques are needed as well.

9.1

ELECTROCHEMICAL METHODS TO UNDERSTAND POLARIZATION CURVE LOSSES A wide variety of steady and transient, in situ and ex situ, AC and DC methods have been developed to study electrochemical system behavior. To fully understand and apply these techniques requires a greater depth than the brief summary in this chapter can provide. For a more detailed explanation, the reader is referred to various texts devoted to electrochemical testing techniques, such as by Bard and Faulkner [1]. This chapter is designed to serve as an introduction to the potential techniques available to obtain a greater understanding and parameterization of the various polarization losses.

9.1.1

Experimental Determination of Kinetic Parameters and Polarization Electrochemical Impedance Spectroscopy A commonly used technique for delineating some polarizations, electrochemical impedance spectroscopy (EIS), is used to study many complex problems in electrochemistry such as corrosion or the kinetics of a given electrode reaction. Advanced laboratory equipment for this purpose is readily available. In each fuel cell, the total voltage loss at a given current density is a result of a combination of ohmic and nonohmic contributions. The ohmic contributions, such as ionic and electronic ohmic resistance in the electrolyte and through the other components, can be studied using direct current (DC) techniques. However, the nonohmic contributions, such as adsorption processes at the electrodes, the charge transfer across the double layer, and the kinetically based concentration polarization, normally have frequency-dependent response times which make them ideal for study using alternating current (AC) techniques. Applying an AC signal of varying frequency over the electrochemical reaction interface causes the electrode–electrolyte interface and redox couple (e.g., H2 /H+ ) to oscillate with the same applied frequency. The characteristic response of the redox couple to the applied oscillation frequency can be used to discern qualitative details of the kinetics and concentration polarization behavior at the electrode. Electrochemical impedance spectroscopy can be applied to a single electrode if a reference electrode is available or used to study the overall behavior of the electrochemical cell, including the anode and cathode. In fuel cells, it is most often applied to study the overall system response so that information on the charge transfer and concentration polarization processes can be gleaned. The EIS data can be utilized to gain a wealth of information on the ohmic, charge transfer, and mass transfer resistances using an equivalent circuit or a first-principles-based modeling approach. Consider the equilibrium charge transfer process occurring at a single electrode in a fuel cell, shown in Figure 9.1.

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9.1 Electrochemical Methods to Understand Polarization Curve Losses

Figure 9.1

455

Simplified illustration of ion exchange process across single electrode.

The charge transfer can be modeled by an equivalent electrical circuit, the most basic of which is illustrated in Figure 9.2. In the electrochemical circuit, there is an electrical resistance, an ionic resistance, and a charge transfer resistance that represent the losses associated with ion transfer through the catalyst and surface, the electrolyte, and across the double layer, respectively. There is also an equivalent capacitor and inductance associated with the charge transfer process across the charge double layer. In the basic equivalent circuit shown in Figure 9.2, the electrode is treated as a flat planar charge transfer surface. In a fuel cell, the electrode is normally a highly three-dimensional porous surface with many parallel charge transfer pathways. In this case, a more complicated line transmission model can be used, where the planar charge transfer circuit is replaced with many such circuits acting in parallel and representing each element of the porous electrode as shown in Figure 9.3 [2]. The equivalent circuit can be expanded to consider the entire fuel cell. Figure 9.4 is an illustration of the charge transfer and current transport process through both electrodes in a fuel cell. A simplified equivalent circuit for this is shown in Figure 9.5. At this point it should be cautioned that the equivalent circuit approach can yield detailed information of the physicochemical processes of ohmic, mass transfer, and kinetic resistances for a given system, but it is subject to the assumptions of the equivalent circuit used. That is, the use of equivalent circuit analysis offers infinite possibilities and combinations of electrical circuits which all can be rearranged in different ways. The EIS ic

metal R e-

C DL

Ri elyte

R CT

ic + i f

Z diff if

Figure 9.2 Basic equivalent circuit used to model electrode in Figure 9.1.

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ie + ii

ie

ie

ie

Re-

Re-

Re-

Re-

ic + if if

RCT

RCT

ic

CDL

RCT CDL

RCT CDL

CDL

Ri

Ri

Ri

ii

ii

ii

Ri

ie + ii

Single Particle

Figure 9.3 [2]).

Line transmission model used to emulate characteristics of porous electrode (based on

Figure 9.4 Simplified illustration of ion exchange process across both electrodes in an electrochemical cell.

ic

ic

R e-anode CDL

Re-cathode

RCT

Zdiff

ic + i f if

CDL

Rielyte

ic + i f

Zdiff

RCT

if

Figure 9.5 Basic equivalent circuit used to model electrochemical cell in Figure 9.4.

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9.1 Electrochemical Methods to Understand Polarization Curve Losses High frequency region – ohmic resistances

Imaginary Impedance

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457

Low frequency region – mass transfer resistances

ω

Real Impedance Figure 9.6 Generalized Nyquist plot for fuel cell showing general regions of polarization losses.

software will solve for many different outcomes depending on the circuit chosen, so to some extent the output is only as reliable as the input model chosen. Additionally, the different capacitive and ohmic resistances often overlap each other, making interpretation more difficult. Sometimes several properties and processes are lumped in a single element so that only partial understanding is possible. Therefore, this approach should be viewed only as a semiquantitative tool to help discern modes of polarization loss, since the results depend on the particular equivalent circuit used to model the electrode processes. Despite the limitations of the equivalent circuit approach, in many cases it is possible to separate the contribution from individual processes to the overall cell resistance. A Nyquist plot1 of the imaginary versus real impedance can be used to map out and determine the limiting polarization behavior, as shown in Figure 9.6. At high frequencies (on the left side of the figure), the imaginary axis intercept represents the ohmic resistance. This value is called the high-frequency resistance (HFR) of the system, discussed later in this chapter, and includes all of the ohmic resistances in the system (i.e., the contact losses, the ionic losses in the electrolyte, and electronic resistances). In the midrange AC frequency region, the semicircle response is a result of charge transfer resistance across the electrochemical double layer. The half-circle diameter is the charge-transfer resistance. A worse electrode would have a larger semicircle. Note that for a full cell there is a charge transfer resistance at the anode and cathode, so that two semicircles often overlap, and it can be difficult to separate the two. At very low frequencies (the right side of the Nyquist plot), the mass transport resistances dominate the response. Other effects such as parallel charge transfer reactions at a given electrode or parallel limiting transport modes with the same order of magnitude can convolute the results. The actual EIS response can be very different from the perfect semicircles predicted for simplified circuits, however. In particular, phenomena 1 The

reader is referred to introductory texts from electrical engineering or control theory for greater detail on Nyquist and related plots.

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with overlapping frequency responses complicate results, and the effects of the porous or partially flooded electrode make perfect fitting with physical relevance very challenging. The effectiveness of EIS can be greatly enhanced with the use of a reference electrode, which has a stable potential at the time of measurement [3]. A suitable reference electrode allows discernment of the different electrode losses from the overall cell response, resulting in a more appropriate equivalent circuit. Ideally, the collective responses of the anode and cathode will add to the full cell resistance. Because the use of a stable reference electrode in many fuel cell systems is difficult, one common way to examine fuel cell behavior is the use of a dynamic hydrogen electrode (DHE). In this case, one of the electrodes is used as the DHE, with hydrogen flow at this location. It is assumed that the losses associated with the DHE are minor, and all polarizations measured can be attributed to the other electrode. This approach can be dubious and is not appropriate when there are phenomena at the DHE that can affect losses, such as anode dryout in a PEFC. Note that the DHE does not have to be the actual anode in the fuel cell but can be used at either electrode to examine the polarization of the opposing electrode. For example, a DHE can be used at the cathode of a DMFC to examine the polarization behavior of the anode in the DMFC. In this case, of course, the reaction does not galvanically proceed in the desired direction, and external power from a galvanostat/potentiostat system must be applied to drive the reaction in the desired direction. Modern EIS test systems are equipped with an equivalent circuit analysis software capability, greatly simplifying data analysis. The EIS analysis can be conducted on an individual electrode or on a full fuel cell for qualitative comparison of the various losses between different materials, electrodes, fuel cell design, or operating conditions. Note that fitting the EIS data to a given electrical circuit does not guarantee the model is correct, only that the data fit the assumed model. A more fundamental approach to EIS data interpretation is based on first principles and attempts to describe the frequency response data directly from analytical models. Both single- electrode and full-cell models have been developed to describe observed EIS data for fuel cells, with successful explanation of some of the EIS response [e.g., 3–10]. This approach has the ultimate goal of being able to fully predict the EIS response for a given electrode configuration, so that optimal surfaces can be developed. While the end goal is ultimately more fundamental than the equivalent circuit approach, the complexity involved with the porous and partially flooded electrode structures found in fuel cells has precluded its extensive application. Cyclic Voltammetry Cyclic voltammetry (CV) is perhaps the most widely used electrochemical technique and is frequently applied for the initial characterization of a redox system. It can provide information about the number of oxidation states as well as qualitative information about the stability of these oxidation states and the electron transfer kinetics. In particular, CV provides quantification of redox potentials of the electroactive species and convenient evaluation of the effect of different materials, morphology, or operating environments upon the redox process. In fuel cell studies, the CV is nondestructive and does not require the fuel cell to be disassembled during operation. Cyclic voltammetry has been used for the following purposes in fuel cell study: 1. To delineate the reactions on an electrode surface as a function of electrode voltage. 2. To determine the ECSA of an electrode.

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3. To determine the presence of adsorbed surface poisons and to identify the effectiveness of various catalyst combinations in tolerance to impurities. 4. To study performance dependence on crystal lattice structure and particle size of the catalyst. 5. To study the catalyst degradation as a function of time, environmental conditions, or service life. Cyclic voltammetry can be used for other measurements as well, including ex situ studies of a single electrode. The general principle of the CV measurement is that the electrode of interest undergoes a steady voltage potential sweep from a low potential to a high potential and the resulting current generated at the electrode is measured. From the plot of the resulting electrode current versus the potential (a voltammogram), detail about the surface reactions for the electrode can be deduced. The sweep rate of the electrode is important and must be chosen to properly resolve the various electrode reactions while being reasonable. In PEFCs, a sweep rate of around 50 mV/s is typical [11]. There are generally two time constants involved, the time constant for the double layer to charge and that for the various faradaic reactions to take place. Both double-layer and faradaic reaction processes will generate some current during the charging process. In a general ex situ electrode CV analysis, reference, counter, and working electrode configurations are used. In a fuel cell situation, often the use of a reference electrode is difficult, and the reference (RE) and counter (CE) electrodes are the same. This is accomplished via the experimental configuration in Figure 9.7. The electrode of interest acts as the working electrode (WE), and nitrogen (or humidified nitrogen in the case of PEFCs) is introduced to eliminate background noise from hydrogen adsorption in addition to the hydrogen evolution/oxidation reaction. Typically, several hundred CV scans are averaged once a steady state is obtained to minimize error. A typical CV from a platinum electrode in an alkaline solution is shown in Figure 9.8, and of a platinum electrode in an acid solution in Figure 9.9. Qualitatively, the results are similar, but some of the reactions are slightly different. At the low-potential region of both curves is the adsorbed hydrogen oxidation region, which may contain several peaks. The peaks are actually a result of different crystalline structures of platinum present on the electrode. These results can be used to select the

Figure 9.7

A CV experimental setup on fuel cell without reference electrode.

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Figure 9.8 Cyclic voltammogram of polycrystalline platinum in 1 M KOH alkaline electrolyte solution at 20◦ C with voltage sweep rate of 100 mV/s. (Reproduced with permission from Ref. [12].)

best crystallographic surface structure for the lowest oxidation potential. In an alkaline electrolyte, hydrogen oxidation follows: Pt–H + OH− → Pt + H2 O + e−

(9.1)

In the acid electrolyte, hydrogen oxidation follows: Pt–H + H2 O → Pt + H3 O+ + e−

(9.2)

Figure 9.9 CV of polycrystalline platinum in acid 0.5 M H2 SO4 electrolyte solution with voltage sweep rate of 50 mV/s. (Reproduced with permission from Ref. [12].)

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At higher potential, ∼0.45–0.55 in an alkaline solution and ∼0.45–0.8 V in an acid solution, there is a plateau region where the current is very low. This region represents the doublelayer charging region with no significant electrochemical reactions. At higher surface potentials, the electrochemical chemisorption of oxygen and platinum oxidation is initiated with the following reactions: In the alkaline solution Pt + OH− → Pt–OH + e−

(9.3)

and above ∼800 mV, platinum oxide formation is observed: Pt–OH + OH− → Pt–O + H2 O + e−

(9.4)

In the acid solution, the reactions are very similar: Pt + H2 O → Pt–OH + e− + H+ Pt–OH + H2 O → Pt–O + H3 O+ + e−

(9.5) (9.6)

At very high potentials, the oxygen evolution reaction occurs in the alkaline electrolyte: 4OH− → O2 + 2H2 O + 4e−

(9.7)

2H2 O → O2 + 4H+ + 4e−

(9.8)

In the acid electrolyte

As the voltage is then swept backward to zero potential, oxygen and Pt–O reduction reactions occur, until hydrogen adsorption on the platinum occurs in the alkaline electrolyte via Pt + H2 O + e− → Pt–H + OH−

(9.9)

Pt + H3 O+ + e− → Pt–H + H2 O

(9.10)

In the acid electrolyte

At very low surface potential, hydrogen evolution begins in the alkaline electrolyte via 2H2 O + 2e− → 2OH− + H2

(9.11)

2H3 O+ + 2e− → 2H2 O + H2

(9.12)

In the acid electrolyte

When the catalyst morphology, type, crystallographic structure, temperature, gaseous environment, or other factors change, the CV response will also change. Comparison of the CV results can reveal information on the reaction kinetics and the potential required for the reaction in a given environment. For example, a CV of the same Pt–H electrode in a gaseous environment poisoned with carbon monoxide will show a shift in the hydrogen oxidation to higher potentials and a reduction in the hydrogen adsorption peak area, since some of the catalyst will be occupied with carbon monoxide.

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Electrochemical Active Surface Area The characterization of the ECSA is a measure of the efficiency of the catalyst loading. The ECSA is an extremely useful tool to compare the efficiency of one electrode to another and also to examine the degradation of the electrode over time resulting from a variety of physical and chemical mechanisms. For the ECSA measurement on a platinum electrode, the experimental configuration shown in Figure 9.7 is used and two assumptions are made [13]: 1. Each platinum site can adsorb only one hydrogen proton. 2. Every available platinum site will be occupied with hydrogen during the transition from hydrogen adsorption to hydrogen evolution. To calculate the ECSA, a plot of the area under the current versus time during the hydrogen adsorption peak in the CV (see Figure 9.10) is used to determine the total charge per superficial electrode area, since the charge is equivalent to the total integrated adsorption current over time. The value of charge is divided by the total catalyst loading. A proportionality constant for a given catalyst is needed to convert the charge per area to effective catalyst active area, based on the charge per unit area of a planar electrode surface:
I (t) dt (9.13) ECSA = = m2 /gcatalyst SC The proportionality constant S used to relate the catalyst area to the charge is 210 µC/cm2 for platinum [14] and C is the loading of the catalyst in grams. Although we have shown the ECSA measurements using the hydrogen absorption area, the technique can also be applied to the hydrogen oxidation area of the curve or, in theory, to any other portion of the curve with repeatable faradaic processes. The same procedure can be used for nonplatinum

Figure 9.10 The area shown under the dashed line represents hydrogen adsorption and can be used to determine electrochemically active catalyst area. CV done on a 5 cm2 active area fuel cell, in-situ. 50 sccm hydrogen on anode, 200 sccm nitrogen on cathode. RH anode/cathode = 100/100%, scan rate 20 mV/sec.

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electrodes as well, providing a new proportionality constant can be found for the particular catalyst. Typical values for the ECSA of a platinum catalyst in a PEFC are around 50 m2 /g Pt [15]. Tafel Plots Electrode kinetic parameter characterization requires data on the electrode kinetic polarization as a function of current density in the absence of (or corrected for) concentration and ohmic effects. For fuel cell electrodes, this can be accomplished ex situ using a variety of methods, most commonly a rotating disk electrode (RDE) with a reference electrode. The RDE is a common electrochemical tool and has a small rotating electrode disk in an electrolyte solution [1]. The rotation rate is used to eliminate concentration polarization, and ohmic, nonuniformity, and crossover effects are all eliminated or corrected for, so that only the pure kinetic response of the electrode of interest is examined. In situ fuel cell testing is useful, too, since it is a direct measurement. This can easily be accomplished in hydrogen fuel cells since the pure hydrogen oxidation reaction (HOR) in low or high temperature is quite facile for fuel cells that are acid or alkaline based. In this case, the anode is used as the dynamic hydrogen electrode, which is the pseudoreference electrode. The cathode becomes the electrode of interest, and all losses are assumed to come from ohmic, crossover (if applicable), and oxidizer reduction reaction (ORR), or   E cell = E ◦ (T, P) − ηa,c  −ηr −ηx

(9.14)

where the terms used have been discussed in Chapter 4. In Eq. (9.14), the concentration polarizations are not explicitly broken out but are considered part of the kinetic expression through the exchange current density. To measure the Tafel slope and extract kinetic parameters, the cell corrected voltage versus effective current density is plotted on a semilog scale, as shown in Figure 9.11 [15]. The cell voltage must be corrected to remove any ohmic or other effects that reduce the voltage besides kinetic losses at a single electrode. In order to correct for ohmic losses, an HFR or current-interrupt technique should be used at each current density, as the value may change with current. Any crossover current density must also be measured and corrected for by adding to the current density, that is, Ieff = Icell + Ix

(9.15)

From Chapter 4, we recall that the Tafel kinetics expression, which is generally valid for the ORR and many other reactions, can be written as     i + ix i Ru T = b ln ln η= αj F io io

(9.16)

where b is the Tafel slope. From a semilog plot like that shown in Figure 9.11, the exchange current density and the Tafel slope can be determined for an electrode as long as the ohmic and crossover losses are properly accounted for and the anode reaction has very small overpotential, which may not be the case for a particular fuel cell, especially if operating on diluted or reformed hydrogen. Another way to present the data is normalized on a catalyst loading basis, as shown in Figure 9.12. In this approach, the ohmic and crossover corrected current density is divided by the catalyst loading per geometric area. From Figure 9.12, it can be seen that on a

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Figure 9.11 Tafel slope preparation from corrected polarization curve data. Data are taken for a 50-cm2 fully humidified PEFC at 80◦ C, 270-kPa anode and cathode in a hydrogen/oxygen environment, for different mass loadings of platinum catalyst. Data are corrected for measured ohmic losses and crossover. (Reproduced with permission from Ref. [15].)

mass-normalized basis the Tafel slopes in an air and oxygen environment for different catalyst loadings can be collapsed, with a Tafel slope of around 0.06 V/decade In a direct alcohol or other nonhydrogen fuel cell, the anode or cathode can be examined using the DHE concept for the opposing electrode. By switching the location of the DHE,

Figure 9.12 Tafel slopes for PEFC electrodes in 50-cm2 hydrogen/air environment and hydrogen/ oxygen PEFC for different mass loadings of platinum catalyst on mass specific current–density basis (A/mg Pt). Data are taken from fuel cell polarization curves of a fully humidified PEFC at 80◦ C, 270-kPa anode and cathode. Data are corrected for measured ohmic losses and crossover, but not concentration losses, which results in deviation from Tafel slope at high current density. (Reproduced with permission from Ref. [15].)

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the performance of both electrodes under normal operating conditions can be examined. One should make sure that the assumptions made in the analysis are always true, however, to avoid erroneous results. For example, in PEFCs, high current can dry the anode and result in erroneously high Tafel slopes if the ohmic losses are not accounted for.

9.1.2 Experimental Determination of Ohmic Parameters and Polarization Ohmic losses consist of contact, ionic, and electronic resistance losses. There are many methods for quantifying the total ohmic losses in a cell (contact and current flow resistances). The two main methods are the current-interrupt and HFR methods. The current-interrupt method is the simplest and only requires an oscilloscope and fuel cell load, but can be difficult to achieve consistent measurements. The HFR technique is precise but requires an electrical impedance analyzer. To determine the contact resistance, several methods are available. Perhaps the simplest is to measure the total ohmic resistance between the two surfaces and compare to the resistance of the individual components. The contact resistance in fuel cells is generally a strong function of compression pressure or surface oxide formation, depending on the fuel cell type. Ohmic losses between two points in a media can be determined using a two- or fourpoint probe technique, as illustrated in Figure 9.13. In the two-probe technique, the voltage drop between two points is measured as a known current is drawn through two points and the resistance is determined through Ohm’s law. This technique has the disadvantage of including the unknown contact resistance between the probes and the substrate. To correct for this, a four-probe technique can be used where the two probes are used to deliver current and two separate probes are used to measure the voltage drop between two different points along the current path. If the distance between the voltage-sensing probes is precisely known, the ohmic resistance of the material can be determined without knowing the contact resistance between the probes and the substrate, since the voltage-sensing probes have almost no current through them and the high-impedance measurement device.

i

Contact resistance

V,I

i (a) two probe

i I V

i

i (b) four probe

Figure 9.13 ment.

Illustration of (a) two- and (b) four-probe techniques for ohmic resistance measure-

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Experimental Diagnostics and Diagnosis V OCV Concentration ∆V = IR ohm polarization adjustment Cell voltage at current, I t

Figure 9.14

Voltage–time behavior for fuel cell during current-interrupt measurement.

Current Interrupt To apply the current-interrupt method, a high-frequency response data acquisition system such as a digital oscilloscope is used. While operating the fuel cell, the oscilloscope is used to record the cell voltage. When the current is suddenly reduced to zero, the ohmic (IR) losses will immediately disappear, and the fuel cell will return to open-circuit conditions. However, the open-circuit voltage is a function of the reactant concentration at the catalyst surface, and the time scale of mass transfer adjustment is sufficiently longer than the nearly instantaneous electrochemical adjustment. Therefore, the voltage history will have a nearly instantaneous jump following the current shutoff that is related to the IR drop in the fuel cell. The voltage will then gradually rise to a steady open-circuit potential, as illustrated in Figure 9.14. The secondary rise in the voltage to open circuit can be used as an indication of the mass transfer resistance (concentration polarization). While this approach is simple in theory, in practice, it is often difficult to define the precise break-off point between the IR-related voltage rise and the mass-transport-related rise. Additionally, some current charging/discharging in the electrolyte and catalyst layers will occur due to the capacitive effects of the double layer and charge transfer processes, so that there are several time scales involved in the voltage recovery. If a PEFC is being analyed, membrane hydration can also impact results. Thus, this technique is more useful as a quick qualitative sensor to determine the relative state of the ohmic losses than as a precision tool. High-Frequency Resistance A more sophisticated approach to measurement of the ohmic losses is the HFR measurement, as discussed in the previous section. In this approach, an AC signal is superposed on the DC from the fuel cell. At very high frequencies, the AC will render the various electrochemical double-layer capacitances to zero, and only the purely ohmic resistance will be measured. Typical frequencies high enough to successfully use this technique are >1 kHz for PEFCs. This approach only measures the path of least resistance however, and care should be taken to properly understand results. For example, in the electrodes, the HFR will normally measure the electrical resistance only, since it is generally much less than the ionic loss in the mixed conductivity structure. Therefore, HFR could not generally be used to determine electrode ionomer performance. 9.1.3

Experimental Determination of Concentration Polarization To measure the concentration polarization, several techniques can be applied. As discussed, the current-interrupt technique can be used to gage the relative significance of the overall

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concentration polarization on the fuel cell performance. Another simple technique involves comparison of performance for different reactant mole fractions in the fuel or oxidizer mixture. For instance, pure oxygen can be used instead of air to delineate oxygen transport limitations. A mixture of helium and oxygen instead of air can also be used. On the anode side, the hydrogen or other fuel concentrations can be varied and the IR, crossover, and kinetic loss corrected data can be compared to identify concentration losses. Due to concentration polarization, the Tafel slope will deviate from the constant value as the current reaches higher values, as shown in Figure 9.12 for a PEFC air cathode. Once the kinetics, crossover, and ohmic portions are well defined, the remainder must be concentration polarization, which can be modeled in several ways, as discussed in Chapter 4. In PEFCs, there is the additional concern of the highly nonlinear concentration polarization caused by electrode, diffusion media, or flow channel flooding. It is extremely difficult to analytically correlate flooding behavior, since it is location dependent, and so sensitive to current density, temperature, and other operating conditions. It is also very difficult to separate the electrode flooding from gas-phase transport limitations, since, ultimately, flooding is a local effect while fuel cell performance is a lumped measurement. One technique that can be applied to delineate the flooding from nonflooding concentration polarization losses is a rapid polarization curve, disussed in Chapter 6. In a rapid polarization curve, the cell is held at OCV for several minutes after operating in a nonflooded (dry) condition, then the cell voltage is rapidly decreased from OCV to low voltages to obtain a polarization curve in a rapid time-scale. In this period of time, the accumulation of liquid water is minimal. By comparison with a true steady-state polarization curve, the liquid flooding effects can be delineated. It should be noted that a dry PEFC membrane will tend to hydrate when going to higher current densities, on the timescale of around 10–20s. Therefore, this approach can be used if the timescale between voltage change is long enough to allow membrane equilibrium (∼20 s) but short enough to preclude liquid accumulation (∼1 min). The transient response of a fuel cell to a voltage change can also be used to identify the hydration or flooded state of the system, because the characteristic response is different between a dry, fully moist, and flooded fuel cell due to the presence or absence of a rehydration or flooding response peaks. 9.1.4 Experimental Determination of Fuel Crossover Fuel crossover is readily oxidized at the cathode due to the high local potential. The magnitude of the voltage decay from normal levels of crossover becomes insignificant at higher current, but it does cause a significant reduction in the OCV, since some overpotential is required to oxidize the fuel at the cathode. Fuel crossover is also indicative of the quality of the fuel cell build, compression, and sealing integrity and is also used as a beginning-of-life quality control metric. Fuel crossover generally affects PEFCs the most and is also used as a metric to determine the durability of a membrane in service. That is, the fuel crossover increases with time of service and is an indirect indication of membrane thinning and pinhole formation. Fuel crossover can also diffuse into and across liquid electrolytes in PAFC, AFC, and MCFC applications. In SOFCs, crossover is generally not a problem, but finite electrical conductivity of the electrolyte results in the same effect of a reduced OCV. The application where crossover causes the greatest performance loss is liquid-fueled DAFCs, where methanol or other fuel crossover can result in a reduction of OCV of 0.5 V or more

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Experimental Diagnostics and Diagnosis Anode

Cathode

Stopped cathode inlet

Flowing or stopped anode flow

Figure 9.15

FM Crossover flowmeter

Bubble gauge measurement in PEFC.

compared to the Nernst value. In order to measure the gas- or liquid-phase crossover, several techniques are available, as described. Gas-Phase Fuel Crossover In the case of gas-phase reactants, there are several methods to determine reactant crossover. The most commonly used are the (1) bubble gauge, (2) the OCV decay test, and (3) the limiting current test. The bubble gauge and OCV decay test can be easily performed and are the most convenient approaches, while the limiting current test requires some additional experimental complexity and can be a little unreliable. In the bubble gauge approach illustrated in Figure 9.15, a highly sensitive mass flowmeter (the term “bubble gage test” comes from a type of highly sensitivity mass flowmeter used for this purpose) is used to measure the crossover flow. A gas-phase pressure difference can be imposed across the anode and cathode to increase the crossover flow for ease of measurement and comparison. The inlet on the nonpressurized side is also closed, and a flowmeter on the nonpressurized side is used to measure the outgoing flow rate, which is the crossover flow. The bubble gauge approach is quite simple, but the mass flowmeter sensitivity to very low levels of crossover is limited since the difference between the crossover and normally expected flow rates is so large. A separate mass flowmeter can be installed prior to each crossover test to eliminate this problem, but this is cumbersome. Another approach to determine the crossover current with high sensitivity is the OCV decay test. In this approach, the cathode and anode flows are shut off, the exits are closed, and the cell is left at open-circuit conditions. The OCV will gradually decay, due to fuel crossover through the membrane. The rate of decay can be correlated with a high level of precision to the crossover flow rate. Variations of this approach can use a pressure differential or flowing fuel to establish a faster or more repeatable decay correlation. In the limiting current approach, the rate of fuel or oxidant crossover to the other electrode can be estimated using cyclic voltammography by employing the same principles discussed for the CV technique. Essentially, one electrode has nitrogen or other inert species (or humidified nitrogen in the case of a PEFC) and the other electrode has hydrogen. The inert electrode is polarized to oxidize any existing hydrogen until a limiting current is reached where the current becomes invariant with additional polarization (until other electrochemical reactions become significant). The rate of fuel or oxidant crossover to the other electrode can be estimated using the maximum current measured during the polarization. Either cyclic or linear sweep voltammetry can be used for this analysis.

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9.2

Physical Probes and Visualization

469

Liquid Fuel Crossover Many DAFCs suffer large performance losses from crossover. In the case of liquid DAFCs, the crossover current can be determined from chemical species measurement of the cathode effluent gas. Since the product of oxidation of methanol or other fuel crossover is mostly carbon dioxide and carbon monoxide, measurement of these gases along with any residual crossover fuel vapor and minor species can be used to perform a carbon mass balance and deduce the crossover fuel current. The liquid fuel crossover can also be measured using the limiting current approach discussed above. Humidified nitrogen or other inert gas flows through the cathode as it is polarized to oxidize any crossover fuel. The limiting current is the crossover current density at the cell conditions.

9.2 PHYSICAL PROBES AND VISUALIZATION 9.2.1 Distributed Diagnostics Besides online sensing and control, laboratory-based diagnostics have been advanced to provide insight into competing phenomena and as benchmark data for fuel cell model validation. The challenge is to gather more revealing distributed and transient data than a normally instrumented fuel cell, where bulk current and voltage information can be misleading. For example, in larger area fuel cells, performance varies between plates in a stack, with location along the flow channels, and locally along the active area. At different locations in a PEFC, the same cell can be simultaneously suffering flooding or drying (PEFCs) or reactant/product transport limitations. This fact alone limits the quantitative usefulness of bulk cell performance data. Multidimensional models are needed to capture these variations, and diagnostic tools are needed to provide model validation data and measure gradients in current, species, temperature, conductivity, and other parameters of interest. Many useful tools have been developed for this purpose and some of the more common approaches are summarized here as an introduction. Current Distribution Measurement One of the key challenges to the advanced understanding of all fuel cell systems is the development of techniques to measure the current distribution of an operating cell. Determination of current distribution is critical to design optimization, material selection, and model validation and to fundamentally understand the interrelated phenomena which determine the localized performance. Different fuel cells have very different current distributions and influences. For example, a small active area portable fuel cell may have a nearly uniform current distribution, while larger area PEFCs have steep gradients that can vary with local humidity, flooding, oxygen concentration, or other effects. In high-temperature fuel cells, electrolyte conductivity is almost solely controlled by temperature, and current distribution generally follows the temperature profile, so that distributed current measurement may not be necessary in solid oxide and molten carbonate fuel cells as long as electrolyte temperature is known. The methodologies to achieve current distribution measurement in lower temperature PEFCs have been well developed and can generally be applied to other fuel cell systems, although some are more suited to a particular fuel cell. Methods for measurement of current distribution in PEFCs include using magnetic loop arrays embedded in the current collector plate, masking different areas or partially catalyzing segments, isolating individual locations of catalyzed anode and

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i7 i8 i9

∆V 9 i4

∆V 4 i3

∆V 8 i5

∆V 5 i2

∆V 2

∆V 7 i6

∆V 6 i1

∆V1

∆V 3 Figure 9.16 Current mapping technique.

opposing cathode from the main cell in order to measure the performance of the desired location, and current mapping [16–21]. In current mapping, individual shunt resistors are located normal to the electrode surface, between the flow field and a current-collecting plate, as illustrated in Figure 9.16. Voltage sensors passively determine the potential drop across each resistor and, through Ohm’s law, current distribution though the flow plate is determined. It is also possible to directly measure the current without the use of shunt resistors using a multichannel galvanostat/potentiostat, eliminating error associated with distributed voltage measurement [22–25]. Figure 9.17 shows an example of a distributed current measurement for a PEFC operating in an oxygen-starved, constant-flow-rate condition. Obviously, the lumped polarization curve that would be obtained without a segmented cell would hide the large local variations in the current that exist in this condition. The current-mapping approach is actively used by many research groups and industry to monitor steady, transient, and long-term distributed performance in PEFCs. Fuel cells with over a hundred separate signals are now used to examine the fundamental distributed degradation and performance over a variety of conditions. Other electrochemical techniques can be combined with a distributed cell to obtain a wealth of data, such as distributed EIS or ECSA measurement. Use of embedded wires in the catalyst layer has also been applied to determine the local in-plane variation in current across the channel-land interface in PEFCs [26]. Species Distribution Measurement Knowledge of the species distribution is critical for understanding the local performance because, depending on the flow field design, there

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Figure 9.17 Nonhomogeneous current distribution observed in a 50 cm2 fuel cell with 100% RH anode, 0% RH cathode inlet, at 80◦ C. (Adapted from Ref. [22].)

may be locations were the performance is low due to reactant limitation. In some fuel cell systems with limited crossover of reactant or products through the electrolyte, the species profile can be predicted simply from knowledge of the current distribution and Faraday’s law. In PEFCs and some liquid electrolyte systems, where significant flux of water and other species can travel through the electrolyte, this approach is complicated by the lack of highly precise transport parameters. If these were perfectly known, the same approach could be used, and direct measurement of the species distribution would not be needed. Conversely, measurement of the species distribution can be used to precisely define transport parameters as a function of materials and environment. Ideally, we would like diagnostics that tell us the precise reactant mole fractions in the through-plane direction from the electrode surfaces into the flow channels, but this is a very difficult task. Some laser-based diagnostics have been used to try to understand the intermediate species involved in reaction at the catalyst surface [27]. At a larger scale, there are techniques for online measurement of the distributed species mole fraction in a fuel cell flow channel. Of particular interest is the water vapor distribution within the gas channels of PEFCs, since this is closely tied to the issue of flooding and electrode dryout. One common way to measure the water balance in an operating fuel cell is through effluent collection. In this approach, the humidified effluent gas from the fuel cell is chilled through a condensing bath or desiccant, and the total water content removed over time can be determined. While this approach can be used to measure net drag coefficients in steady state, it does not provide transient or distributed data on the water throughout the cell, which could vary widely depending on operating conditions, current distribution, and local nonisotropic transport parameters. Real-time measurement of species distribution in the flow channels can be accomplished with real-time gas analyzer (RTGA) systems [28]. These devices continuously sample a small stream of flow diverted from the channel location of interest so that species mole fractions at selected locations along the reactant

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Figure 9.18 Water vapor distribution near the middle of a single serpentine path cathode. Liquid droplet peaks are evident at this downstream location near the cathode channel exit. (Adapted from Ref. [28].)

gas flow paths can be monitored. This provides detailed understanding and perspective of the time scales of the various intercoupled multiphase dynamic transport phenomena. Figures 9.18 and 9.19 are examples of the instantaneous species mole fractions measured with the RTGA system. In Figure 9.18, the cathode mole fraction changes are observed for changes in the system operating voltage. Figure 9.19 shows the transient response of the anode of a PEFC for a step change in current conditions. The transient responses in PEFCs are strong functions of heat transfer membrane humidity and operating conditions, among other variables. This approach has also been used to efficiently measure the mass transport coefficients when used in conjunction with current density techniques [30]. 100

20 18

80

16 14

60

12

Hydrogen Water

10

40

8

0.4 V

0.7 V

6

20

4

Water mole fraction

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0 360

365

370

375 Time (min)

380

385

390

Figure 9.19 Transient anode species response at x/L = 83% for voltage perturbation (0.7–0.4 V) for a relatively dry anode, A/C RH = 0/75. (Adapted from Ref. [29].)

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Temperature Distribution Measurement The temperature distribution in fuel cells can be of critical importance to the kinetics, electrolyte conductivity, material compatibility issues (high-temperature fuel cells), internal reformation process (high-temperature fuel cells), and other kinetic and transport phenomena known to be functionally dependent on temperature. Since the SOFC is dominated by the electrolyte resistance, which is a strong function of temperature, the current distribution in these systems closely follows the temperature profile. Several techniques can be used to measure the temperature distribution in a fuel cell. An embedded thermistor or thermocouple can be used when carefully placed. Additionally, infrared temperature measurement is a fascinating way to observe real-time temperature variation in a fuel cell. Infrared scanners can be used to look at temperature distribution in a specially modified single fuel cell and have been useful to “see” the phase change processes from ice to liquid in a low-temperature fuel cell [31]. For the PEFC, the water balance is highly coupled to the temperature distribution, as discussed. However, direct measurement of localized temperature is difficult, due to the two-phase nature of flow in the gas channels and the small through-plane dimensions of a typical electrolyte. Besides infrared measurement, the most commonly applied technique is the direct embedding of a thermocouple or thermistor within the bipolar plate. This approach is acceptable for most fuel cell varieties. If all thermal transport parameters, such as specific heat, thermal conductivity, and contact resistance, are known, calculation of the temperature profiles within the fuel cell can be accomplished using embedded thermocouple data and analytical or computational heat transfer models. For fundamental research where the thermal parameters are not precisely known and to define unknown thermal transport parameters, we would like to directly measure the temperature profile within the electrolyte. To approach this problem, a thermocouple can be embedded directly in the diffusion media of a PEFC [32, 33]. However, the contact resistance between the diffusion media and the thermocouple becomes another unknown parameter. To circumvent these difficulties, Burford et al. invented a method to embed an array of microthermocouples directly between two 25-µm-thick Nafion electrolyte sheets of a membrane electrode assembly [34, 35]. Local temperature variation in PEFCs was determined to reach >10◦ C at high current density for a thick diffusion media (>400 µm for woven cloth media). This proved that an isothermal assumption is typically not justified over a full range of performance and indicates phase change plays a role in water transport in PEFCs. An even smaller MEMs-based thermosensor array has been developed using vapor deposition [36] and has been embedded within a PEFC electrolyte, providing precise locational control of the sensor position. Impedance Distribution Measurement The localized impedance profile can also be a great tool to characterize local design, material, and performance. For a well-built and designed fuel cell, the dominating ohmic loss is typically from the electrolyte. With a segmented fuel cell for distributed measurements, a full electrical impedance spectra can be used to examine the local performance losses. This information can be enormously valuable to the design engineer, because the spatial variations in the EIS are often obscured when the full cell is examined using EIS. Additionally, the HFR measurement can be used in a distributed cell to yield detailed information about local membrane conductance. For a PEFC, this is directly related to water content and also directly impacts durability. For a higher temperature fuel cell such as an SOFC, the HFR profile can be an indirect

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d

a

g

c

Figure 9.20 Example of comparison of high-frequency resistance profiles at 0.7 V for three conditions of very different inlet humidity; all other conditions are the same along a concurrent flow path. The current density, HFR, and species profile is highly nonuniform for a underhumidified inlet conditions. (Adapted from Ref. [29].)

measurement of temperature. Figure 9.20 is shown as an example of the detail that can come from such measurement in a PEFC and shows a very nonhomogeneous conductance distribution, indicating some localized dryout of the electrolyte is occurring near the inlet section. Since accelerated electrolyte degradation has been associated with high-temperature, lowmoisture conditions, this figure indicates the anode inlet region should be most susceptible to decreased performance over time. The bulk full-cell HFR cannot show this detail and can be very misleading, since the HFR measurement will be indicative of the bulk resistance and will not indicate the true local conditions. Thus, bulk HFR measurements are unlikely to correlate well to localized membrane degradation behavior. 9.2.2

In Situ Measurement and Visualization Direct Visualization Techniques Fuel cell visualization tools are also of great value, especially for low-temperature PEFCs fueled by hydrogen or alcohol solutions where blockage of reactant flow by electrode, gas diffusion layer, and channel-level flooding hinders performance. The most common technique to directly image the water droplet formation and motion in the flow channel and on the catalyst surface of a PEFC is direct optical imaging [37–40]. In this approach, a small window is embedded above the channel allowing visual access. A video camera can focus on the flow channel or on the catalyst surface if the diffusion media is removed or replaced by a metal mesh at that location. Figure 9.21 shows an image of a liquid droplet emerging on a diffusion media surface taken with an optical model fuel cell. This technique has revealed a variety of interesting phenomena and has high spatial resolution on the order of micrometers, although some intrusion and change in heat transfer conditions is needed to image the catalyst surface. Since one side of

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Figure 9.21

Physical Probes and Visualization

475

Direct photographic image of water on surface of DM in visualization fuel cell.

the fuel cell is imaged in a small location, this approach is ideal for fundamental study of liquid motion but is not appropriate for full-sized cell study. Careful attention to the thermal boundary condition is also needed to ensure physically relevant results are achieved. Another tool that is of great help in imaging two-phase water distribution in a fully operational PEFC is neutron radiography (NR) [41–46]. Neutron radiography is analogous to X-ray imaging, except that neutron attenuation on hydrogen is extremely high. As a result, liquid water is easily distinguished from flow channels, gas diffusion layers, and so on, as shown in Figure 9.22. On the left side of Figure 9.22, the neutron image of the 50-cm2 PEFC has a water wedge in it to provide a calibration standard from which the total liquid water content in the fuel cell can be quantified. The image on the right is an expansion of the active area

Figure 9.22 (a) Neutron radiograph image of 50-cm2 fuel cell and calibration water wedge; (b) magnified image of active area showing locations of liquid water accumulation. (Image location at Penn State Breazeale Nuclear Reactor Fuel Cell Imaging Laboratory.)

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of the same fuel cell, digitally processed to eliminate background noise and remove all nonliquid water content, leaving an image of only the liquid water in the fuel cell. In Figure 9.22 the lighter areas indicate liquid accumulations. Advanced data analysis techniques can quantify liquid water amounts and even measure flow velocities of droplets or relative liquid thickness distributions between the DM and channels. Another advantage of the neutron imaging technique is that the entire fuel cell, even full-sized stack plates, can be imaged in real time, so that the design of full-sized plates can be rapidly improved. Using neutron computed tomography, a three-dimensional imaging can be accomplished, although the spatial and temporal resolution is significantly reduced [47]. Optimal geometric and temporal resolution can range from 10 µm and 30 frames per second, respectively and further development in this technology is expected. Table 9.1 shows a comparison of some of the various imaging approaches for PEFCs. Note that there is always a trade-off between resolution and field of view. That is, resolution is increased as the field of view is decreased, which is a classic limitation of any imaging technology. Another visualization approach is particle image velocimetry (PIV), which has been used to study gas-phase flow contours in the channels [48] but is only suitable for gas channel manifold flow and cannot look into the porous media surface. Magnetic resonance imaging (MRI) [49] is a high-resolution technique that has been used in small operating fuel cells, but because it relies on a strong magnetic force, magnetic metals cannot be used. As a result, highly altered and small fuel cells must be used. Recently, X-ray microtomography [50], used in the past for soil saturation analysis, has been adopted in ex situ studies of water saturation in diffusion media of a PEFC in a nonoperating environment. This technique may someday be used in an operating fuel cell with further development. Other technologies are being developed for water imaging purposes and may become useful in the future. Other Techniques As indicated, the field of fuel cell diagnostics is far too broad to discuss every technique here. Since flooding in a PEFC is such an important technical challenge, there have been many systems developed to try to measure liquid water content, distribution, and storage in the PEFC. Besides neutron imaging, MRI, and direct visualization, several more conventional technologies can be exploited to gain some additional information. Since liquid water storage in the PEFC will change with time, the weight of the PEFC will also vary with time according to the stored water content:   dm W  dW  =g (9.17) dt FC dt FC The main limitation with this approach is that the fuel cell generally weighs many orders of magnitude more than the water content change, so that finding a precision scale to handle the weight of the fuel cell and still give adequate resolution for the water content is difficult. To circumvent this, the fuel cell can be built for a quick opening, and the soft goods (MEA) can be extracted from the fuel cell, weighed, and resealed in the fuel cell. This approach is obviously somewhat intrusive but can be used with relative ease on a properly designed laboratory fuel cell. Another technique to measure liquid water content in diffusion media is based on the pressure drop through the media. Since the pressure drop increases with water saturation, the pressure drop through an interdigitated flow field can be used as a qualitative measure

Steady-State measurement Steady-State measurement 5 fps

∼25–100 µm ∼10 µm ∼50 µm

Lens resolutioncan be sub-micron

Magnetic Resonance Imaging (MRI) X-Ray micro tomography

Particle Image Velocimetry

Optical Imaging Lens fieldof-view

3–4 mm2

∼ 5 mm component

Up to full-size stack single cell ∼5 cm2 cell

Field of View

Yes—with a modified cell to allow optical access Yes—with a modified cell to allow optical access

Yes

Yes—with a highly modified cell

Yes—with an unmodified cell

Potential for use in an operating cell?

Imaging cell must be non-metal, and alters the water distribution unreasonably [49, 52]. Water must be artificially imbibed or purged through a DM, not an operating fuel cell [50]. Accurate tool for flow in the channel only [48]. Limited to low speed laminar flow. Accurate tool for flow for channel-level flow only. Catalyst layer images require alteration of the diffusion media and heat transfer boundary conditions.

Only about a dozen institutions in the world can perform this.

Limitations

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30 fps or greater

25–100 µm

Neutron Imaging

Temporal Resolution

Spatial Resolution

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Summary of Various Direct Visualization Techniques Which Have Been Applied to PEFCs

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of the liquid content. One research group [51] has designed a unique fuel cell that has a conventional flow field that can be quickly switched to an interdigitated design during operation. From pressure-versus-time traces, the cell design can be used to delineate liquid flooding in the diffusion media from the catalyst layer in a PEFC and estimate the total liquid blockage in the cell. Dynamic response-based methods can also be used to determine flooding status, and are especially useful in stacks, where sensor options are much more limited. The characteristic voltage time behavior of individual cells can be used to determine general cell status.

9.3

DEGRADATION MEASUREMENTS Although beginning-of-lifetime performance and modeling are critical, the behavior of the fuel cell as a function of load cycles, environment, or service time is also of great importance to meet consumer needs. In order to determine the various factors governing degradation of the components, many experimental techniques have been devised. In terms of general performance, the techniques discussed in Section 9.1 to examine the various polarization losses can be applied as a function of cycle number or service time to delineate the losses observed. For example, catalyst sintering will result in a loss of ECSA that can be measured by CV techniques. Other online techniques can be used to examine the change in electrode or electrolyte materials. If parts of the electrode or electrolyte are lost due to reaction, finite vapor pressure, or other reasons, analysis of the effluent product can often be correlated to the particular loss mechanism. For example, in PEFCs, one mode of physicochemical electrolyte degradation is accompanied by loss of the fluorine ion, which can be detected by measurement of the effluent condensed water fluorine content. Also, if carbon corrosion is occurring, carbon monoxide or carbon dioxide gas is produced, and this can be measured with a sufficiently sensitive device. In general, if there is a chemical reaction causing the degradation, the product species from this can be detected in the effluent and correlated with the measured loss. In many cases, however, the degradation is physical and affects the properties of the materials. For example, the wetting properties of the PEFC and AFC diffusion media surface can change with time due to contamination from gaskets and hoses in the fuel cell system. These types of degradation are purely physical, and the only way of measuring them is through indirect correlation (e.g., a noted performance loss) or by ex situ examination after removal from the fuel cell. There are too many material analysis techniques to list here, but microscopic imaging, surface area and morphological measurement, and mechanical integrity testing are all readily available and ubiquitously used in fuel cell research.

9.4

SUMMARY New diagnostic approaches and methods are being constantly developed and are part of the ever-evolving and exciting field of fuel cell research and development. In this chapter, some of the most common techniques for analyzing fuel cell behavior and deriving various electrochemical parameters were discussed. The field of electrochemical analysis is too broad for a single chapter, so only the most commonly used approaches were presented. In

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particular, EIS and CV methods were discussed. The EIS measurement is based on applying an AC with varying frequency and measuring the electrochemical response. When used ex situ with a reference electrode or in situ with a dynamic hydrogen electrode, the EIS approach can be used to comparatively examine ohmic, charge transfer, and mass transfer resistances for different electrode and fuel cell systems. At the extreme high-frequency range of the impedance spectra, the HFR represents the summation of purely ohmic resistances. The current-interrupt technique is also used to determine the ohmic contribution to losses but is difficult to precisely apply. The CV approach can be used to determine the ECSA and compare the electrode loading efficiency and electrode kinetic performance as a function of operation history and environment. The same configuration can also be used to measure the crossover current through the electrode with a limiting current measurement. Crossover can also be quantified using a flowmeter or the OCV decay approach. In order to examine the various transport and physicochemical processes within an operating fuel cell and provide detailed model validation, techniques for distributed current, temperature, and species measurement were discussed. Data from these distributed diagnostic cells can be used to close energy, electrical, and mass conservation equations on a local level, providing a much greater level of detail than a single-cell lumped polarization curve. Various sensors and visualization techniques were discussed, particularly as applied to PEFCs and observation of liquid water and flooding phenomena. Neutron imaging, direct visualization cells, magnetic resonance imaging, and other approaches have been used, but all have particular limitations that must be considered. There is always a trade-off between field of view and spatial resolution for imaging analysis.

APPLICATION STUDY: DEVELOPING AN EXPERIMENTAL TEST PROGRAM In this text, we have learned of many of the various phenomena which control fuel cell performance. Many readers will not have any laboratory or work experience on which to put the understanding gained into a practical perspective, however. In this chapter, a few of the basic methods to quantify fuel cell performance have been discussed. For this application study, you will develop an experimental program. Consider that you are asked to develop a workable fuel cell model to describe a new fuel cell you have no data for but want to understand the following: 1. What is (are) the limiting polarization(s)? 2. What are the main factors controlling these polarizations? 3. What are the parameters needed to develop an analytical model similar to that described in Chapter 4 to predict the fuel cell behavior as a function of operating conditions? Prepare a list of experimental tests that must be completed and the parameters you will vary during testing (e.g., you will need to determine kinetic parameters as a function of temperature and species mole fraction). List the methods you will use and the tests that must be performed to obtain all of the values and functional dependencies you will need to completely define a zero-dimensional model of this new fuel cell.

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PROBLEMS 9.1 What is meant by ohmic and nonohmic resistance contributions? 9.2 Describe the basic physical principle on which EIS is based. 9.3 A cyclic voltammogram is obtained by varying the potential on an electrode surface and measuring the resulting current. Could the process be changed to measure the voltage change at a constant current? Would this have any advantages? Hint: Read ref. [4]. 9.4 What is the physical meaning of the proportionality constant used in determining the ECSA? Would the value of 210 µC/cm2 for platinum be good for a nickel electrode in a SOFC? Why or why not? 9.5 How would you measure or obtain the proportionality constant used in determining the ECSA? 9.6 What are some of the degradation effects listed in Chapter 6 for PEFCs that would result in loss of ECSA for PEFCs? 9.7 Would a flooded or dried PEFC electrode affect the EIS results? Qualitatively sketch a EIS Nyquist plot for a normal, dried, and flooded PEFC electrode situation. 9.8 What would the effect of electrolyte contamination and degradation of an AFC be on the expected Nyquist EIS plot? 9.9 In a PEFC, the high-current-density performance can be low as a result of flooding the electrode or anode dryout. How could you experimentally delineate the difference? 9.10 Does the use of a dynamic hydrogen electrode become more or less appropriate at high current density? Why or why not? 9.11 Qualitatively sketch a current-interrupt voltage versus time response for a solid oxide, direct methanol, and polymer electrolyte fuel cell system. Remember to think about what is limiting each fuel cell under normal operation. 9.12 Why does the Tafel slope in Figure 9.12 deviate from linearity? Would a higher pressure cathode feed delay the departure?

9.15 Can you calculate the electrolyte temperature from a temperature probe in the bipolar plate of a PEFC or would a sensor have to be directly in the electrolyte? What sort of temperature difference between the bipolar plate and the catalyst layer do you anticipate at 1 A/cm2 ? 9.16 What practical experimental concerns would you have if you are replacing a portion of the bipolar plate in a PEFC with a plexiglass window to observe liquid water formation and motion? 9.17 Assume that you have a method in your laboratory for perfect species mole fraction measurement at selected locations along a single channel in a PEFC. Experimentally, describe how you could measure the diffusivity of water in the electrolyte/catalyst layer/DM membrane electrode assembly. Hint: Consider developing an along-the-channel model to use with your experimental data. 9.18 In a PEFC, there are often phase change processes such as vaporization, condensation, and freezing or melting. If you were using an infrared device to observe the instantaneous temperature distribution in a PEFC, what would you expect to see during the various phase change events, an increase or decrease in the local temperature? Would the phase change affect the overall energy balance in the fuel cell? 9.19 Is a technique for current distribution measurement necessary with the SOFC? What can be used instead of a direct distributed current measurement? 9.20 Would the ohmic resistance measured with the HFR technique be over- or underestimated if the frequency chosen was not sufficiently high? 9.21 One potential way to measure the liquid water accumulation and depletion in a PEFC is by weighing the cell during operation. What is the practical limitation with this approach? Could it work? 9.22 In an AFC, carbon dioxide impurity can degrade the performance of the electrolyte over time. How can the effect of CO2 impurity on the electrolyte be precisely quantified and modeled?

9.13 Discuss some of the limitations and advantages of EIS. What parameters can you get from its use?

9.23 In a MCFC, it is believed that the current-collecting grid structure corrosion is causing performance degradation over time. How could this be experimentally confirmed or refuted?

9.14 Would any of the current distribution methods discussed be applicaple in a full-size stack?

9.24 How could you measure the loss of electrolyte from a PAFC system due to vaporization?

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References 9.25 In a PAFC system you are operating, it is suspected that the catalyst on an electrode is somehow dissolving at high potential conditions >0.8 V. How would you propose to experimentally confirm or refute and model this occurrence? 9.26 Deduce a one-dimensional model to explain how the species profile can be predicted from knowledge of the current density in an SOFC. Could the approach be used to deduce the current distribution if the species profiles are known? 9.27 Deduce a one-dimensional model to explain how the species profile can be predicted from knowledge of the current density in a PEFC. What are the main complicating

481

uncertainties in this model? Could the approach be used to deduce the current distribution if the species profiles are known?

Open-Ended Problems 9.28 Go online and find a few references that discuss the use of a reference electrode for a fuel cell or the development of a reference electrode for fuel cell use. Explain why this has been difficult to apply in practice. 9.29 It has long been a challenge to observe the liquid water accumulation and motion within the catalyst layer of a PEFC. Are there any experimental techniques you can think of or that have been developed to accomplish this?

REFERENCES 1. A. J. Bard and L. R. Faulkner, Electrochemical Methods, 2nd ed., Wiley, New York, 2001. 2. M. G. Parthasarathy and J. W. Weidner, “Analysis of Electrochemical Impedance Spectroscopy in Proton Exchange Membrane Fuel Cells,” Int. J. Energy Res., Vol. 29, pp. 1133–1151, 2005. 3. H. Kuhn, B. Andreaus, A. Wokaun, and G. G. Scherer, “Electochemical Impedance Spectroscopy Applied to Polymer Electrolyte Fuel Cells with a Pseudo Reference Electrode Arrangement,” Electrochim. Acta, Vol. 51, No. 8/9, pp. 1622–1628, 2006. 4. T. E. Springer, T. A. Zawodzinski, M. S. Wilson, and S. Gottesfeld, “Characterization of Polymer Electrolyte Fuel Cells Using AC Impedance Spectroscopy,” J. Electrochem Soc., Vol. 142, pp. 587–599, 1996. 5. P. M. Gomadam, J. W. Weidner, T. A. Zawodzinski, and A. P. Saab, “Theoretical Analysis for Obtaining Physical Properties of Composite Electrodes,” J. Electrochem Soc., Vol. 150, pp. E371–E376, 2003. 6. T. E. Springer and I. D. Raistrick, “Electrical Impedance of a Pore Wall for the FloodedAgglomerate Model of Porous Gas-Diffusion Electrodes,” J. Electrochem Soc., Vol. 136, pp. 1594–1603, 1989. 7. M. Eikerling and A. A. Kornyshev, “Electrochemical Impedance of the Cathode Catalyst Layer in Polymer Electrolyte Fuel Cells,” J. Electroanal. Chem., Vol. 475, pp. 107–123, 1999. 8. F. Jaouen, G. Lindberg, and K. Wiezell, “Transient Techniques for Investigating Mass-Tranport Limitations in Gas-Diffusion Electrodes: I. Experimental Characterization of the PEFC Cathode,” J. Electrochem Soc., Vol. 150, pp. A1711–A1717, 2003. 9. Q. Guo and R. E. White, “A Steady-State Impedance Model for a PEMFC Cathode,” J. Electrochem Soc., Vol. 151, pp. E133–E149, 2004. 10. Q. Guo, M. Cayetano, Y. Tsou, E. S. De Castro, and R. E. White, “Study of Ionic Conductivity Profiles of the Air Cathode of a PEMFC by AC Impedance Spectroscopy,” J. Electrochem Soc., Vol. 150, pp. A1440–A1449, 2003. 11. W. Vielstich, “Cyclic Voltammetry,” in Handbook of Fuel Cells, Technology and Applications, Vol. 2, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, Chichester, 2003, pp. 153–162. 12. C. H. Hamann, A. Hamnett, and W. Vielstich, Electrochemistry, Wiley-VCH, Weinheim, 1998. 13. D. A. Stevens, and J. R. Dahn, “Electrochemcial Characterization of the Active Surface in Carbon-Supported Platinum Electrocatalysts for PEM Fuel Cells,” J. Electrochem Soc., Vol. 150, pp. A770–A775, 2003.

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Experimental Diagnostics and Diagnosis 14. M. Sogaard, M. Odgaard, and E. M. Skou, “An Improved Method for the Determination of the Electrochemical Active Area of Porous Composite Platinum Electrodes,” Solid State Ionics, Vol. 145, pp. 31–35, 2001. 15. H. A. Gasteiger, W. Gu, R. Makharia, M. F. Mathias, and B. Sompalli, “Beginning-of-life MEA Performance—Efficiency loss contributions,” in Handbook of Fuel Cells—Fundamentals, Technology and Applications, Vol. 3, W. Vielstich, A. Lamm, and H. A. Gasteiger, Eds., Wiley, New York, 2003, pp. 593–610. 16. A. B. Geiger, R. Eckl, A. Wokaun, and G. G. Scherera, “An Approach to Measuring Locally Resolved Currents in Polymer Electrolyte Fuel Cells,” J. Electrochem Soc., Vol. 151, pp. A394–A398, 2004. 17. M. Noponen, J. Ihonen, A. Lundblad, and G. Lindbergh, “Current Distribution Measurements in a PEFC with Net Flow Geometry,” J. Appl. Electrochem., Vol. 34, pp. 255–262, 2004. 18. C. Wieser, A. Helmbold, and E. G¨ulzow, “A New Technique for Two-Dimensional Current Distribution Measurements in Electrochemical Cells,” J. Appl. Electrochem., Vol. 30, pp. 803–807, 2000. 19. D. J. L. Brett, S. Atkins, N. P. Brandon, V. Vesovic, N. Vasileiadis, and A. R. Kucernak, “Measurement of the Current Distribution along a Single Flow Channel of a Solid Polymer Fuel Cell,” Electrochem. Commun., Vol. 3, pp. 628–632, 2001. 20. S. Cleghorn, C. Derouin, M. Wilson, and S. Gottesfeld, “A Printed Circuit Board Apporach to Measuring Current Distribution in a Fuel Cell,” J. Appl. Electrochem., Vol. 28, pp. 663–672, 1998. 21. J. Stumper, S. Campell, D. Wilkinson, M. Johnson, and M. Davis, “In Situ Methods for the Determination of Current Distributions in PEM Fuel Cells,” Electrochim. Acta, Vol. 43, pp. 3773–3783, 1998. 22. Q. Dong, M. M. Mench, S. Cleghorn, and U. Beuscher, “Distributed Performance of Polymer Electrolyte Fuel Cells Under Low-Humidity Conditions,” J. Electrochem. Soc., Vol. 152, pp. A2114–A2122, 2005. 23. M. M. Mench, C. Y. Wang, and M. Ishikawa, “In Situ Current Distribution Measurements in Polymer Electrolyte Fuel Cell,” J. Electrochem Soc., Vol. 150, A1052–A1059, 2003. 24. M. M. Mench and C. Y. Wang, “An In Situ Method for Determination of Current Distribution in PEM Fuel Cells Applied to a Direct Methanol Fuel Cell,” J. Electrochem Soc., Vol. 150, pp. A79–A85, 2003. 25. M. Noponen, T. Mennola, M. Mikkola, T. Hottinen, and P. Lund, “Measurement of Current Distribution in a Free-Breathing PEMFC,” J. Power Sources, Vol. 106, pp. 304–312, 2002. 26. S. A. Freunberger, M. Reum, J. Evertz, A. Wokaun, and F. N. B¨uchi, “Measuring Current Distribution in PEFCs with Sub-Millimeter Resolution I. Methodology,” J. Electrochem. Soc., Vol. 153, pp. A2158–A2165, 2006. 27. Q. Fan, C. Pu, and E. S. Smotkin, “In-Situ FTIR-diffuse reflection study of Methanol Oxidation Machanisms on Fuel Cell Anodes,” Energy Conversion Engineering Conference, Proceedings of the 31st Intersociety, Vol. 2, pp. 1112–1116, 1996. 28. Q. Dong, J. Kull, and M. M. Mench, “Real-Time Water Distribution in a Polymer Electrolyte Fuel Cell,” J. Power Sources, Vol. 139, pp. 106–114, 2005. 29. Q. Dong, S. He, and M. M. Mench, “Dynamic Response of Current, Species, and Temperature of Polymer Electrolyte Fuel Cells,” in Proceedings of the 206th Meeting of the ECS, Proton Conducting Membrane Fuel Cells, Vol. 4, M. Murthy Ed., Honolulu, HI, pp. 551–564, 2004. 30. Q. L. Dong, Ph.D. Thesis, “Distributed Measurement and Determination of Transport Parameters in PEFCs,” The Pennsylvania State University, University Park, PA, August 2006.

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31. Y. Ishikawa, T. Morita, and M. Shiozawa, “Behavior of Water below the Freezing Point in PEFCs,” ECS Trans., Vol. 3, No. 1, Proton Exchange Membrane Fuel Cells, Vol. 6, T. Fuller, C. Bock, S. Cleghorn, H. Gasteiger, T. Jarvi, M. Mathias, M. Murthy, T. Nguyen, V. Ramani, E. Stuve, and T. Zawodzinski, Eds., pp. 889–895, 2006. 32. P. J. S. Vie, “Characterization and Optimization of the Polymer Electrolyte Fuel Cell,” Ph.D. Thesis, NTN University, Trondheim, Norway, 2002. 33. P. J. S. Vie and S. Kjelstrup, “Thermal Conductivities from Temperature Profiles in the Polymer Electrolyte Fuel Cell,” Electrochem. Acta, Vol. 49, pp. 1069–1077, 2004. 34. D. J. Burford, T. W. Davis, and M. M. Mench, “In Situ Temperature Distribution Measurements in an Operating Polymer Electrolyte Fuel Cell,” in Proceedings of the 2003 International Mechanical Engineering Congress and Exposition (IMECE), Symposium, Paper No. 42393, Washington, DC, November 2003. 35. D. J. Burford, T. W. Davis, and M. M. Mench, “Heat Transport and Temperature Distribution in PEFCs,” in Proceedings of the 2004 International Mechanical Engineering Congress and Exposition (IMECE), IMECEC 2004–59497, Anaheim, CA, November 2004. 36. S. He, M. M. Mench, and S. Tadigadapa, “Thin Film Temperature Sensor for Real-Time Measurement of Electrolyte Temperature in a Polymer Electrolyte Fuel Cell,” Sensors and Actuators A: Physical, Vol. 125, No. 2, pp. 170–177, 2006. 37. K. T¨uber, D. Pocza, and C. Hebling “Visualization of Water Buildup in the Cathode of a Transparent PEM Fuel Cell,” J. Power Sources, Vol. 124, pp. 403–414, 2003. 38. X. G. Yang, F. Y. Zhang, A. L. Lubawy, and C. Y. Wang, “Visualization of Liquid Water Transport in a PEFC,” Electrochem. Solid State Lett., Vol. 7, No. 11, pp. A408–A411, 2004. 39. H. S. Kim, T. H. Ha, S. J. Park, K. Min, and M. Kim, “Visualization Study of Cathode Flooding with Different Operating Conditions in a PEM Unit Fuel Cell, in ASME Proceedings of Fuelcell2005, Third International Conference on Fuel Cell Science, Engineering and Technology, Paper No. 74051, Ypsilanti, MI, 2005. 40. E. C. Kumbur, K. V. Sharp, and M. M. Mench, “Liquid Droplet Behavior and Instability in a Polymer Electrolyte Fuel Cell Flow Channel,” J. Power Sources, Vol. 161, pp. 335–345, 2006. 41. J. J. Kowal, A. Turhan, K. Heller, J. S. Brenizer, and M. M. Mench, “Liquid Water Storage, Distribution, and Removal from Diffusion Media in PEFCs,” J. Electrochem. Soc., Vol. 153, pp. A1971–A1978, 2006. 42. P. A. Chuang, A. Turhan, A. K. Heller, J. S. Brenizer, T. A. Trabold, and M. M. Mench, in ASME Proceedings of FuelCell2005, Third International Conference on Fuel Cell Science, Engineering and Technology, Paper No. 74051, Ypsilanti, MI, 2005. 43. A. B. Geiger, A. Tsukada, E. Lehmann, P. Vontobel, A. Wokaun, and G. G. Scherer, “In Situ Investigation of Two-Phase Flow Patterns in Flow Fields of PEFC’s using Neutron Radiography,” Fuel Cells, Vol. 2, pp. 92–98, 2002. 44. R. J. Bellows, M. Y. Lin, M. Arif, A. K. Thompson, and D. Jacobson, “Neutron Imaging Technique for In Situ Measurements of water Transport Gradients with Nafion in Polymer Electrolyte Fuel Cells,” J. Electrochem. Soc., Vol. 146, pp. 1099–1103, 1999. 45. R. Satija, D. L. Jacobson, M. Arif, and S. A. Werner, “In Situ Neutron Imaging Technique for Evaluation of Water Management Systems in Operating PEM Fuel Cells,” J. Power Sources, Vol. 129, pp. 238–245, 2005. 46. A. Turhan, A. K. Heller, J. S. Brenizer, and M. M. Mench, “Quantification of Liquid Water Accumulation and Distribution in a Polymer Electrolyte Fuel Cell Using Neutron Imaging,” J. Power Sources, Vol. 160, pp. 1195–1203, 2006.

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Fuel Cell Engines Matthew M. Mench

A

Copyright © 2008 by John Wiley & Sons, Inc.

Appendix Some selected journals which publish fuel cell articles: Applied Catalysis A- General Catalysis Today Chemical Reviews Electrochimica Acta Electrochemical and Solid State Letters Electrochemistry Electrochemistry Communications Fuel Cells International Journal of Heat and Mass Transfer International Journal of Hydrogen Energy Journal of Applied Electrochemistry Journal of Catalysts Journal of Electroanalytical Chemistry Journal of Fuel Cell Science and Technology Journal of New Materials for Electrochemical Systems Journal of Physical Chemistry B Journal of Power Sources Journal of the American Ceramic Society Journal of the Electrochemical Society Journal of Materials Science Journal of Membrane Science Solid State Ionics Some selected general interest Websites: http://www.fuelcells.org/ Regularly updated fuel cell information site http://www.cafcp.org/ California fuel cell vehicle partnership site http://www.sae.org/fuelcells/fuelcells.htm American Society of Automotive Engineers Fuel Cell site http://www.hfcletter.com/ Hydrogen and fuel cell letter http://www.fuelcelltoday.com/ Regularly updated fuel cell information site

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Appendix

http://www.fuelcellsworks.com/ Regularly updated fuel cell information site http://www.fuelcelleurope.org/ European fuel cell information site http://www.eere.energy.gov/hydrogenandfuelcells/ U.S. Department of Energy, Energy Efficiency and Renewables program information site http://www.fossil.energy.gov/programs/powersystems/fuelcells/ U.S. Department of Energy, fuel cells program information site http://www.hydrogenassociation.org/general/fuelingSearch.asp National Hydrogen association site http://webbook.nist.gov/chemistry/ National Institute of Standards and Technology site for thermofluidic property data. http://www.convertit.com/ Units conversion calculator

Table A.1

Critical Properties of Selected Fuel Cell Gases

Specie Air Carbon Dioxide, CO2 Carbon Monoxide, CO Ethanol, C2 H5 OH Hydrogen, H2 Methanol, CH3 OH Nitrogen, N2 Oxygen, O2 Water, H2 O

Critical Pressure (kPa)

Critical Temperature (K)

37,700 73,900 35,000 63,800 13,000 79,600 33,900 50,500 220,900

133 304 133 516 33.2 513 126 154 647.3

Source: Adapted from M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 3rd Edition, Wiley, New York, 1995.

Table A.2 Heats of Formation, Gibbs Heat of Formation, and Absolute Entropy of Selected Species at STP Conditions (298 K and 1 atm) Specie Carbon Dioxide, CO2 Carbon Monoxide, CO Ethanol, C2 H5 OHg Ethanol, C2 H5 OH1 Hydrogen, H2 Methane, CH4g Methanol, CH3 OHg Methanol, CH3 OH1 Nitrogen, N2 Oxygen, O2 Water, H2 Og Water, H2 O1

h¯ of (kJ/kmol)

g¯ of (kJ/kmol)

s¯ o (kJ/kmol K)

−393,520 −110,530 −235,310 −277,690 0 −74,850 −200,890 −238,810 0 0 −241,820 −285,830

−394,380 −137,150 −168,570 174,890 0 −50,790 −162,140 −166,290 0 0 −228,590 −237,180

213.69 197.54 282.59 160.70 130.57 186.16 239.70 126.80 191.50 205.03 188.72 69.95

Source: Adapted from M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 3rd Edition, Wiley, New York, 1995.

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Appendix Table A.3

487

Ideal Gas Properties of Air a h

pr

u

vr

so

200 210 220 230 240

199.97 209.97 219.97 230.02 240.02

0.3363 0.3987 0.4690 0.5477 0.6355

142.56 149.69 156.82 164.00 171.13

1707. 1512. 1346. 1205. 1084.

1.29559 1.34444 1.39105 1.43557 1.47824

250 260 270 280 285

250.05 260.09 270.11 280.13 285.14

0.7329 0.8405 0.9590 1.0889 1.1584

178.28 185.45 192.60 199.75 203.33

979. 887.8 808.0 738.0 706.1

1.51917 1.55848 1.59634 1.63279 1.65055

290 295 300 305 310

290.16 295.17 300.19 305.22 310.24

1.2311 1.3068 1.3860 1.4686 1.5546

206.91 210.49 214.07 217.67 221.25

676.1 647.9 621.2 596.0 572.3

1.66802 1.68515 1.70203 1.71865 1.73498

315 320 325 330 340

315.27 320.29 325.31 330.34 340.42

1.6442 1.7375 1.8345 1.9352 2.149

224.85 228.42 232.02 235.61 242.82

549.8 528.6 508.4 489.4 454.1

1.75106 1.76690 1.78249 1.79783 1.82790

350 360 370 380 390

350.49 360.58 370.67 380.77 390.88

2.379 2.626 2.892 3.176 3.481

250.02 257.24 264.46 271.69 278.93

422.2 393.4 367.2 343.4 321.5

1.85708 1.88543 1.91313 1.94001 1.96633

400 410 420 430 440

400.98 411.12 421.26 431.43 441.61

3.806 4.153 4.522 4.915 5.332

286.16 293.43 300.69 307.99 315.30

301.6 283.3 266.6 251.1 236.8

1.99194 2.01699 2.04142 2.06533 2.08870

450 460 470 480 490

451.80 462.02 472.24 482.49 492.74

5.775 6.245 6.742 7.268 7.824

322.62 329.97 337.32 344.70 352.08

223.6 211.4 200.1 189.5 179.7

2.11161 2.13407 2.15604 2.17760 2.19876

500 510 520 530 540

503.02 513.32 523.63 533.98 544.35

8.411 9.031 9.684 10.37 11.10

359.49 366.92 374.36 381.84 389.34

170.6 162.1 154.1 146.7 139.7

2.21952 2.23993 2.25997 2.27967 2.29906

T

(Continued)

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Appendix Table A.3

(Continued) h

pr

u

vr

so

550 560 570 580 590

554.74 565.17 575.59 586.04 596.52

11.86 12.66 13.50 14.38 15.31

396.86 404.42 411.97 419.55 427.15

133.1 127.0 121.2 115.7 110.6

2.31809 2.33685 2.35531 2.37348 2.39140

600 610 620 630 640

607.02 617.53 628.07 638.63 649.22

16.28 17.30 18.36 19.84 20.64

434.78 442.42 450.09 457.78 465.50

105.8 101.2 96.92 92.84 88.99

2.40902 2.42644 2.44356 2.46048 2.47716

650 660 670 680 690

659.84 670.47 681.14 691.82 702.52

21.86 23.13 24.46 25.85 27.29

473.25 481.01 488.81 496.62 504.45

85.34 81.89 78.61 75.50 72.56

2.49364 2.50985 2.52589 2.54175 2.55731

700 710 720 730 740

713.27 724.04 734.82 745.62 756.44

28.80 30.38 32.02 33.72 35.50

512.33 520.23 528.14 536.07 544.02

69.76 67.07 64.53 62.13 59.82

2.57277 2.58810 2.60319 2.61803 2.63280

750 760 770 780 790

767.29 778.18 789.11 800.03 810.99

37.35 39.27 41.31 43.35 45.55

551.99 560.01 568.07 576.12 584.21

57.63 55.54 53.39 51.64 49.86

2.64737 2.66176 2.67595 2.69013 2.70400

800 820 840 860 880

821.95 843.98 866.08 888.27 910.56

47.75 52.59 57.60 63.09 68.98

592.30 608.59 624.95 641.40 657.95

48.08 44.84 41.85 39.12 36.61

2.71787 2.74504 2.77170 2.79783 2.82344

900 920 940 960 980

932.93 955.38 977.92 1000.55 1023.25

75.29 82.05 89.28 97.00 105.2

674.58 691.28 708.08 725.02 741.98

34.31 32.18 30.22 28.40 26.73

2.84856 2.87324 2.89748 2.92128 2.94468

1000

1046.04

114.0

758.94

25.17

2.96770

T

aT

so

(K), h and u (kJ/kg), (kJ/kg·K). Source: Adapted from K. Wark, Thermodynamics, 4th ed., McGraw-Hill, New York, 1983, as based on J. H. Keenan and J. Kaye, Gas Tables, Wiley, New York, 1945.

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Appendix Table A.4

489

Ideal Gas Properties of Carbon Dioxide (CO2 )a h¯

u¯

s¯ o

0 220 230 240 250

0 6,601 6,938 7,280 7,627

0 4,772 5,026 5,285 5,548

0 202.966 204.464 205.920 207.337

260 270 280 290 298

7,979 8,335 8,697 9,063 9,364

5,817 6,091 6,369 6,651 6,885

208.717 210.062 211.376 212.660 213.685

300 310 320 330 340

9,431 9,807 10,186 10,570 10,959

6,939 7,230 7,526 7,826 8,131

213.915 215.146 216.351 217.534 218.694

350 360 370 380 390

11,351 11,748 12,148 12,552 12,960

8,439 8,752 9,068 9,392 9,718

219.831 220.948 222.044 223.122 224.182

400 410 420 430 440

13,372 13,787 14,206 14,628 15,054

10,046 10,378 10,714 11,053 11,393

225.225 226.250 227.258 228.252 229.230

450 460 470 480 490

15,483 15,916 16,351 16,791 17,232

11,742 12,091 12,444 12,800 13,158

230.194 231.144 232.080 233.004 233.916

500 510 520 530 540

17,678 18,126 18,576 19,029 19,485

13,521 13,885 14,253 14,622 14,996

234.814 235.700 236.575 237.439 238.292

550 560 570 580 590

19,945 20,407 20,870 21,337 21,807

15,372 15,751 16,131 16,515 16,902

239.135 239.962 240.789 241.602 242.405

T

(Continued)

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Appendix Table A.4

(Continued) h¯

u¯

s¯ o

600 610 620 630 640

22,280 22,754 23,231 23,709 24,190

17,291 17,683 18,076 18,471 18,869

243.199 243.983 244.758 245.524 246.282

650 660 670 680 690

24,674 25,160 25,648 26,138 26,631

19,270 19,672 20,078 20,484 20,894

247.032 247.773 248.507 249.233 249.952

700 710 720 730 740

27,125 27,622 28,121 28,622 29,124

21,305 21,719 22,134 22,552 22,972

250.663 251.368 252.065 252.755 253.439

750 760 770 780 790

29,629 30,135 30,644 31,154 31,665

23,393 23,817 24,242 24,669 25,097

254.117 254.787 255.452 256.110 256.762

800 810 820 830 840

32,179 32,694 33,212 33,730 34,251

25,527 25,959 26,394 26,829 27,267

257.408 258.048 258.682 259.311 259.934

850 860 870 880 890

34,773 35,296 35,821 36,347 36,876

27,706 28,125 28,588 29,031 29,476

260.551 261.164 261.770 262.371 262.968

900 910 920 930 940

37,405 37,935 38,467 39,000 39,535

29,922 30,369 30,818 31,268 31,719

263.559 264.146 264.728 265.304 265.877

950 960 970 980 990

40,070 40,607 41,145 41,685 42,226

32,171 32,625 33,081 33,537 33,995

266.444 267.007 267.566 268.119 268.670

1000

42,769

34,455

269.015

T

(K), h¯ and u¯ (kJ/kmol), s¯ o (kJ/kmol·K), h¯ ◦f = −393,520 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

aT

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Appendix Table A.5

491

Ideal Gas Properties of Carbon Monoxide (CO)a h¯

u¯

s¯ o

0 220 230 240 250

0 6,391 6,683 6,975 7,266

0 4,562 4,771 4,979 5,188

0 188.683 189.980 191.221 192.411

260 270 280 290 298

7,558 7,849 8,140 8,432 8,669

5,396 5,604 5,812 6,020 6,190

193.554 194.654 195.173 196.735 197.543

300 310 320 330 340

8,723 9,014 9,306 9,597 9,889

6,229 6,437 6,645 6,854 7,062

197.723 198.678 199.603 200.500 201.371

350 360 370 380 390

10,181 10,473 10,765 11,058 11,351

7,271 7,480 7,689 7,899 8,108

202.217 203.040 203.842 204.622 205.383

400 410 420 430 440

11,644 11,938 12,232 12,526 12,821

8,319 8,529 8,740 8,951 9,163

206.125 206.850 207.549 208.252 208.929

450 460 470 480 490

13,116 13,412 13,708 14,005 14,302

9,375 9,587 9,800 10,014 10,228

209.593 210.243 210.880 211.504 212.117

500 510 520 530 540

14,600 14,898 15,197 15,497 15,797

10,443 10,658 10,874 11,090 11,307

212.719 213.310 213.890 214.460 215.020

550 560 570 580 590

16,097 16,399 16,701 17,003 17,307

11,524 11,743 11,961 12,181 12,401

215.572 216.115 216.649 217.175 217.693

T

(Continued)

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Char Count=

Appendix Table A.5

(Continued) h¯

u¯

s¯ o

600 610 620 630 640

17,611 17,915 18,221 18,527 18,833

12,622 12,843 13,066 13,289 13,512

218.204 218.708 219.205 219.695 220.179

650 660 670 680 690

19,141 19,449 19,758 20,068 20,378

13,736 13,962 14,187 14,414 14,641

220.656 221.127 221.592 222.052 222.505

700 710 720 730 740

20,690 21,002 21,315 21,628 21,943

14,870 15,099 15,328 15,558 15,789

222.953 223.396 223.833 224.265 224.692

750 760 770 780 790

22,258 22,573 22,890 23,208 23,526

16,022 16,255 16,488 16,723 16,957

225.115 225.533 225.947 226.357 226.762

800 810 820 830 840

23,844 24,164 24,483 24,803 25,124

17,193 17,429 17,665 17,902 18,140

227.162 227.559 227.952 228.339 228.724

850 860 870 880 890

25,446 25,768 26,091 26,415 26,740

18,379 18,617 18,858 19,099 19,341

229.106 229.482 229.856 230.227 230.593

900 910 920 930 940

27,066 27,392 27,719 28,046 28,375

19,583 19,826 20,070 20,314 20,559

230.957 231.317 231.674 232.028 232.379

950 960 970 980 990

28,703 29,033 29,362 29,693 30,024

20,805 21,051 21,298 21,545 21,793

232.727 233.072 233.413 233.752 234.088

1000

30,355

22,041

234.421

T

(K), h¯ and u¯ (kJ/kmol), s¯ o (kJ/kmol·K), h¯ ◦f = −110,530 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

aT

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Appendix Table A.6

493

Ideal Gas Properties of Hydrogen (H2 ) a h¯

u¯

s¯ o

0 260 270 280 290

0 7,370 7,657 7,945 8,233

0 5,209 5,412 5,617 5,822

0 126.636 127.719 128.765 129.775

298 300 320 340 360

8,468 8,522 9,100 9,680 10,262

5,989 6,027 6,440 6,853 7,268

130.574 130.754 132.621 134.378 136.039

380 400 420 440 460

10,843 11,426 12,010 12,594 13,179

7,684 8,100 8,518 8,936 9,355

137.612 139.106 140.529 141.888 143.187

480 500 520 560 600

13,764 14,350 14,935 16,107 17,280

9,773 10,193 10,611 11,451 12,291

144.432 145.628 146.775 148.945 150.968

640 680 720 760 800

18,453 19,630 20,807 21,988 23,171

13,133 13,976 14,821 15,669 16,520

152.863 154.645 156.328 157.923 159.440

840 880 920 960 1000

24,359 25,551 26,747 27,948 29,154

17,375 18,235 19,098 19,966 20,839

160.891 162.277 163.607 164.884 166.114

T

(K), h¯ and u¯ (kJ/kmol), s¯ o (kJ/kmol·K), h¯ ◦f = 0 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

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Appendix Table A.7

Ideal Gas Properties of Oxygen (O2 ) a h¯

u¯

s¯ o

0 220 230 240 250

0 6,404 6,694 6,984 7,275

0 4,575 4,782 4,989 5,197

0 196.171 197.461 198.696 199.885

260 270 280 290 298

7,566 7,858 8,150 8,443 8,682

5,405 5,613 5,822 6,032 6,203

201.027 202.128 203.191 204.218 205.033

300 310 320 330 340

8,736 9,030 9,325 9,620 9,916

6,242 6,453 6,664 6,877 7,090

205.213 206.177 207.122 208.020 208.904

350 360 370 380 390

10,213 10,511 10,809 11,109 11,409

7,303 7,518 7,733 7,949 8,166

209.765 210,604 211.423 212.222 213.002

400 410 420 430 440

11,711 12,012 12,314 12,618 12,923

8,384 8,603 8,822 9,043 9,264

213.765 214.510 215.241 215.955 216.656

450 460 470 480 490

13,228 13,535 13,842 14,151 14,460

9,487 9,710 9,935 10,160 10,386

217.342 218.016 218.676 219.326 219.963

500 510 520 530 540

14,770 15,082 15,395 15,708 16,022

10,614 10,842 11,071 11,301 11,533

220.589 221.206 221.812 222.409 222.997

550 560 570 580 590

16,338 16,654 16,971 17,290 17,609

11,765 11,998 12,232 12,467 12,703

223.576 224.146 224.708 225.262 2250.808

T

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Appendix Table A.7

495

(Continued) h¯

u¯

s¯ o

600 610 620 630 640

17,929 18,250 18,572 18,895 19,219

12,940 13,178 13,417 13,657 13,898

226.346 226.877 227.400 227.918 228.429

650 660 670 680 690

19,544 19,870 20,197 20,524 20,854

14,140 14,383 14,626 14,871 15,116

228.932 229.430 229.920 230.405 230.885

700 710 720 730 740

21,184 21,514 21,845 22,177 22,510

15,364 15,611 15,859 16,107 16,357

231.358 231.827 232.291 232.748 233.201

750 760 770 780 790

22,844 23,178 23,513 23,850 24,186

16,607 16,859 17,111 17,364 17,618

233.649 234.091 234.528 234.960 235.387

800 810 820 830 840

24,523 24,861 25,199 25,537 25,877

17,872 18,126 18,382 18,637 18,893

235.810 236.230 236.644 237.055 237.462

850 860 870 880 890

26,218 26,559 26,899 27,242 27,584

19,150 19,408 19,666 19,925 20,185

237.864 238.264 238.660 239.051 239.439

900 910 920 930 940

27,928 28,272 28,616 28,960 29,306

20,445 20,706 20,967 21,228 21,491

239.823 240.203 240.580 240.953 241.323

950 960 970 980 990

29,652 29,999 30,345 30,692 31,041

21,754 22,017 22,280 22,544 22,809

241.689 242.052 242.411 242.768 243.120

1000

31,339

23,075

243.471

T

(K), h¯ and u¯ (kJ/kmol), s¯ ◦ (kJ/kmol·K), h¯ ◦f = 0 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

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Appendix Table A.8

Ideal Gas Properties of Water Vapor (H2 O) a h¯

u¯

s¯ o

0 220 230 240 250

0 7,295 7,628 7,961 8,294

0 5,466 5,715 5,965 6,215

0 178.576 180.054 181.471 182.831

260 270 280 290 298

8,627 8,961 9,296 9,631 9,904

6,466 6,716 6,968 7,219 7,425

184.139 185.399 186.616 187.791 188.720

300 310 320 330 340

9,966 10,302 10,639 10,976 11,314

7,472 7,725 7,978 8,232 8,487

188.928 190.030 191.098 192.136 193.144

350 360 370 380 390

11,652 11,992 12,331 12,672 13,014

8,742 8,998 9,255 9,513 9,771

194.125 195.081 196.012 196.920 197.807

400 410 420 430 440

13,356 13,699 14,043 14,388 14,734

10,030 10,290 10,551 10,813 11,075

198.673 199.521 200.350 201.160 201.955

450 460 470 480 490

15,080 15,428 15,777 16,126 16,477

11,339 11,603 11,869 12,135 12,403

202.734 203.497 204.247 204.982 205.705

500 510 520 530 540

16,828 17,181 17,534 17,889 18,245

12,671 12,940 13,211 13,482 13,755

206.413 207.112 207.799 208.475 209.139

550 560 570 580 590

18,601 18,959 19,318 19,678 20,039

14,028 14,303 14,579 14,856 15,134

209.795 210.440 211.075 211.702 212.320

T

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Appendix Table A.8

497

(Continued) h¯

u¯

s¯ o

600 610 620 630 640

20,402 20,765 21,130 21,495 21,862

15,413 15,693 15,975 16,257 16,541

212.920 213.529 214.122 214.707 215.285

650 660 670 680 690

22,230 22,600 22,970 23,342 23,714

16,826 17,112 17,399 17,688 17,978

215.856 216.419 216.976 217.527 218.071

700 710 720 730 740

24,088 24,464 24,840 25,218 25,597

18,268 18,561 18,854 19,148 19,444

218.610 219.142 219.668 220.189 220.707

750 760 770 780 790

25,977 26,358 26,741 27,125 27,510

19,741 20,039 20,339 20,639 20,941

221.215 221.720 222.221 222.717 223.207

800 810 820 830 840

27,896 28,284 28,672 29,062 29,454

21,245 21,549 21,855 22,162 22,470

223.693 224.174 224.651 225.123 225.592

850 860 870 880 890

29,846 30,240 30,635 31,032 31,429

22,779 23,090 23,402 23,715 24,029

226.057 226.517 226.973 227.426 227.875

900 910 920 930 940

31,828 32,228 32,629 33,032 33,436

24,345 24,662 24,980 25,300 25,621

228.321 228.763 229.202 229.637 230.070

950 960 970 980 990

33,841 34,247 34,653 35,061 35,472

25,943 26,265 26,588 26,913 27,240

230.499 230.924 231.347 231.767 232.184

T

(K), h¯ and u¯ (kJ/kmol), s¯ o (kJ/kmol·K), h¯ ◦f = −241,820 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

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Appendix Table A.9

Ideal Gas Properties of Nitrogen (N2 ) a h¯

u¯

s¯ o

0 220 230 240 250

0 6,391 6,683 6,975 7,266

0 4,562 4,770 4,979 5,188

0 182.639 183.938 185.180 186.370

260 270 280 290 298

7,558 7,849 8,141 8,432 8,669

5,396 5,604 5,813 6,021 6,190

187.514 188.614 189.673 190.695 191.502

300 310 320 330 340

8,723 9,014 9,306 9,597 9,888

6,229 6,437 6,645 6,853 7,061

191.682 192.638 193.562 194.459 195.328

350 360 370 380 390

10,180 10,471 10,763 11,055 11,347

7,270 7,478 7,687 7,895 8,104

196.173 196.995 197.794 198.572 199.331

400 410 420 430 440

11,640 11,932 12,225 12,518 12,811

8,314 8,523 8,733 8,943 9,153

200.071 200.794 201.499 202.189 202.863

450 460 470 480 490

13,105 13,399 13,693 13,988 14,285

9,363 9,574 9,786 9,997 10,210

203.523 204.170 204.803 205.424 206.033

500 510 520 530 540

14,581 14,876 15,172 15,469 15,766

10,423 10,635 10,848 11,062 11,277

206.630 207.216 207.792 208.358 208.914

550 560 570 580 590

16,064 16,363 16,662 16,962 17,262

11,492 11,707 11,923 12,139 12,356

209.461 209.999 210.528 211.049 211.562

T

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Appendix Table A.9

499

(Continued) h¯

u¯

s¯ o

600 610 620 630 640

17,563 17,864 18,166 18,468 18,772

12,574 12,792 13,011 13,230 13,450

212.066 212.564 213.055 213.541 214.018

650 660 670 680 690

19,075 19,380 19,685 19,991 20,297

13,671 13,892 14,114 14,337 14,560

214.489 214.954 215.413 215.866 216.314

700 710 720 730 740

20,604 20,912 21,220 21,529 21,839

14,784 15,008 15,234 15,460 15,686

216.756 217.192 217.624 218.059 218.472

750 760 770 780 790

22,149 22,460 22,772 23,085 23,398

15,913 16,141 16,370 16,599 16,830

218.889 219.301 219.709 220.113 220.512

800 810 820 830 840

23,714 24,027 24,342 24,658 24,974

17,061 17,292 17,524 17,757 17,990

220.907 221.298 221.684 222.067 222.447

850 860 870 880 890

25,292 25,610 25,928 26,248 26,568

18,224 18,459 18,695 18,931 19,168

222.822 223.194 223.562 223.927 224.288

900 910 920 930 940

26,890 27,210 27,532 27,854 28,178

19,407 19,644 19,883 20,122 20,362

224.647 225.002 225.353 225.701 226.047

950 960 970 980 990

28,501 28,826 29,151 29,476 29,803

20,603 20,844 21,086 21,328 21,571

226.389 226.728 227,064 227.398 227.728

1000

30,129

21,815

228.057

T

(K), h¯ and u¯ (kJ/kmol), s¯ ◦ (kJ/kmol·K), h¯ f = 0 kJ/kmol Source: Adapted from K. Wark, Thermodynamics, 4th Edition, McGraw-Hill, New York, 1983, as based on the JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.

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Appendix Table A.10 Saturated Water Vapor Temperature Tablea Temperature (◦ C) −40 −35 −30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

Saturation Pressure (kPa) 0.0128 0.0223 0.0379 0.0632 0.1031 0.1650 0.2595 0.4011 0.6102 0.87 1.23 1.71 2.34 3.17 4.25 5.63 7.39 9.60 12.36 15.77 19.96 25.05 31.21 38.61 47.43 57.89 70.21 84.64 101.45 120.94 143.43 169.24 198.74 232.31 270.36 313.32 361.64 415.80 476.29

below 0◦ C are based on the Goff–Gratch equation to correlate for saturation vapor pressure over ice [1, 2]:

a Data

log10 (10 · Psat ) = −9.09718(273.16/T − 1) − 3.56654 log10 (273.16/T ) +0.876793(1 − T /273.16) + log10 (6.1071) where T is in Kelvin and Psat is in kPa, and the equation is valid from −100 to 0◦ C. Source: Data at 0–150◦ C from E.W. Lemmon, M.O. McLinden and D.G. Friend, “Thermophysical Properties of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg MD, 20899 (http://webbook.nist. gov).

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References Table A.11

501

Surface Tension of Water in Contact with Air

Temperature (◦ C)

Surface Tension (N/m)

0 5 10 20 30 40 50 60 70

7.56 × 10−2 7.49 × 10−2 7.42 × 10−2 7.28 × 10−2 7.12 × 10−2 6.96 × 10−2 6.79 × 10−2 6.62 × 10−2 6.44 × 10−2

Source: International Association for the Properties of Water Steam, Viscosity of Thermal Conductivity of Heavy Water Substance in Physical Chemistry of Aqueous Systems: Proceedings of the 12th International Conference on the Properties of Water and Steam, Orlando, FL, 1994, al07–al38.

Other Useful Relations: Saturation pressure of vapor over liquid water [3]: ln Psat = −34.625 + 0.258T − 4.8419 × 10−4 T 2 + 3.3282 × 10−7 T 3 where T is in Kelvin, and Psat is in Pa.

REFERENCES 1. J. A. Goff and S. Gratch, “ Low-Pressure Properties of Water from −160 to 212 ◦ F,” in Transactions of the American Society of Heating and Ventilating Engineers, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, pp. 95–122, 1946. 2. J. A. Goff, “Saturation Pressure of Water on the New Kelvin Temperature Scale, Transactions of the American Society of Heating and Ventilating Engineers, presented at the semi-annual meeting of the American Society of Heating and Ventilating Engineers, Murray Bay, Que. Canada, pp. 347–354, 1957. 3. J. M. Prausnitz, R. C. Reid, and T. K. Sherwood, The Properties of Gases and Liquids, – 3, McGraw-Hill, New York, 1997.

Matthew M Mench Copyright

2008 by Iohn Wiley & Sons, Inc

Index a, see Roughness factor Activation polarization losses, 126–132 and Butler–Volmer (BV) kinetic model, 132–154 and electrical double layer, 126–127 factors influencing, 128–129 Active humidification, 296–297 AFCs, see Alkaline fuel cells Age of fuel cell, and activation polarization losses, 129 Alkaline fuel cells (AFCs), 9, 10, 16, 17, 23, 410–418 advantages of, 417 conductivity of, 159 disadvantages of, 417–418 electrode materials in, 417 electrolyte system in, 413–416 gas-phase flow in, 219–220 operating conditions for, 411–413 stack configuration in, 416–417 α, see Charge transfer coefficient αd , see Net drag coefficient Aluminum, commercial production of, 30 Ammonia, hydrogen generation from, 443 Amp`ere, Andr´e-Marie, 36 Ampere (unit), 36 Ampere-hour (Ah), 37 Anions, 31 Annular mist flow regime, 240–244 Anode, 31, 32, 35 Anode kinetics, in direct methanol fuel cells, 349–350 Anode side, microporous layer on, 323 Anodic stoichiometry, 49 Apollo space program, 412 Area specific resistance (ASR), 209 Asahi Glass Co., Ltd., 196 ASR (area specific resistance), 209 Assembly, cell, 164–166 Asymmetric channel properties, 330–331 Atomic-level energy storage, 70 ATR (autothermal reformation), 441

Automotive fuel cells, 346, 453 Autothermal reformation (ATR), 441 Bacon, Sir Francis, 23, 411, 412, 417 Ballard Power Systems, Inc., 11, 20 Batteries, 30 fuel cells vs., 5–6 metal air, 418 nickel metal hydride, 434 Beginning of life (BOL) performance, 356 β, see Symmetry factor Biofuel cells, 418 Biological hydrogen production, 442–443 Bipolar plate, 51, 294 BMW, 381 Boiling, evaporation vs., 95 BOL (beginning of life) performance, 356 Boltzmann’s constant, 85, 226 Broers, G. H. J., 392 Bruggeman correlation, 218–220 Bubble flow regime, 240, 243, 244 Bubbling pressure, 262 Bulk diffusion, 211 Burns, Larry, 191 Butler–Volmer (BV) kinetic model, 132–154 charge transfer coefficient in, 137–140 exchange current density in, 140–141 fundamental assumption of, 133 roughness factor in, 141–143 simplified equations, 141–154 symmetry factor in, 134–137 Calcium hydride, 434 Canada, fuel-cell-related patents in, 1, 2 Capillary condensation, 262–263 Capillary pressure, 251–254 Capillary transport in fuel cell diffusion media, 251–263 and capillary pressure, 251–254 Leverett approach, 254–257 microporous layer, effect of, 257–258 modified Leverett approach, 255–256 PEFC, local saturation in diffusion media of, 259–260

503

504

Index

Carbide-derived carbons (CDCs), 438 Carbon dioxide, 17, 350, 396, 413, 439 Carbon monoxide, 359, 361–362, 383–384, 406, 439 Carbon storage (of hydrogen), 437–438 Carman–Kozeny equation, 249 Carnot cycle, 29 Carroll, Eugene, 29 Catalyst layer (H2 PEFC), 288–290 Caterpillar, 392 Cathode, 31, 32, 35 Cathode side, microporous layer on, 321–323 Cathodic stoichiometry, 49 Cations, 31 CDCs (carbide-derived carbons), 438 Cell interconnect, 51 Ceramic electrolytes, ion transport in, 202–205 Ceramic Fuel Cells Unlimited, 381 Ceria, doped, 382 Channels: multiphase flow in, 239–244 single-phase flow in, 233–239 and consumption of reactant, 238–239 and frictional losses, 234–238 and pressure drop, 233–234 Charge, 36–37 conservation of, 33–35 and current, 37 Charge transfer coefficient (α), 137–140 Chemical hydrides, 433–434 Chemical hydrogen production, 439–441 Chemical reactions, electrochemical vs., 29–31 Chilingarian, G. V., 219 CHP systems, see Combined heat and power systems Cogeneration, for fuel cells, 278–279 Cold combustion, 393n.2 Colebrook, C. F., 237–238 Combined heat and power (CHP) systems, 274, 381 Compressed hydrogen, 428–431 Concentration polarization, 168–175 cause of, 168 determination of, 173–174, 466–467 and effects of change in oxygen concentration, 170–171 and flow stoichiometry, 174–175 and mass-limiting current density, 171–173 and restriction of rate of transport to electrode, 168–169

Condensation: capillary, 262–263 and evaporation, 95–96 Conductance (G), 40–41, 158 Conduction, heat transfer by, 264–267 Conductivity (σ ), 158 defined, 41 dependence of, on operational parameters, 41–42 and ion transport, 195 Constant-pressure specific heat (c p ), 71 Constant-volume specific heat (cv ), 71 Contact angle, as multiphase flow parameter, 246, 247 Contact resistance, 161–163 Control volume, thermodynamic, 6 Convection: heat transfer by, 267–272 as mechanism of ion transport, 192–193 Coolants, 274–275, 359 Cooling: evaporative, 95–96 liquid, 295–296 Copper sheets, production of, 31 Corrosion, separator plate, 397 Coulomb, Charles Augustin, 36 Coulomb (unit), 36–37 c p (constant-pressure specific heat), 71 Crossover losses, 176–181 Cryogenic liquid hydrogen, 431–433, 444–445 Current, 31, 32, 34 defined, 36 distribution of, in PEFC, 364–368, 469–470 flow of, 35–36 Current collector, 51 Current flow, and ion transport, 191 Current-interrupt method, 466 CV, see Cyclic voltammetry cv (constant-volume specific heat), 71 Cyclic voltammetry (CV), 458–461 DAFCs, see Direct alcohol fuel cells Darcy’s law, 249, 259, 333 Decal method (catalyst layer manufacturing technique), 290 Degradation, PEFC, 356–362 chemical modes of, 359–362 and carbon monoxide poisoning, 361–362 irreversible, 360–361 reversible, 359 measurements of, 478

Index physical modes of, 356–359 irreversible, 357–359 reversible, 356–357 Delphi (company), 381 DHE (dynamic hydrogen electrode), 458 Diagnostic tools, 453–479 degradation measurements, 478 distributed diagnostics, 469–474 current distribution measurement, 469–470 impedance distribution measurement, 473–474 species distribution measurement, 470–472 temperature distribution measurement, 473 electrochemical methods, 454–469 concentration polarization, determination of, 466–467 fuel crossover, determination of, 467–469 kinetic parameters and polarization, determination of, 454–465 ohmic parameters and polarization, determination of, 465–466 in situ measurement and visualization, 474–478 alternative techniques, 476, 478 direct visualization techniques, 474–477 Diffusion: bulk, 211 of hydrogen and oxygen in water vapor, 216–218 multicomponent approaches to, 215–216 surface, 233 Diffusion coefficient, 211–214 Diffusion medium (DM) layer, 7, 55, 286, 288, 290–293 Dimethoxymethane (DMM), 341–342, 355 Dimethyl ether (DME), 341–342, 352–354 Dimethyl oxalate (DMO), 341–342, 355–356 DIR (direct internal reformation), 396 Direct alcohol fuel cells (DAFCs), 17, 339–356, 438. See also Direct methanol fuel cells (DMFCs) dimethoxymethane/trimethoxymethane in, 355 dimethyl ether in, 352–354 dimethyl oxalate in, 355–356 drawbacks of, 340 ethanol in, 355 ethylene glycol in, 356 formaldehyde in, 352 formic acid in, 352

505

non-hydrogen fuels for (table), 341–342 trends in, 351 trioxane in, 355 Direct FuelCell, 392 Direct internal reformation (DIR), 396 Direct methanol fuel cells (DMFCs), 11, 13, 19, 343–351 advantages of, 344 anode kinetics in, 349–350 carbon dioxide blockage/removal in, 350 global electrochemical reactions for, 343 methanol crossover in, 348–349 safety issues, 351 technical issues with, 344 water management in, 345–348 Direct visualization tools, 474–477 Distributed diagnostics, 469–474 current distribution measurement, 469–470 impedance distribution measurement, 473–474 species distribution measurement, 470–472 temperature distribution measurement, 473 Dittus–Boelter equation, 272 DME, see Dimethyl ether DMFCs, see Direct methanol fuel cells DM layer, see Diffusion medium layer DMM, see Dimethoxymethane DMO, see Dimethyl oxalate DOE, see U.S. Department of Energy Doped ceria, 382 Dow, H. H., 30 Dow Chemical, 196 Drag, electro-osmotic, 312–314 Drainage, 261–262 Dryout, 357 Durability: of molten carbonate fuel cells, 396–397 of phosphoric acid fuel cells, 408–409 of polymer electrolyte fuel cells, see Degradation, PEFC of solid oxide fuel cells, 390–391 Dynamic hydrogen electrode (DHE), 458 E ◦ , see Maximum expected voltage E ◦◦ , see Thermal voltage E. I. DuPont de Nemours and Company, 196 The Economist, 380 ECS (Electrochemical Society), 30 ECSA, see Electrochemically active surface area Edison, Thomas, 30 Efficiency, Faradic, 48–49

506

Index

Efficiency, thermodynamic, 96–106 calculation example, 102–106 of CHP systems, 274 and heating value, 102 and LeChatelier’s principle, 101–102 and maximum electrical work for reversible process, 96–97 and maximum expected voltage, 97 and temperature change, 100–101 and thermal voltage, 97–99 EG, see Ethylene glycol EIS, see Electrochemical impedance spectroscopy Electrical double layer, 126–127 Electrical power, 42–43 Electrical shorts, polarization losses due to, 175–176 Electrochemical diagnostic methods, 454–469 concentration polarization, determination of, 466–467 fuel crossover, determination of, 467–469 gas-phase fuel crossover, 468 liquid fuel crossover, 469 kinetic parameters and polarization, determination of, 454–465 cyclic voltammetry, 458–461 electrochemical active surface area, 462–463 electrochemical impedance spectroscopy, 454–458 Tafel plots, 463–465 ohmic parameters and polarization, determination of, 465–466 current interrupt, 466 high-frequency resistance, 466 Electrochemical engines, fuel cells as, 3–6 Electrochemical hydrogen production, 441–442 Electrochemical impedance spectroscopy (EIS), 454–458 Electrochemically active surface area (ECSA), 288–289, 462–463 Electrochemical reactions, 29–35 chemical vs., 29–31 components of, 31–32 conservation of charge in, 33–35 Electrochemical Society (ECS), 30 Electrodes: in alkaline fuel cells (AFCs), 417 behavior of individual, 39–40 Electrolysis (for production of hydrogen), 440–442

Electrolyte(s), 32 conductivity/resistivity values for, 159 and limitation of reactant crossover, 177–179 loss of, 360, 397, 407 transport in, see Transport in fuel cell systems Electrolyte fracture, 357–358 Electrolyte system, in alkaline fuel cells, 413–416 Electrolytic reactions, 34, 35 Electron-based economy, 426 Electron transport, 209–210, 325 Electro-osmotic drag, 312–314 Electroplating, 30, 34 Elementary charge transfer step, 137 Energy, internal (U ), 69–70 Engines, 3–4 Enthalpy (H ), 70–71. See also Enthalpy, determination of change in defined, 70 determination of, of a single species, 77–78 sensible, 75 total, 77 Enthalpy, determination of change in: for nonreacting species/mixtures, 78–82 entropy, change in, 88 example, 79 ideal gas mixture, 79–82 for reacting species/mixtures, 83–91 entropy, change in, 84–88 example, 83–84 and Gibbs function, 88–91 Enthalpy of formation, 74–75 defined, 74 table, 98 Entropy: change in: for nonreacting species/mixtures, 88 for reacting species/mixtures, 84–88 as concept, 84–86 and Gibbs function, 88–91 for ideal gas, 86–87 for nonreacting gas mixture, 88 for nonreacting liquids/solids, 87–88 for reacting gas mixture, 88 eq (equivalent electrons), 44 Equilibrium, mechanical vs. thermodynamic, 62 Equivalent electrons (eq), 44 Equivalent weight (EW), 198 Ethanol, 341–342, 355 Ethylene glycol (EG), 341–342, 356 Evaporation, 95–96

Index Evaporative cooling, 95–96 EW (equivalent weight), 198 Exchange current density (i 0 ), 132, 140–141 Expected voltage, maximum, 97 F (Faraday’s constant), 44 Faraday, Michael, 45 Faraday’s constant (F), 44 Faraday’s laws, 45–48, 177, 180 Faradic efficiency, 48–49 FCE, see Fuel Cell Energy Fick’s law, 177, 211, 231 Fick’s second law, 212 Flooding, 243, 299–301, 307, 308, 317–321, 357 Flow, calculation of maximum water uptake in a, 94–95 Flow field design (PEFCs), 325–339 asymmetric channel properties, 330–331 considerations in, 325–326 and direction of flow, 331–332 manifold, 336–339 mesh designs, 330 patterns, 328–329 for portable and automotive applications, 334–336 and reactant bypass, 332–334 trade-offs in, 326–327 Flow work, 70 Ford, William C., Jr., 62 Formaldehyde, 341–342, 352 Formic acid, 341–342, 352 Fourier’s law of heat conduction, 264, 273 Fracture, electrolyte, 357–358 Freeze damage, 406 Frictional losses, for single-phase flow in channels, 234–238 Froth flow regime, 240, 243 Fuel cell(s): advantages of, 2–3 basic operating principles of, 6–7 batteries, 5–6 classification of, 9–17 cogeneration for, 278–279 development of, 23–24 as electrochemical engines, 3–6 generic, 50–56 heat engines vs., 3–5 potential applications/markets for, 17–23 socioeconomic impact of, 24–25 technical limitations of, 3

507

Fuel Cell Energy (FCE), 14, 20, 392 Fuel cell stack(s), 7–9 in alkaline fuel cells (AFCs), 416–417 calculations for, 47–48 heat dissipation from, 274 manifold design for, 336–339 orientation of, and flow direction, 331–332 for portable and automotive applications, 334–336 Fuel-cell vehicles, 121 Fuel crossover, experimental determination of, 467–469 gas-phase fuel crossover, 468 liquid fuel crossover, 469 Fueling, hydrogen, 445–446 Fuji Electric Company, 398 Fuller, T. F., 313 G, see Conductance; Gibbs function Galvanic reactions, 34, 35 Gas channels, multiphase flow in, 239–244 Gas diffusion layer (GDL), 7 Gaskets, degradation of, 360–361 Gas-phase fuel crossover, experimental determination of, 468 Gas-phase mass transport, 210–233 in alkaline fuel cells, 219–220 binary gas-phase diffusion coefficients, calculation of, 214–215 and characteristic times for gas-, liquid-, and solid-state diffusion, 213 and diffusion in general, 210–218 hydrogen and oxygen in water vapor, estimation of diffusivity of, 216–217 interfacial flow between phases, 228–232 mass flux across phase boundary, 229–230 PEFC, mass transfer limiting current density for, 231–232 solid electrolyte, crossover through, 230–231 Knudsen diffusion, 223–226 liquids, diffusion through, 226–227, 321 multicomponent diffusion approaches for, 215–216 polymer electrolyte, diffusion through, 227–228 porous media, 218–223 calculation of gas-phase transport limited current density for, 220–222 factors affecting, 218 surface diffusion, 233

508

Index

Gas-phase specific heat, 71–73 GDL (gas diffusion layer), 7 Gemini space program, 23, 412 General Electric, 23 General Motors, 191, 413 Georgetown University, 11, 399 Gibbs function (G) (Gibbs free energy), 88–91, 96–97 Global hydrogen–oxygen redox reaction, 32–33 Grotthuss mechanism, 198 Grove, Sir William, 23 Grubb, William, 23 H, see Enthalpy H2 PEFCs, see Hydrogen PEFCs Hagen–Pouiseville flow, 237 Hall, C. M., 30 Hall–Heroult process, 30 Handheld entertainment system, 12 Heat, 4–5. See also Specific heat generation of, 263–264 latent, 75–77 Heat engines, fuel cells vs., 3–5 Heat flux, 269, 314 Heating value, 102 Heat of formation, 74–75 Heat transport: as PEFC design consideration, 325 single-phase, 264–275 and conduction, 264–267 and convection, 267–272 and radiation, 273–274 Henry’s law, 229–231 Heroult, P. L., 30 HFR, see High-frequency resistance HHV, see High heating value High-frequency resistance (HFR), 457, 465, 466 High heating value (HHV), 102–104 High-power-density (HPD) design, 387 Hindenburg disaster, 430, 431 Hitachi, 392 HOR, see Hydrogen oxidation reaction Hoses, degradation of, 360–361 HPD (high-power-density) design, 387 Humidification (of H2 PEFC), 295–298 active, 296–297 passive, 297–298 Humidity, relative, 92 Humidity ratio, 91 Hydraulic permeability, 312

Hydride storage, 433–437 chemical hydrides, 433–434 metal hydrides, 434–437 Hydrogen, 426–449 amount needed, calculation of, 427–428 delivery of, 443–446 and fueling, 445–446 by pipeline, 444–445 by truck, 444 diffusivity of oxygen and, in water vapor, 216–218 generation of, 438–443 alternative methods, 443 biological production, 442–443 chemical production, 439–441 electrochemical production, 441–442 and infrastructure development, 446–449 safety/environmental concerns with, 444 storage of, 426–438 calculation of amount needed, 427–428 carbon storage, 437–438 compressed gas, 428–431 cryogenic liquid, 431–433 hydride storage, 433–437 liquid fuel storage, 438 volume, calculation of, 67–69 Hydrogen air fuel cell, Nernst equation for, 107–110 Hydrogen economy, 191, 426 Hydrogen oxidation reaction (HOR), 33, 34, 463 Hydrogen PEFCs (H2 PEFCs), 9, 11, 13, 17, 285–298 advantages of, 285 bipolar plate/flow field in, 294 catalyst layer in, 288–290 diffusion media compression in, 291–293 diffusion media in, 290–291 electro-osmotic drag in, 314 humidification of, 296–298 active, 296–297 passive, 297–298 microporous layer in, 293–294 solid polymer electrolyte in, 288 subsystems in, 295–298 technical design issues with, 285–287 Hydrogen reformation, 296 Hydrogen sulfide, 409 I0 , see Exchange current density Ideal gas equation of state, 64–65 IFC, see International Fuel Cells

Index IHP (inner Helmholtz plane), 126 Imbibition, 261–262 Impedance distribution, measurement of, 473–474 Impurities: and activation polarization losses, 129 ionic, 360 Independent half-cell global reaction, 39 Indirect internal reformation (IRR), 396 Ingriselli, Frank, 285 Inner Helmholtz plane (IHP), 126 In-plane design (SOFC), 388 In situ measurement and visualization, 474–478 alternative techniques, 476, 478 direct visualization techniques, 474–477 Intermec Technologies, 340 Intermolecular collisions, 211 Internal combustion engine, 4 Internal energy (U ), 69–70 International Fuel Cells (IFC), 398, 399 Ionic conductivity, 158 Ionic impurities, contamination from, 360 Ionic resistance, 158 Ion transport, 191–209 in ceramic electrolytes, 202–205 and conductivity, 195 and current flow, 191 in liquid electrolytes, 205–209 dilute electrolyte solution, 206–207 MCFC electrolyte, 207–209 mechanisms of, 191–193 convection, 192–193 mass diffusion, 191–192 migration, 193 Nernst–Planck equation governing, 193–194 in solid polymer electrolytes, 195–202 and Nafion ionic conductivity, 201–202 and water uptake, 198–201 IRR (indirect internal reformation), 396 Irrigational frost protection, 76 Ise, M., 313 Japan: fuel-cell-related patents in, 1 phosphoric acid fuel cell development in, 398–399 solid oxide fuel cell development in, 381 Joule, 37 Keith, David, 426 Ketelaar, J. A. A., 392 Kia Motor Company, 21

509

Kinetic energy, translational, 69 Kn (Knudsen number), 224 Knudsen diffusion, 223–226, 233 Knudsen number (Kn), 224 Kordesch, K., 21, 413 Kreuer, K. D., 313 λ, see Water uptake Langmuir model of kinetics, 155–157 Latent heat, 75–77 defined, 75 of vaporization, 76–77 LeChatelier’s principle, 101–102 Leverett function, 254–257 LHV, see Low heating value Lilliputian Systems, 381 Liquids, gas-phase diffusion through, 226–227, 321 Liquid cooling, 295–296 Liquid electrolytes, ion transport in, 205–209 Liquid fuel crossover, experimental determination of, 469 Liquid fuel storage (of hydrogen), 438 Liquid hydrogen, 431–433 Liquid-phase specific heat, 74 Lithium aluminum hydride, 434 Longevity of fuel-cell systems, U.S. Department of Energy goals for, 286 Los Alamos National Laboratory, 23 Low heating value (LHV), 102–104 Magnesium hydride, 434 Magnetic resonance imaging (MRI), 476 Manifold flow, stack, 336–339 Marubeni, 392 Mass diffusion, as mechanism of ion transport, 191–192 Mass transport, gas-phase, see Gas-phase mass transport Maximum expected voltage (reversible voltage) (E ◦ ), 97, 106–114 MCFCs, see Molten carbonate fuel cells Mechanical equilibrium, 62 Metal air batteries, 418 Metal hydrides, 434–437, 446 Metal organic frameworks (MOFs), 438 Methanol, 341–342, 351 Methanol crossover, 348–349 MFCs (microbial fuel cells), 17 Mho, 40 Microbial fuel cells (MFCs), 17

510

Index

Microporous layer (MPL), 257–258 and capillary transport, 257–258 in hydrogen PEFCs, 290, 293–294 in polymer electrolyte fuel cells (PEFCs), 321–323 Migration, as mechanism of ion transport, 193 Mitsubishi Electric Company, 398–399 Mitsubishi Heavy Industries, 381 R fuel cell technology, 12 Mobion
Modified Leverett function, 255–256 MOFs (metal organic frameworks), 438 Molten carbonate fuel cells (MCFCs), 8–10, 14, 15, 20, 23, 381, 392–398 advantages of, 397–398 conductivity of, 159 development of, 392 disadvantages of, 398 durability of, 396–397 heat generation from, 263 internal reformation of fuel gas in, 396 ionic conductivity of, 207–209 operating conditions for, 392–396 Monolithic design (SOFC), 389 MPL, see Microporous layer MRI (magnetic resonance imaging), 476 MTI Micro Fuel Cells, 13, 340 MTU Friedrichshafen, 392 Mud cracking, 324 Nafion, 196, 198–202, 228, 230, 311–312 NASA, 23, 412 Nernst, Walther, 381 Nernst equation, 106–114, 138 and concentration polarization, 168, 169 for hydrogen air fuel cell (example), 107–110 and species crossover losses, 176–177, 179 steps for solving problems using, 107 Nernst–Planck equation, 193–194 Nernst voltage, 106–114, 396 Net drag coefficient (αd ), 314–315 NetGen, 381 Neutron radiography (NR), 475 Newman, J., 313 New York City, 402 NFCEP Eco Soul, 35 Nickel metal hydride batteries, 434 Nickel shorting, 397 Nonideal behavior, 64–67 NR (neutron radiography), 475 Nusselt number, 270–271, 273 Nyquist plots, 457

Ohm, Georg Simon, 42 Ohmic polarization, 157–167 calculation/estimation examples, 159–161, 163–164, 166–167 and contact resistance, 161–166 and electronic/ionic resistance, 158–161 Ohm’s law, 42–43, 158, 193, 465 OHP (outer Helmholtz plane), 126 ONSI (company), 398, 399 Open-current voltage, calculation of expected, 111–114 ORRs, see Oxidation reduction reactions Oswald ripening, 358 Outer Helmholtz plane (OHP), 126 Oxalic acid, 341–342 Oxidation, electrochemical, 31 Oxidation reduction reactions (ORRs), 7, 17, 33, 463 Oxygen: diffusivity of hydrogen and, in water vapor, 216–218 effects of change in concentration of, 170–171 Oxygen enhancement, effect of, 110–111 Ozone hole, 444 P, see Pressure; Water vapor pressure PAFCs, see Phosphoric acid fuel cells Partial oxidation (for hydrogen production), 441 Particle image velocimetry (PIV), 476 Particulate matter, intrusion of unwanted, 357 Passive humidification, 297–298 Patents, fuel-cell-related, 1, 2 PDA/smart phone, 12 PEFCs, see Polymer electrolyte fuel cells Peltier heating, 264 PEM fuel cells, 9. See also Polymer electrolyte fuel cells (PEFCs) Performance characterization of fuel cell systems, via polarization curve, see Polarization curve Permeability: hydraulic, 312 as multiphase flow parameter, 248–250 Petroleum, as fuel source, 24–25 Phosphoric acid fuel cells (PAFCs), 9, 10, 15, 16, 23, 380, 398–410 advantages of, 406–407, 409 conductivity of, 159 configurations of, 403–407 development of, 398–402

Index disadvantages of, 410 durability of, 408–409 electrode/electrolyte system in, 407 electrolyte loss over time in, 407–408 operation of, 402–403 PEFC vs., 403–404 Physical spray deposition (catalyst layer manufacturing technique), 289–290 Pinhole formation, 358–359 Pipeline, hydrogen delivery by, 444–445 PIV (particle image velocimetry), 476 Planar design (SOFC), 385, 386 Platinum: as cost factor, 403–404 dissolution and migration of, 360 Polarization curve, 121–186, 300–301 application study, 185–186 and concentration polarization, 168–175 diagnostic tools for measuring losses, see Diagnostic tools electrical shorts, losses due to, 175–176 model summary, 181–183 predicting change in, 182–183 region I losses, 126–157 and activation polarization, 126–132 and Butler–Volmer (BV) kinetic model, 132–154 and electrical double layer, 126–127 and Langmuir/Tekmin model of kinetics, 154–157 region II losses, 157–167 calculation examples, 159–161, 163–164, 166–167 and cell assembly, 164–166 and contact resistance, 161–163 and electronic/ionic resistance, 158–161 region III losses, 168–175 region IV losses, 175–181 regions of, 121–123 species crossover, losses due to, 176–181 and zero-dimensional steady-state model, 125–126 Police Barracks (Central Park, New York City), 402 Polymer electrolyte fuel cells (PEFCs), 6–7, 11, 13, 15–17, 19, 23, 285–371. See also Hydrogen PEFCs alternatives to, 380–381 capillary flow in, 259–260 cell ohmic loss limiting current calculation for, 163–164

511

conductivity of, 41, 159 degradation of, 356–362 chemical modes, 359–362 physical modes, 356–359 diffusion in, 227–228 diffusion media in, 323–324 direct alcohol PEFCs, 339–356 electron transport in, 210 equivalent ohmic loss thermal network for, 166 estimated temperature gradient inside, 272–273 flow field configurations and stack design for, 325–339 asymmetric channel properties, 330–331 considerations in, 325–326 direction of flow, 331–332 manifold, 336–339 mesh designs, 330 patterns, 328–329 for portable and automotive applications, 334–336 and reactant bypass, 332–334 trade-offs in, 326–327 gas-phase flow in, 219–222 and heat dissipation from stacks, 274–275 heat generation from, 263 heat transfer in, 264–265, 272–273 interfacial flow between phases and film resistance in, 228–229, 231–233 interfacial/morphological effects in, 324–325 microporous layer in, 321–323 mud cracking in, 324 multidimensional effects in, 362–368 current distribution, 364–368, 469–470 temperature distribution, 363, 364, 473 water and species distribution, 363, 364, 470–472 multiphase flow in, 247, 250, 259–260 PAFC vs., 403–404 resistance calculation for, 166–167 solid polymer electrolyte in, 195. See also Solid polymer electrolytes sweep rate of, 459 water balance in, 298–321 and flooding, 299–301 importance of, 298–301 local balance, 310–321 overall balance, 302–310 Polymer electrolyte membrane (PEM) fuel cells, 9

512

Index

Polytetrafluoroethylene (PTFE), 195, 196, 247–248, 255–256 Porosity, 218, 245 Porous media, gas-phase flow in, 218–223 Porous media, multiphase flow in, 243–263 basic governing parameters for, 245–250 contact angle, 246, 247 permeability, 248–250 porosity, 245 saturation, 246 surface tension, 246–248 wettability, 245 capillary transport, 251–263 and capillary pressure, 251–254 Leverett approach, 254–257 microporous layer, effect of, 257–258 modified Leverett approach, 255–256 PEFC, local saturation in diffusion media of, 259–260 and imbibition/drainage, 261–262 PEFC porous media, 243–245, 259–260 and phase change, 262–263 Portable fuel cells, 19 Potassium carbonate, 17 Potassium hydroxide, 411 Power, 42–43 Prandtl number, 271, 273 Pressure (P), 63–64 open-circuit voltage dependence on temperature and, 101–102 single-phase flow and drop in, 233–239 from consumption of reactant, 238–239 from frictional losses, 234–238 thermodynamic effect of increase in, 111 Proton hopping, 198 Psat (saturation water vapor pressure), 92 Psychrometrics, 91–96 defined, 91 and evaporation/condensation, 95–96 maximum water uptake in flow, calculation of, 94–95 PTFE, see Polytetrafluoroethylene PureMotionTM fuel cell, 11 Radiation, heat transfer by, 273–274 Raney metals, 417 Rate of reaction, 34 RDE (rotating disk electrode), 463 Reactant, consumption of, for single-phase flow in channels, 238–239 Reactant bypass, 332–334

Reactant starvation, 357 Reactant utilization efficiency, measures of, 48–50 Reduction, electrochemical, 31 Regenerative fuel cells, 22 Relative humidity, 92 Relative permeability, 249–250 Resistance, 40–41, 158 contact, 161–163 estimating total fuel-cell, 159–161 Resistivity (ρ), 41, 158–159 Reversible fuel cell systems, 34, 35 Reversible process, maximum electrical work for, 96–97 Reversible voltage, see Maximum expected voltage (E ◦ ) Rolls Royce Fuel Cell Systems (RRFCS), 381 Rotating disk electrode (RDE), 463 Rotational motion (of molecules), 70 Roughness factor (a), 141–143 RRFCS (Rolls Royce Fuel Cell Systems), 381 Salem, H. S., 219 Saturation, as multiphase flow parameter, 246 Saturation water vapor pressure (Psat ), 92 Schmidt number, 273 Schrempp, J¨urgen, 453 Schroeder’s paradox, 201 SECA, see Solid State Energy Conversion Alliance Second law of thermodynamics, 211, 213 Segmented-cell-in-series design (SOFC), 389–390 Sensible enthalpy, 75 Sensors, electrochemical, 30 Separator plate corrosion, 397 Service history, fuel-cell, and activation polarization losses, 129 SHE, see Standard hydrogen electrode Siemens, Werner von, 41 Siemen (S) (unit), 40–41 Siemens (Siemens-Westinghouse), 13, 274, 381, 385, 387 σ , see Conductivity Silicon phosphate, 407 Single-walled nanotubes (SWNTs), 437 Slug flow regime, 240–244, 299, 300, 302–304 Slurry tape casting (catalyst layer manufacturing technique), 290 Socioeconomic impact, of fuel cells, 24–25 Sodium borohydride, 433

Index Sodium hydroxide, 411 Solid oxide fuel cells (SOFCs), 8–10, 13–16, 23, 381–392 advantages of, 391 conductivity of, 41, 159 design issues with, 382–385 development of, 381 disadvantages of, 391–392 durability of, 390–391 heat generation from, 263 in-plane design, 388 ion transport in, 202–205 manufacturing of, 382 monolithic design, 389 ohmic losses in, as function of electrolyte thickness, 203–205 operating temperature of, 381–382 planar design, 385, 386 segmented-cell-in-series design, 389–390 stress tubular design, 385–388 Solid-phase specific heat, 74 Solid polymer electrolyte (SPE) fuel cells, 9 Solid polymer electrolytes: in H2 PEFCs, 288 ion transport in, 195–202 and Nafion ionic conductivity, 201–202 and water uptake, 198–201 Solid State Energy Conversion Alliance (SECA), 14, 381 South Korea, 1, 392 Soviet Union, 16, 23 Space flight, 16, 23, 412–413 Space Shuttle, 16, 412 Species crossover, losses due to, 176–181 Species distribution, measurement of, 470–472 Specific heat, 71–74 constant-pressure, 71 constant-volume, 71 gas-phase, 71–73 liquid- and solid-phase, 74 SPE (solid polymer electrolyte) fuel cells, 9 Stacks, see Fuel cell stack(s) Standard hydrogen electrode (SHE), 38–40 Standard temperature and pressure (STP), 74 Startup power systems, 296 Steam reformation (for hydrogen production), 440–441 Stefan–Boltzmann constant, 273 Stefan–Maxwell diffusion model, 216 Stoichiometric ratio, 49

513

Stoichiometry: defined, 49 flow, 174–175 and utilization, 49–50 Stokes–Einstein equation, 226 STP (standard temperature and pressure), 74 Stress tubular design (SOFC), 385–388 Sulfonated PTFE, 196 SuperGrid, 445 Surface diffusion, 233 Surface tension, as multiphase flow parameter, 246–248 Sweep rate, 459 SWNTs (single-walled nanotubes), 437 Symmetry factor (β), 134–137 T, see Temperature Tafel plots, 463–465 Tafel reaction, 33 Technology, fuel-cell, 1 Temkin model of kinetics, 155–156 Temperature (T ), 63 distribution of, in PEFC, 363, 473 and heat flux driven flow, 314 and liquid viscosity, 194 maximum efficiency and change in, 100–101 open-circuit voltage dependence on pressure and, 101–102 Texas Instruments, 392 Thermal voltage (E ◦◦ ), 97–99, 106 Thermodynamics, defined, 62 Thermodynamic control volume, 6 Thermodynamic equilibrium, 62 Thermodynamics of fuel cell systems, 62–116 change of enthalpy: nonreacting species/mixtures, 78–82 reacting species/mixtures, 83–91 efficiency, thermodynamic, 96–106 enthalpy, 70–71, 77–78 enthalpy of formation, 74–75 example, 67–69 expected open-current voltage, calculation of, 111–114 internal energy, 69–70 latent heat, 75–77 and Nernst voltage, 106–114 nonideal behavior, 64–67 oxygen enhancement, effect of, 110–111 pressure, 63–64 pressure increase, effect of, 111 psychrometrics, 91–96

514

Index

Thermodynamics of fuel cell systems (Continued) sensible enthalpy, 75 specific heat, 71–74 temperature, 63 Thermodynamic systems, 5–6 3M, 196 ti , see Transference number TMM, see Trimethoxymethane Tortuosity, 218 Toshiba, 19, 392 Toyota, 121 TPB, see Triple-phase boundary Transference number (ti ), 175–176 Transportation applications, 21–22 Transport in fuel cell systems, 191–279 channels, single-phase flow in, 233–239 and consumption of reactant, 238–239 and frictional losses, 234–238 and pressure drop, 233–234 channels and porous media, multiphase flow in, 239–263 basic governing parameters, 245–250 capillary transport, 251–263 gas channels, 239–244 PEFC porous media, 243–245 electron transport, 209–210 and heat generation, 263–264 heat transport, single-phase, 264–275 and conduction, 264–267 and convection, 267–272 and radiation, 273–274 ion transport, 191–209 in ceramic electrolytes, 202–205 and conductivity, 195 and current flow, 191 in liquid electrolytes, 205–209 mechanisms of, 191–193 Nernst–Planck equation governing, 193–194 in solid polymer electrolytes, 195–202 mass transport, gas-phase, 210–233 and diffusion in general, 210–218 interfacial flow between phases, 228–232 Knudsen diffusion, 223–226 liquids, diffusion through, 226–227 polymer electrolyte, diffusion through, 227–228 porous media, 218–223 surface diffusion, 233

Trimethoxymethane (TMM), 341–342, 355 Trioxane, 341–342, 355 Triple-phase boundary (TPB), 53–54 Truck, hydrogen delivery by, 444 U, see Internal energy Union Carbide, 413 United Kingdom, fuel-cell-related patents in, 1, 2 United States: fuel-cell-related patents in, 1, 2 hydrogen production in, 449 molten carbonate fuel cell development in, 392 phosphoric acid fuel cell development in, 398 space program in, 16, 23 U.S. Army, 14–15, 392 U.S. Department of Energy (DOE), 14, 286, 287, 381, 427, 437 United Technologies Corporation (UTC), 8, 15, 19, 23, 329 United Technologies Corporation Fuel Cells (UTC Fuel Cells), 398 University of California–Davis, 399 UTC, see United Technologies Corporation UTC Power Corporation, 11, 15, 22 V (volt), 37 Van der Veer, Jeroen, 1 Van der Waals, Johannes Diderik, 65 Van der Waals equation of state, 65 Vaporization, latent heat of, 76–77 Vehicles, fuel-cell, 121 Vibrational motion, 69 Virial equations of state, 65 Viscosity, and temperature, 194 Visualization tools, fuel cell, 474–477 Volmer reaction, 33 Volt (V), 37 Volta, Alessandro, 37 Voltage, 37–39 maximum expected, 97 reversible, 97 thermal, 97–99 Voltage reversal, 357 W. L. Gore and Associates, 196 Wantanabe, M., 178 Waste heat, 4 Water balance (in PEFCs), 298–325 and flooding, 299–301 importance of, 298–301

Index local balance, 310–321 calculation example, 316, 317 and catalyst layer mass balance, 315–316 and electro-osmotic drag, 312–314 and gas-phase transport, 321 and heat flux driven flow, 314 and hydraulic permeability, 312 liquid accumulation, location of, 317–321 Nafion, diffusion and water uptake in, 311–312 and net transport coefficient, 314–315 and water flux in membranes, 310 and maintenance of high-performance electrode, 321–325 overall balance, 302–310 calculation example, 305–306 drying condition, adjustment for, 307 flooding condition, adjustment for, 307, 308 and memory effect, 308–309 time scale for liquid water accumulation, 309–310 with transient operation, 306–307 visualization techniques for determining, 476–478 Water–gas shift (WGS) reaction, 439

515

Water management: in direct methanol fuel cells (DMFCs), 345–348 in phosphoric acid fuel cells (PAFCs), 406 Water uptake (λ), in Nafion, 198–201, 312 Water uptake in a flow, calculation of maximum, 94–95 Water vapor pressure (P), 92 Watt-hour, 37 Westinghouse, 385. See also Siemens (Siemens-Westinghouse) Wettability, 245 Wetting fluid, 245 WGS (water–gas shift) reaction, 439 Wiedemann–Franz law, 267 Work, 4 flow, 70 maximum electrical, for reversible process, 96–97 X-ray microtomography, 476 Yale University, 14 Yttria-stabilized zirconia (YSZ), 202–203, 381, 382 Zawodzinski, T. A., 313 Zero-dimensional steady-state model, 125–126