Proton Exchange Membrane Fuel Cells Modeling E-Book

Fei Gao

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 221

Veröffentlichungsjahr: 2013

Beschreibung

The fuel cell is a potential candidate for energy storage and conversion in our future energy mix. It is able to directly convert the chemical energy stored in fuel (e.g. hydrogen) into electricity, without undergoing different intermediary conversion steps. In the field of mobile and stationary applications, it is considered to be one of the future energy solutions.
Among the different fuel cell types, the proton exchange membrane (PEM) fuel cell has shown great potential in mobile applications, due to its low operating temperature, solid-state electrolyte and compactness.
This book presents a detailed state of art of PEM fuel cell modeling, with very detailed physical phenomena equations in different physical domains. Examples and a fully coupled multi-physical 1.2 kW PEMFC model are given help the reader better understand how to use the equations.

Leseprobe

Table of Contents

Introduction

Nomenclature

PART 1: State of the Art: Of Fuel Cells Modeling

Chapter 1: General Introduction

1.1. What is a fuel cell?

1.2. Types of fuel cells

Chapter 2: PEMFC Structure

2.1. Bipolar plates

2.2. Membrane electrode assembly

Chapter 3: Why Model a Fuel Cell?

3.1. Advantages of modeling and simulation

3.2. Complex system modeling methods

3.3. Modeling goals

Chapter 4: How Can a Fuel Cell be Modeled?

4.1. Space dimension: 0D, 1D, 2D, 3D

4.2. Temporal behavior: static or dynamic

4.3. Type: analytical, semi-empirical, empirical

4.4. Modeled areas: stack, single cell, individual layer

4.5. Modeled phenomena

Chapter 5: Literature Models Synthesis

5.1. 50 models published in the literature

5.2. Model classification

PART 2: Modeling of the Proton Exchange Membrane Fuel Cell

Chapter 6: Model Structural and Functional Approaches

Chapter 7: Stack-Level Modeling

7.1. Electrical domain

7.2. Fluidic domain

7.3. Thermal domain

Chapter 8: Cell-Level Modeling (Membrane-Electrode Assembly, MEA)

8.1. Electrical domain

8.2. Fluidic domain

8.3. Thermal domain

Chapter 9: Individual Layer Level Modeling

9.1. Electrical domain

9.2. Fluidic domain

9.3. Thermal domain

Chapter 10: Finite Element and Finite Volume Approach

10.1. Conservation of mass

10.2. Conservation of momentum

10.3. Conservation of matter

10.4. Conservation of charge

10.5. Conservation of energy

PART 3: 1D Dynamic Model of a Nexa Fuel Cell Stack

Chapter 11: Detailed Nexa Proton Exchange Membrane Fuel Cell Stack Modeling

11.1. Modeling hypotheses

11.2. Modeling in the electrical domain

11.3. Modeling in the fluidic domain

11.4. Thermal domain modeling

11.5. Set of adjustable parameters

Chapter 12: Model Experimental Validation

12.1. Multiphysical model validation with a 1.2 kW fuel cell stack

Bibliography

Index

First published 2012 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKJohn Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.iste.co.ukwww.wiley.com

© ISTE Ltd 2012

The rights of Fei Gao, Benjamin Blunier & Abdellatif Miraoui to be identified as the author of this work have been asserted by themin accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Proton exchange membrane fuel cells modeling / edited by Fei Gao, Benjamin Blunier, Abdellatif Miraoui.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-339-5

1. Proton exchange membrane fuel cells--Mathematical models. I. Gao, Fei, 1983- II. Blunier, Benjamin. III. Miraoui, Abdellatif.

TK2933.P76P76 2011

621.31'2429--dc23

2011042579

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-339-5

Introduction

The fuel cell is a potential candidate for energy storage and conversion in our future energy mix. Indeed, a fuel cell is able to directly convert the chemical energy stored in fuel (e.g. hydrogen) into electricity, without undergoing different intermediary conversion steps. In the field of mobile and stationary applications, it is considered to be one of the future energy solutions.

Currently, the production costs of fuel cells are still relatively high, and there remain problems that must be dealt with before they can be mass-produced (e.g. life expectancy, electrolyte, degradation, catalyst cost, etc.).

Among the different fuel cell types, the proton exchange membrane (PEM) fuel cell has shown great potential in mobile applications, due to its low operating temperature, solid-state electrolyte, and compactness. Currently, it is still in the research & development stage, but already shows great promise for its potential applications in the stationary and mobile domains. However, many problems persist, which are slowing its launch onto the market:

– its life expectancy must be improved in order to reach 500 hours of operation in automotive applications;

– its cost must be reduced to under 40 EUR per kilowatt (cost of an internal combustion engine);

– its auxiliaries, especially the air compressor and power converters, still require considerable optimization in terms of performance and compactness;

– clean, competitive solutions for the production and distribution of hydrogen must be put into place and generalized.

Many experts considered the low-temperature PEM fuel cell to be the future of embarked energy, especially for terrestrial transportation. Intensive research in this field has led to new modeling methods for the fuel cells and system design. The mathematical models must be based on the description of the physical phenomena occurring within the fuel cell, and require detailed knowledge of the microscopic processes of chemical and electrochemical reactions.

The fuel cell modeling is a solution which allows us to better understand the physical phenomena occuring during fuel cell operation. A better understanding of its operation can improve its design (e.g. more compact stacks), performance, and life expectancy on the one hand, and help us to consider control laws on the other hand.

This book offers a guide to mathematical modeling of PEM fuel cells and a fairly detailed theoretical description of fuel cell physics, with particular emphasis on multiphysical modeling. The models discussed in this book can be used by researchers, engineers, and industrialists in order to access information on the dimensioning and design of fuel cells.

Therefore, the main objective of this book is to provide the tools that are used in the modeling of PEM-type fuel cells by adopting a systemic approach. It was written for engineers, students, or postgraduates who wish to develop a multiphysical fuel cell model quickly without a priori extensive fuel cell knowledge.

The authors’ experience in the fields of fuel cells, either as teachers or researchers, has enabled them to write this book in a structured, pedagogic, and accessible manner.

Part 1 of this book introduces the fundamental principles of fuel cells, along with different existing fuel cell technologies thereby providing the fundamental elements and the vocabulary used in fuel cell modeling. This part also proposes a classification of the different fuel cell modeling criteria following a structural and functional approach. On the basis of these criteria, Chapter 5 offers a classification of different models recently published in the literature.

Part 2 of this book presents the fundamental elements of fuel cell modeling on three different levels: the stack level (stack of cells), the single cell level (stack of individual layers), and the individual layer level (membrane, diffusion layers, bipolar plate, etc.). Physical phenomena are detailed, along with the fundamental or empirical equations published in the literature.

Part 3 of this book presents a complete model for a commercial fuel cell (Ballard Nexa stack), based on equations shown in Part 2. The presented model is a dynamic, 1D, multiphysical PEM fuel cell stack model, which covers the electrical (or electrochemical), fluidic, and thermal physical domains. The proposed modular modeling structure will enable easy improvement of the model in any of the levels or physical domains without requiring the rectification of the other parts: readers will thus be able to adapt this model to different PEM fuel cells. Chapter 12 is dedicated to the experimental validation and temporal/spatial analysis of the developed model.

The authors would like to heartily thank all their colleagues from the University of Technology of Belfort-Montbéliard (UTBM, France), especially the researchers at the Systems and Transports Laboratory (SeT) and of FCLAB (Fuel Cell Lab) who were kind enough to proofread and edit this book. Their fruitful discussions and feedback throughout the elaboration of the models and the book have undoubtedly improved the quality of this publication.

Nomenclature

Symbols

SymbolDescriptionUnitsAsection aream2awwater activity—c(sub)concentrationmol/m3cddischarge coefficient—cdldouble layer capacitanceFCpthermal capacity at constant pressureJ/(kg K)Cvthermal capacity at constant volumeJ/(kg K)Ddiffusion coefficientm2/sDhydrohydraulic diametermDpr,avgpore mean diametermEthermodynamic voltageVFFaraday constantC/molfDDarcy factor—Hsubheightmh(sub)heat exchange coefficientW/(m2 K)HhHenry constantm3 Pa/molHγwater evaporation heat (by unit mass)J/kgicurrentAjcurrent densityA/m2KDlinear coefficient of nozzle flow—Kecelectrokinetic permeabilitym2Khydrohydraulic permeabilitym2L(sub)lengthmmmassmM(sub)molar masskg/molmratiomass ratio—molar flow ratemol/sN(sub)number—ndragelectro-osmotic coefficient—PpressurePaPratiopressure ratio—qmass flow ratekg/sQenergy flow rateJ/sRideal gas constantJ/(mol K)R(sub)electrical resistanceΩr(sub)electrical resistivityΩ mReReynold’s number—sstoichiometry—ShSherwood number—Ssatreduced water saturation coefficient—TtemperatureKttimesUperimetermu(sub)velocitym/sVvolumem3V(sub)voltageVXratio—x(sub)molar fraction—γthermal capacity ratio—δ(sub)thicknessmΔHenthalpy changeJ/molΔSentropy changeJ/(mol K)εerror—ε0electrical constantF/mεrstatic electromagnetic permittivity—θemissivity—λ(sub)thermal conductivityW/(m K)λwwater content—µsubviscosityPa sξtortuosity—ρdensitykg/m3σStefan-Boltzmann constantW/(m2 K4)σ(sub)electrical conductivityS/mτ(sub)time constantsφ(sub)GDL void fraction (porosity)—

Subscripts

Superscripts

PART 1

State of the Art: Of Fuel Cells Modeling

Chapter 1

General Introduction

1.1. What is a fuel cell?

The operating principle of the fuel cell is quite old. This principle was introduced by two researchers (Christian Friedrich Schönberg and William Grove) within a span of one month in 1839. The principle is based on the reaction between two gases: hydrogen (or a hydrogen-rich gas) used as fuel and oxygen used as oxidant. The operating principle of the fuel cell is relatively straightforward: it can be described as inverse electrolysis. More precisely, it consists of a controlled electrochemical combustion between oxygen and hydrogen resulting in the simultaneous production of electricity, water, and heat, following the global formula:

This electrochemical reaction takes place in a system which consists of two electrodes (cathode and anode) separated by an electrolyte. Depending on the type of the fuel cell, the reaction can take place at different temperatures, from a few dozens of degrees Celsius for proton exchange membrane fuel cells (PEMFC) to almost one thousand degrees Celsius for solid-oxide fuel cells (SOFC).

Although this operating principle is valid for all types of fuel cells, differences in electrolytes and operating temperatures result in different characteristics for different types of fuel cells, so that they are more or less adapted for certain applications.

For example, the operating principle of proton exchange membrane fuel cells is shown in Figure 1.1:

Figure 1.1. Operating principle of the proton exchange membrane fuel cell (PEMFC or PEFC) [BLU 09]

– the fuel cell is fed by hydrogen at the anode (negative terminal) and oxygen at the cathode (positive terminal);

– hydrogen molecules are dissociated through a platinum-based catalytic reaction and each hydrogen atom loses its only electron. Since the electron cannot pass through the membrane (insulator), it passes through the electrical circuit and creates an electrical current (Figure 1.1). Without its electron, the hydrogen ion (now H+, a proton) can pass through the membrane to the cathode;

– electrons coming from the anode through the electrical circuit, protons migrating from the anode through the membrane and oxygen molecules (O2) combine at the cathode to form water molecules containing two hydrogen atoms and one oxygen atom (H2O).

Water and electricity are thus produced. As the reaction is not perfect, it also produces heat that can be harnessed for various purposes (e.g. heating).

The fuel cell is an energy converter, and not an energy source. It converts the chemical energy of a fuel (hydrogen) directly into electricity and heat.

The conversion process from hydrogen to electricity is non-polluting, as the only byproduct is water. The fuel, hydrogen, is an energy carrier: it carries energy. Hydrogen is not a source of energy because it requires energy to be produced (hydrogen exists only in small quantities in nature). Hydrogen can be extracted from a primary energy source (gasoline, methane, ethanol, etc.) or produced from electrolysis of water (which is the separation of the water molecule into hydrogen and oxygen) [BLU 09].

1.2. Types of fuel cells

Various fuel cell technologies exist, where each technology has its specific advantages and drawbacks. These advantages and drawbacks render them more or less suitable for certain applications. For example, low-temperature fuel cells such as PEMFC or AFC (see section 1.2.1), start up faster than the high-temperature fuel cells, which makes them more suitable than other fuel cell technologies for transportation applications. However, these low-temperature fuel cells require larger quantities of catalyst and more bulky heat exchangers, due to the small temperature difference between the fuel cell and environment: these constraints make these fuel cells less suitable for transportation applications, in which space constraint is a key issue. For high-temperature fuel cells, the opposite is the case: they have a relatively long start-up time but require less space due to smaller heat exchangers.

The choice of the type of a fuel cell for any given application is therefore always a compromise between its inherent advantages and drawbacks. In order to overcome certain drawbacks, researchers tend to look to:

1) increase the operating temperature of low-temperature fuel cells (to approximately 120°C) for transportation applications, so as to decrease the size of the fuel cell and improve water management;

2) lower the operating temperature of high-temperature fuel cells, thereby reducing thermal constraints, start-up time and costs, while extending the lifetime of the fuel cell. An example of such an improved cell is the IT-SOFC (Intermediate-Temperature Solid Oxide Fuel Cell).

Operating temperature of the optimal fuel cell seems to be around 150–200°C [MEN 08], which corresponds to the temperature of which, in turn, has other drawbacks unfortunately.

Table 1.1. Summary of different fuel cell technologies

Fuel cell classification is generally based on the type of electrolyte, since the electrolyte determines the operating temperature of the cell and the type of ion which will ensure ionic conduction. The most commonly used technologies are as follows (Table 1.1):

– polymer electrolyte fuel cells (PEFC) or proton exchange membrane fuel cells (PEMFC), operating at around 80°C;

– alkaline fuel cells (AFC), operating at around 100°C;

– phosphoric acid fuel cells (PAFC), operating at around 200°C;

– molten carbonate fuel cells (MCFC), operating at around 700°C;

– solid oxide fuel cells (SOFC), operating at around 800–1000°C.

1.2.1. Proton exchange membrane fuel cell (PEMFC, PEFC)

Proton exchange membrane fuel cells operate at temperatures under 100°C, with a stack efficiency of the order of 50%. Its low-operating temperature enables these fuel cells to start up relatively quickly, making this technology particularly well adapted to transportation applications. The typical PEMFC power range is from a few milliwatts to a few hundred kilowatts.

The electrolyte of PEMFC is generally a perfluorinated polymer membrane capable of carrying hydrogen ions (i.e. protons).

The primary advantages of PEMFC are as follows:

– the electrolyte is solid: there is no risk of electrolyte leakage;

– the operating temperature is low, which means that the cell does not need a long time to warm up before being fully operational;

– the specific power is high, and can be as high as 1 kW/kg;

However, they have their own drawbacks:

– the membranes must be kept in a good degree of hydration in order to transfer hydrogen protons. If this condition is not met, there is a risk of membrane deterioration, which would lead to the degradation of the fuel cell itself;

– the necessity of platinum makes the fuel cells susceptible to contamination from carbon monoxide (CO), which poisons catalytic sites.

Besides problems associated with fabrication of the fuel cell stack, certain technical problem have to be overcome:

1) manufacturing cells capable of cold-starting in low-temperature conditions, particularly under 0°C;

2) heat and water management;

3) durability, especially in the conditions commonly found in transportation (thermal and electrical cycling, vibrations, climactic conditions, etc.).

1.2.2. Alkaline fuel cells (AFC)

During the 1960s, the Apollo missions relied on alkaline fuel cells to generate water and electricity onboard the spacecraft. In atmospheric pressure, operating temperature of these fuel cells is between 80°C and 90°C, with a stack efficiency of about 50%. However, under certain conditions (pressurized environment and highly concentrated electrolyte), this temperature can increase upto 250°C.

These fuel cells have several applications. Most importantly, they were used by NASA in the Apollo programs [BLU 09] and were used for the shuttles (three cells for each) to provide power of between 2 and 12 kW (with maximum power 16 kW) and an output voltage of 28–32 V. Siemens also developed alkaline fuel cells in the 1970s and 1980s, including a 20 kW cell for use in submarines. The power of alkaline fuel cells ranges between 1 and 100 kW.

Unlike platinum-based PEM fuel cells, alkaline fuel cells have the advantage of using nickel-based anode catalysts and active coal-based cathode catalysts, thereby reducing production costs.

The primary drawback of this type of fuel cell is its sensitivity to carbon monoxide. This sensitivity implies that alkaline fuel cells require an advanced hydrogen purification process (ensuring the total elimination of carbon monoxide) if this hydrogen is acquired through steam reformation of a hydrocarbonated fuel. For this reason, among others, AFC are infrequently used for transportation applications. Another reason is the fact that the electrolyte is a liquid and corrosive, and could leak under the conditions commonly found in transportation (vibration, acceleration, etc.).

1.2.3. Phosphoric acid fuel cells (PAFC)

Phosphoric acid fuel cell technology is more mature in terms of its development and commercialization. Indeed, there are stationary PAFC installations of upto 50 MW, and about 200 testing sites have been operational worldwide. Cogeneration (the simultaneous production of both electricity and heat) is the main advantage of phosphoric acid fuel cells. The power range of PAFC is between 200 kW and 50 MW. Its operating temperature is between 180 and 210°C.

Since phosphoric acid fuel cells use liquid electrolytes, they have drawbacks that are similar to that of alkaline fuel cells. At low temperatures (around 40°C), the electrolyte solidifies and its ion conductivity decreases, which means that the cell must be maintained above this temperature. Finally, the acid’s strong corrosiveness causes the electrodes to deteriorate over time.

1.2.4. Molten carbonate fuel cells (MCFC)

Molten carbonate fuel cells are primarily used for stationary applications. An example of such a fuel cell would be a 2 MW mini-reactor running on natural gas in the United States, which can run for approximately 4,000 hours. The power of molten carbonate fuel cells ranges from 500 kW to 10 MW for operating temperatures between 600 and 700°C.

In MCFC, the chemical reactions are more complex than those of proton exchange membrane, alkaline, or phosphoric acid fuel cells. Ionic conduction is done through the migration of carbonate ion from the anode to the cathode through the electrolyte (which consists of molten carbonates).

One of the particularities of MCFC (such as solid oxide fuel cell) is that its operating temperature allows the use of carbon monoxide as fuel gas. Carbon monoxide can be produced from the hydrocarbon reforming process. Therefore, there can be two sorts of electrochemical reactions occurring at the anode. The first is the primary reaction, which consists of converting the energy within hydrogen into electricity. The secondary reaction can take place if carbon monoxide is present in the mixed fuel gas, which consists of converting the carbon monoxide and the vapor into hydrogen and carbon dioxide (and therefore does not take place if the fuel cell is fed with pure hydrogen).

High operating temperature of the molten carbonate fuel cells gives them certain advantages:

– they have a better tolerance to impurities in hydrogen, especially to carbon monoxide (CO) which can be used directly as combustible along with hydrogen;

– hydrocarbon reform (methane, propane, etc.) can occur within the cell, thereby avoiding the need for pure hydrogen;

– the high operating temperature allows for cogeneration;

– noble metals for catalyst such as platinum are not required, which decreases the costs of production.

However, this fuel cell faces a problem that relates to corrosion of nickel oxide by the electrolyte. In addition, management of CO2 that is taken at the anode and re-injected at the cathode complicates the system design. Finally, the MCFC start-up time is extremely long, which makes them suitable only for stationary applications which usually provide continuous power supply.

1.2.5. Solid oxide fuel cells (SOFC)

SOFC are, to have date, the cells that have the longest development time: work on this technology began in the late 1950s. Their operating temperature is between 800 and 1000°C and about 550°C for their “low”-temperature equivalent, called IT-SOFC (Intermediate Temperature Solid Oxide Fuel Cells). At such high temperatures, ceramic electrolyte exhibits an excellent ionic conductivity; below these temperatures, the ionic conductivity is strongly reduced.

Solid oxide fuel cells are primarily used for stationary applications but some of the automobile manufacturers also see a future in these fuel cells, since they accept a wide range of combustibles such as methane (natural gas). The power range of solid oxide fuel cells tested to date is between 1 kW and 10 MW. Efficiencies of these cells can be relatively high and reach 60% [MEN 08].

Like MCFC, SOFC can use carbon monoxide as combustible due to its high operating temperature range.

SOFC technology has many advantages:

– high-operating temperature allows for the possibility of cogeneration, resulting in overall efficiency of about 80%;

– the resistance to sulfur is twice that of phosphoric acid or molten carbonate fuel cells;

– noble metals such as platinum are not required for catalyst, which decreases the costs of production;

– it tolerates carbon monoxide, which can poison PEMFC due to the latter’s use of platinum as a catalyst.

However, it does have some drawbacks:

– the use of specific materials which can withstand thermal stress is necessary;

– at such high-operating temperatures, material corrosion is fast;

– its power density is lower than that of PEMFC, especially for tubular SOFC;

– its start-up time is very long and the fuel cell sometimes requires auxiliary heaters to warm it up (e.g. a burner) so as to reach temperatures at which the electrolyte’s ionic conductivity is acceptably high.

A major challenge of solid oxide fuel cells is reduction of their operating temperatures, so as to reduce their thermal stress on materials (especially on the seals) and start-up time.

1.2.6. Direct methanol fuel cells (DMFC)

This technology is fairly recent (1990s) but has already demonstrated its utility in portable applications. It is seen as an interesting alternative to lithium-based batteries, which have already achieved their highest energy densities for “nomad cell technology” at present. The DMFC technology is similar to that of proton exchange membrane fuel cells (PEMFC) but for the fuel: PEMFC uses gaseous hydrogen, DMFC runs on liquid methanol, making it easier to use. DMFC electrolytes are also based on proton exchange membrane, and achieve ionic conductivity through the transfer of H+ ions: liquid methanol (CH3OH) is oxidized with water at the anode and produces CO2, hydrogen ions, and the electrons in turn will produce electrical current for the external electric load. Hydrogen ions go through the membrane electrolyte and react at the fuel cell cathode with oxygen and electrons from the electric circuit to form water.

However, this technology is beset with certain problems which are yet to resolved:

– the management of two-phase flows (liquid and gas) at both anode and cathode;

– the migration of methanol through the membrane from the cathode toward the anode (fuel crossover);

– the weak platinum activity requires vast quantities of catalyst with respect to PEFC (about 50 times more platinum compared to the best polymer electrolyte fuel cells).

Chapter 2

PEMFC Structure

A proton exchange membrane fuel cell stack consists of a series of elementary fuel cells, where each cell is made up of different layers performing one or more functions (Figure 2.1).

A single fuel cell can be divided into two main parts:

– bipolar plates which enable the arrival of gas, the collection of electrical current, the cell’s mechanical support and eventually the cooling of the cell;

– membrane electrode assembly (MEA). A MEA can be split into three sub-parts: the diffusion layer (porous section of the electrode), the catalyst layer (active reaction zone, interface between the electrode and the membrane) and the membrane.

Fuel cells require various functions to be carried out during operation (Figure 2.1) [BAR 05b]:

1) gas (reactant) supply to the diffusion layers from channels is supported by the bipolar plates;

2) reactant diffusion to reaction sites is achieved by the diffusion layers;

3) electrochemical reactions at both the anode and cathode sides is achieved by the catalyst layer (active area of electrode);

Figure 2.1. Fuel cell stack and elementary cell structure

4) proton transfer from the anode to the cathode while avoiding electron transfer, is done by the polymer membrane;

5) conduction of the electrical current is undertaken by all the conductive parts of the cell (electrodes and bipolar plates);