Table Of ContentIntroduction to Transfer Phenomena
in PEM Fuel Cells
Series Editor
Alain Dollet
Introduction to Transfer
Phenomena in PEM
Fuel Cells
Bilal Abderezzak
First published 2018 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter 1. Introduction to Hydrogen Technology . . . . . . . . . . . . . 1
1.1. Hydrogen as an energy vector . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1. Production methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2. Storage technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.3. Distribution networks and associated risks . . . . . . . . . . . . . . . 10
1.1.4. Advantages and challenges to raise . . . . . . . . . . . . . . . . . . . 11
1.2. Types of fuel cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1. The different fuel cell technologies . . . . . . . . . . . . . . . . . . . 13
1.2.2. Fuel cell and their applications . . . . . . . . . . . . . . . . . . . . . . 32
1.2.3. Advantages and issues to improve . . . . . . . . . . . . . . . . . . . . 34
1.3. The proton-exchange membrane fuel cell . . . . . . . . . . . . . . . . . . 35
1.3.1. The basic structure of the PEMFC . . . . . . . . . . . . . . . . . . . . 37
1.3.2. PEMFC design and configuration . . . . . . . . . . . . . . . . . . . . 45
1.3.3. Operation and aging problem . . . . . . . . . . . . . . . . . . . . . . . 47
1.3.4. The fuel cell and its technical system
entourage technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
1.5. Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 2. Charge Transfer Phenomena . . . . . . . . . . . . . . . . . . . 53
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2. Thermodynamics and chemistry of
the PEM fuel cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.1. The base reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.2. Heat reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.3. Electrical work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
vi Introduction to Transfer Phenomena in PEM Fuel Cells
2.2.4. Empty voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.5. Effect of pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2.6. Effect of temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2.7. Theoretical efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.3. The flow rates of reactants and products . . . . . . . . . . . . . . . . . . . 65
2.3.1. Oxygen flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.3.2. Hydrogen flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3.3. Amount of water produced . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4. Electrochemistry of the fuel cell . . . . . . . . . . . . . . . . . . . . . . . 67
2.4.1. Electrode kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4.2. Activation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4.3. Reaction rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.4. Exchange current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.5. Current density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.5. Polarization phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.5.1. Activation polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.5.2. Ohmic polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.5.3. Concentration polarization . . . . . . . . . . . . . . . . . . . . . . . . 75
2.5.4. Real cell voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5.5. Polarization curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5.6. Optimum operating range . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.6. Modeling of charge transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.7. Overview of analytical models . . . . . . . . . . . . . . . . . . . . . . . . 79
2.7.1. Simple analytical models . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.7.2. Complex analytical models . . . . . . . . . . . . . . . . . . . . . . . . 80
2.8. Empirical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.9. Current transport and charge conservation . . . . . . . . . . . . . . . . . 81
2.10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Chapter 3. Mass Transfer Phenomena . . . . . . . . . . . . . . . . . . . . . 85
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2. Flow of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3. Mass transfer by convection . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4. Mass transfer in porous diffusers . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.1. Conservation of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.2. The conservation of species . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.3. Some parametric laws . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5. Mass transfer in the catalyst layers (electrodes) . . . . . . . . . . . . . 101
3.5.1. Low current model (Butler–Volmer) . . . . . . . . . . . . . . . . . 102
3.5.2. Agglomerate model with strong current . . . . . . . . . . . . . . . . 103
Contents vii
3.6. Mass transfer in the membrane . . . . . . . . . . . . . . . . . . . . . . . . 105
3.6.1. Schröeder’s paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.6.2. Microscopic scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.6.3. Mesoscopic scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.6.4. Macroscopic scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.6.5. Parametric laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Chapter 4. Heat Transfer Phenomena . . . . . . . . . . . . . . . . . . . . . 125
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.2. Energy balances for a PEMFC . . . . . . . . . . . . . . . . . . . . . . . . 127
4.2.1. Energy balance for a stack . . . . . . . . . . . . . . . . . . . . . . . . 127
4.2.2. Energy balance for compounds and gases . . . . . . . . . . . . . . . 130
4.2.3. Energy balance for the gas phase . . . . . . . . . . . . . . . . . . . . . 130
4.2.4. Energy balance for the solid structure . . . . . . . . . . . . . . . . . . 131
4.3. The heat flow in the different layers of the PEMFC . . . . . . . . . . . . 131
4.3.1. Heat transfer by conduction . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3.2. Heat dissipation by natural convection and radiation . . . . . . . . . 133
4.4. Thermal management in a PEMFC . . . . . . . . . . . . . . . . . . . . . . 134
4.4.1. Cooling systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.4.2. Convection cooling of the airflow at the cathode . . . . . . . . . . . 134
4.4.3. The effect of temperature on the performance
of the PEMFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5. Heat sources in the PEMFC . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5.1. In the polymer membrane . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.5.2. At the electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.5.3. In the GDLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.5.4. Water evaporation and condensation . . . . . . . . . . . . . . . . . . 145
4.6. Temperature distribution between two
cathodes: case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Preface
The recognition of new sources of energy that are green and renewable is
a necessity for young audiences in the scientific and technical field. These
non-polluting energies contribute to a more protected environment against
dangerous emissions, such as greenhouse emissions or those that affect air
quality.
The operating principles of energy conversion devices that convert these
renewable sources into useful energy must be known and controlled.
This educational book develops a broad overview of the different
physical phenomena that take place within a fuel cell. This book is intended
for students and young researchers in technical fields. It is essentially
composed of five sections as follows.
Chapter 1 introduces hydrogen as an energy vector that can be produced
in different ways and used in many applications. The different fuel
cell technologies are presented in this chapter. A special interest in the
proton-exchange membrane fuel cell is presented at the end of this chapter.
In addition, a quiz specific to this introduction is provided as a good
summary of the principles of hydrogen technology and PEM fuel cells.
In Chapter 2, charge transfer phenomena are discussed. This chapter
covers the thermodynamic and chemistry aspects of a fuel cell, the flow rates
of the reactants and products as well as some electrochemical notions. At the
end of the chapter, polarization phenomena and an overview of charge
transfer models are described.
