ABSTRACT
MEA area in the stack, cm2 AMEA total MEA area in the stack, cm2 B0 PEM d’Arcy permeability, cm2 ci,0 concentration of species i at equilibrium, mol cm−3 ci,α concentration of species i in layer α, mol cm−3 ci,b concentration of species i in bulk phase, mol cm−3 ci,ref reference concentration of species i, mol cm−3 dM,A anode metal catalyst nanoparticle diameter, cm dM,C anode metal catalyst nanoparticle diameter, cm Di,ae effective diffusion coefficient of species i in
layer α, cm2 s−1 Eμ activation energy for viscosity of water, J mol−1 E ,r F0 activation energy for electrode reaction ρ at
equilibrium (Nernst) potential, J mol−1 E ,C F0 cathode effective activation energy for oxygen
reduction reaction, J mol−1 F Faraday’s constant, 96,487 C eq−1 i current density, A cm−2 of geometric MEA area iρ electrode ρ current density, A cm−2 geometric
MEA area iρ,X electrode ρ crossover current density, A cm−2
iρ,0 exchange current density for electrode reaction ρ, A cm−2
iρ,L electrode ρ limiting current density, A cm−2 i*r current density, A cm−2 ECSA i*r,0 exchange current density, A cm−2 ECSA iA ref, ,* 0 anode reference exchange current density,
A cm−2 ECSA IStack total current in stack, A ki permeability of gaseous species i in PEM kr forward rate constant for electrode reaction ρ kr reverse rate constant for electrode reaction ρ Kρ thermodynamic equilibrium constant for elec-
trode reaction ρ LB electrolyte layer thickness, cm LD GDL layer thickness, cm mM,A anode catalyst loading, g cm−2 mM,C cathode catalyst loading, g cm−2 NAv Avogadro’s number NCell number of cells in a stack Ni,z flux of species i in the membrane along the z
direction, mol s−1 cm−2 MEA NH2 molar flux of H2 generated in the PEM-WE, mol
s−1 cm−2 MEA ni molar flow rate of species i, mol s−1
CONTENTS
Nomenclature ......................................................................................................................................................................... 243 Greek Symbols ........................................................................................................................................................................ 244 Subscripts/Superscripts ........................................................................................................................................................ 244 Abbreviations ......................................................................................................................................................................... 244 12.1 Introduction ................................................................................................................................................................. 245 12.2Thermodynamic Analysis ......................................................................................................................................... 248 12.3Electrode Reaction Mechanism and Kinetics ......................................................................................................... 250 12.4Transport Limitations ................................................................................................................................................. 252 12.5Gas Crossover .............................................................................................................................................................. 253 12.6Ohmic Resistance ........................................................................................................................................................ 258 12.7Cell Polarization .......................................................................................................................................................... 258 12.8Cell Power Requirement and Efficiency .................................................................................................................. 259 12.9Compressed Hydrogen Generation .......................................................................................................................... 263 12.10Stack Design and Analysis ........................................................................................................................................ 263 12.11 Conclusion .................................................................................................................................................................... 265 References ................................................................................................................................................................................ 265
P power density, W cm−2 pi partial pressure of species i, atm Pi,α permeance of species i in layer α, mol cm−1 Q heat exchange between PEM-WE and sur-
roundings, J mol−1 〈Q〉 vehicle, or carrier, molecule for diffusing
ion in electrolyte layer rratio of PEM to water partial molar volume R gas constant RI interfacial resistance, Ω T temperature, K Tref reference temperature, 298 K V cell voltage, V V0 thermodynamic (Nernst) cell voltage, V v water convective velocity in PEM, cm s−1 Vmax maximum theoretical cell voltage deter-
mined from ΔH, V VStack stack voltage, V Wt electric work per mol of H2 generation, or
specific energy consumption, J mol−1 Wt total power consumption in water electro-
lyzer, W xi mole fraction of species i
β degree of acid dissociation in Nafion βρ symmetry factor for electrode reaction/step
ρ, typically 1/2 br
× symmetry factor of the RDS in electrode step ρ, typically 1/2
γM roughness factor, ratio of active ECSA area to MEA area
δratio of mutual to matrix effective diffusion coefficients
ΔGGibbs free energy change KJ mol−1 ΔH enthalpy change KJ mol−1 ε fuel cell efficiency εi Faradaic efficiency εV voltage efficiency εΔG Second law efficiency εΔH First law efficiency ηA anode overpotential, V ηρ overpotential of electrode reaction ρ =
Φρ − Φρ,0, V ηB Ohmic overpotential in electrolyte layer, V ηC overpotential, cathode, V κi,α partition coefficient of species i in layer α Lr forward pre-exponential factor for reaction ρ Lr reverse pre-exponential factor for reaction ρ λ number of water molecules per sulfonic
acid group in Nafion
νρi stoichiometric coefficient of species i in reaction ρ
nre-stoichiometric coefficient of electrons in reaction ρ
n r× ,e-stoichiometric coefficient of electrons in the RDS in electrode reaction ρ
ξelectro-osmotic drag coefficient of water ρM,A anode catalyst metal density, g cm−3 ρM,C cathode catalyst metal density, g cm−3 σB effective electrolyte conductivity, S cm−1 φI fraction of metal surface in contact with
ionomer Φelectrode potential, V Φρ,0 half-cell thermodynamic (Nernst) potential
of electrode reaction ρ, V Fr,0o standard half-cell thermodynamic (Nernst)
potential of electrode reaction ρ, V ωI mass fraction of ionomer in catalyst layer
• rate-determining step 0equilibrium A anode layer B electrolyte layer C cathode layer D diffusion/gas diffusion layer e− electron i species Kkinetic Llimiting o standard conditions ref reference X crossover z charge number ρreaction step, or electrode reaction (anode
or cathode)
AEM anion-exchange membrane DGM dusty-gas model DMFCdirect methanol fuel cell GDL gas-diffusion layer ECSAelectrochemical surface area HER hydrogen evolution reaction HOR hydrogen oxidation reaction LAEliquid alkaline electrolyte LAEWEliquid alkaline electrolyte water electrolyzer
MEA membrane electrode assembly OCV open circuit voltage OR overall reaction OER oxygen evolution reaction ORR oxygen reduction (or electrode) reaction PEM polymer electrolyte membrane PEM-FC polymer electrolyte membrane fuel cell PEM-WE polymer electrolyte membrane water
electrolyzer QE quasi-equilibrium RDS rate-determining step SHE standard hydrogen electrode SPE solid polymer electrolyte TPI three-phase interface
The realization of the so-called hydrogen economy (Bockris, 1975; Turner, 2004; Bockris and Veziroglu, 2007), a potentially environmentally benign and sustainable energy scenario, is predicated on economical and widespread availability of hydrogen as the energy vector. While hydrogen is produced industrially on a very large scale, principally from fossil resources, that is, via natural gas and coal gasification at the moment (Kothari et al., 2008; Holladay et al., 2009), its storage and transportation from such centralized hydrogen generation plants present significant technological and
cost challenges. Consequently, distributed hydrogen generation is attractive, for which polymer electrolyte membrane (PEM), also called solid polymer electrolyte (SPE), water electrolyzers have significant potential, especially when coupled with renewable but intermittent sources of electricity such as solar cells and wind turbines (Turner, 2004; Barbir, 2005; Bockris and Veziroglu, 2007; Levene et al., 2007; Abbasi and Abbasi, 2011; Andrews and Shabani, 2012) (Figure 12.1) to provide carbon-free hydrogen. Another advantage of PEM water electrolyzer (PEM-WE) is that the same stack can serve the dual purpose of hydrogen generation in the electrolysis mode and power generation in the PEM fuel cell (PEM-FC) mode (Choi et al., 2006), that is, as a unitized regenerative fuel cell, or URFC (Mitlitsky et al., 1998; Ioroi et al., 2002). This chapter describes the basic modeling of PEM-WE individual cells or stacks (Selamet et al., 2011), so that appropriate design and analysis may be facilitated. Such quantitative models can also provide insights that can lead to improved performance and design.
