Modeling ammonia-fueled co-flow dual-channel protonic-ceramic fuel cells

ABSTRACT

This paper reports the model development for a dual-channel protonic-ceramic fuel cell (PCFC) operating on ammonia fuel. The model considers the coupled interactions of several physical and chemical processes, including three-dimensional heat conduction within the bipolar plates and the membrane-electrode assembly (MEA), one-dimensional flow within the fuel and air channels, detailed heterogeneous catalytic reactions within the porous composite anode structure, Butler–Volmer representation of the charge-transfer chemistry, and Nernst–Planck transport of three charged defects (protons, oxygen vacancies, and small polarons) within the dense electrolyte membrane. The membrane-electrode assembly is composed of a Ni-BCZYYb ($\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{e}}_{0.7}\mathrm{Z}{\mathrm{r}}_{0.1}{\mathrm{Y}}_{0.1}\mathrm{Y}{\mathrm{b}}_{0.1}{\mathrm{O}}_{3-\delta }$) anode, a BCZYYb electrolyte membrane, and a BCFZY ($\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{o}}_{0.4}\mathrm{F}{\mathrm{e}}_{0.4}\mathrm{Z}{\mathrm{r}}_{0.1}{\mathrm{Y}}_{0.1}{\mathrm{O}}_{3-\delta }$) cathode. Chemical and physical parameters for the MEA model are established using previously published button-cell data. One aspect of the study is to investigate the partial ammonia decomposition upstream of the fuel cell. Such fuel cracking increases the H${ }_2$ content of the fuel entering the PCFC, which may have benefits. However, endothermic ammonia pyrolysis within the composite anode structure assists with thermal control of the cell. The dual-channel model can be considered as the unit cell of a full fuel-cell stack.

KEYWORDS:

• Protonic ceramic fuel cell
• ammonia
• Co-flow channels
• NH₃ cracking

Acknowledgment(s)

This work was supported by the Advanced Research Projects Agency-Energy (ARPA-E) through the REFUEL program (Award No. DE-AR0000808). We gratefully acknowledge insightful discussions on protonic ceramics and ammonia chemistry with our colleagues Profs. Sandrine Ricote, Ryan O’Hayre, Neal Sullivan, Robert Braun and Colin Wolden.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

$A_{\mathrm{c}}$ Channel cross-section flow ara

$B_{\mathrm{g}}$ Permeability

$A_i$ Pre-factor of the Arrhenius form of the $i$ reaction

$C_{\mathrm{s}}$ Solid-phase specific heat capacity

$D_{\mathrm{h}}$ Channel hydraulic diameter

$D_k$ Diffusion coefficients of defects

$D_k^{\circ }$ Pre-factors for defect diffusion coefficients

$D_{k,\mathrm{K}\mathrm{n}}^{\mathrm{e}}$ Effective Knudsen diffusion coefficients

$D_{k\mathrm{\ell }}^{\mathrm{e}}$ Effective binary diffusion coefficients

$E$ Total internal energy of gas mixture

$e$ Specific internal energy of gas mixture

$E_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}$ Cell potential

$E_k$ Activation energy of defect diffusion coefficients

$E^{\circ }$ Standard electric-potential difference

$E^{\mathrm{e}\mathrm{q}}$ Equilibrium electric-potential difference

$E_{\mathrm{a}}^{\mathrm{e}\mathrm{q}}$ Equilibrium electric-potential difference in the anode

$E_{\mathrm{c}}^{\mathrm{e}\mathrm{q}}$ Equilibrium electric-potential difference in the cathode

$F$ Faraday constant

$f$ Channel flow friction factor

$\mathrm{G}z$ Graetz number

$h$ Heat enthalpy of the gas-phase mixtures

$h_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}$ Convective heat-transfer coefficient

$h_k$ Species heat enthalpy

$i_{\mathrm{B}\mathrm{V}}$ Charge-transfer rate in Butler-Volmer equation

${\mathbf{i}}_{\mathrm{c}}$ Charge-flux due to defect concentration gradients

$i_{\mathrm{e}}$ Current density

${\mathbf{i}}_{\mathrm{e}\mathrm{d}}$ Current density in the electronic-conducting phase

${\mathbf{i}}_{\mathrm{e}\mathrm{l}}$ Current density in the ionic-conducting phase

$i_0$ Exchange current density

$i_0^{\ast }$ Prefactor for exchange current density

$i_0^0$ Exchange current-density factor

${\mathbf{j}}_k$ Gas-phase species mass flux

${\mathbf{J}}_k$ Species mole flux

$J_k^{\mathrm{M}}$ Gas-phase species mole flux from MEA

$k_{\mathrm{b},i}$ Backward rate constant of $i$-th reaction

$k_{\mathrm{b},{\mathrm{H}}_2}$ Backward rate constant of ${\mathrm{H}}_2$ incorporation

$k_{\mathrm{b},{\mathrm{O}}_2}$ Backward rate constant of ${\mathrm{O}}_2$ incorporation

$k_{\mathrm{b},{\mathrm{H}}_2\mathrm{O}}$ Backward rate constant of ${\mathrm{H}}_2\mathrm{O}$ incorporation

$k_{\mathrm{b},\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{p}}$ Backward rate constant of trap reaction

$K_{\mathrm{c}}$ Concentration-based Equilibrium constant

$k_{\mathrm{f},i}$ Forward rate constant of $i$-th reaction

$k_{\mathrm{f}}$ Forward rate constant

$k_{\mathrm{f},{\mathrm{H}}_2}$ Forward rate constant of ${\mathrm{H}}_2$ incorporation

$k_{\mathrm{f},{\mathrm{O}}_2}$ Forward rate constant of ${\mathrm{O}}_2$ incorporation

$k_{\mathrm{f},{\mathrm{H}}_{2}O}$ Forward rate constant of ${\mathrm{H}}_2\mathrm{O}$ incorporation

$k_{\mathrm{f},\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{p}}$ Forward rate constant of trap reaction

$K_{\mathrm{g}}$ Number of gas-phase species

$K_{{\mathrm{H}}_2}$ Equilibrium constant of ${\mathrm{H}}_2$ adsorption

$K_{{\mathrm{H}}_2\mathrm{O}}$ Equilibrium constant of ${\mathrm{H}}_2\mathrm{O}$ adsorption

$K_{{\mathrm{O}}_2}$ Equilibrium constant of ${\mathrm{O}}_2$ adsorption

$K_{\mathrm{p}}$ Pressure-based Equilibrium constant

$K_{\mathrm{s}}$ Number of surface-adsorbed species

$L_{\mathrm{a}}$ Anode thickness

$L_{\mathrm{c}}$ Cathode thickness

$L_{\mathrm{e}\mathrm{l}}$ Electrolyte thickness

$\mathrm{N}\mathrm{u}$ Nusselt number

$p$ Pressure

$P_{\mathrm{h}}$ Channel hydrodynamic perimeter

$p_{{\mathrm{H}}_2}$ ${\mathrm{H}}_2$ partial pressure

$p_{{\mathrm{H}}_2}^{\ast }$ ${\mathrm{H}}_2$ reference pressure

$p_{{\mathrm{H}}_2\mathrm{O}}$ ${\mathrm{H}}_2\mathrm{O}$ partial pressure

$p_{{\mathrm{H}}_2\mathrm{O}}^{\ast }$ ${\mathrm{H}}_2\mathrm{O}$ reference pressure

$P_{\mathrm{M}}$ Channel interface perimeter with MEA

$p_{{\mathrm{O}}_2}$ ${\mathrm{O}}_2$ partial pressure

$p_{{\mathrm{O}}_2}^{\ast }$ ${\mathrm{O}}_2$ reference pressure

$\mathrm{P}\mathrm{r}$ Prandtl number

$q$ Convective heat flux of channel flow

$q^{\mathrm{M}}$ Heat fluxes of MEA-channel species transport

$q_{\mathrm{a}}^{\mathrm{M}}$ Heat fluxes of MEA-fuel channel species transport

$q_{\mathrm{c}}^{\mathrm{M}}$ Heat fluxes of MEA-air channel species transport

$q_{\mathrm{M}\mathrm{E}\mathrm{A}}$ Volumetric heat generation rate from MEA

$q_{\mathrm{T}}$ Convective heat flux of channel walls

${\dot{q}}_{{\mathrm{H}}_2}$ Rate of progress of ${\mathrm{H}}_2$ incorporation

${\dot{q}}_{{\mathrm{H}}_2\mathrm{O}}$ Rate of progress of ${\mathrm{H}}_2\mathrm{O}$ incorporation

${\dot{q}}_{{\mathrm{O}}_2}$ Rate of progress of ${\mathrm{O}}_2$ incorporation

${\dot{q}}_{\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{p}}$ Rate of progress of trap reaction

$R$ Universal gas constant

${\dot{r}}_k$ Species production rate

$r_{\mathrm{N}\mathrm{i}}$ Ni particle radius

$r_{\mathrm{B}\mathrm{C}\mathrm{Z}\mathrm{Y}\mathrm{Y}\mathrm{b}}$ BCZYYb particle radius

$r_{\mathrm{B}\mathrm{C}\mathrm{F}\mathrm{Z}\mathrm{Y}}$ BCFZY particle radius

$\mathrm{R}\mathrm{e}$ Reynolds number

${\dot{s}}_k$ Defect production rates

${\dot{s}}_{{\mathrm{O}\mathrm{H}}_{\mathrm{O}}^{\bullet }}$ Production rate of ${\mathrm{O}\mathrm{H}}_{\mathrm{O}}^{\bullet }$

${\dot{s}}_{{\mathrm{O}}_{\mathrm{O}}^{\bullet }}$ Production rate of ${\mathrm{O}}_{\mathrm{O}}^{\bullet }$

${\dot{s}}_{{\mathrm{O}}_{\mathrm{O}}^{\times }}$ Production rate of ${\mathrm{O}}_{\mathrm{O}}^{\times }$

${\dot{s}}_{{\mathrm{V}}_{\mathrm{O}}^{\bullet \bullet }}$ Production rate of ${\mathrm{V}}_{\mathrm{O}}^{\bullet \bullet }$

${\dot{s}}_{{(\mathrm{X}}_{\mathrm{B}}^{\prime }{-\mathrm{O}}_{\mathrm{O}}^{\bullet })}$ Production rate of ${(\mathrm{X}}_{\mathrm{B}}^{\prime }-{\mathrm{O}}_{\mathrm{O}}^{\bullet })$

$T$ Gas-phase temperature

$t$ Time

$T_{\mathrm{a}}$ Fuel channel flow temperature

$T_{\mathrm{c}}$ Air channel flow temperature

$T_{\mathrm{m}}$ MEA temperature

$t_{\mathrm{M}\mathrm{E}\mathrm{A}}$ MEA thickness

$T_{\mathrm{s}}$ Solid-phase temperature

$u$ Channel flow velocity

$V_{\mathrm{m}}$ Lattice molar volume

$\bar{W}$ Mean molecular weight

$W_k$ Species molecular weight

$x$ Spatial coordinate

$X_k$ Species mole fractions

$[X_k]$ Species mole concentrations

$[X_{\mathrm{T}}]$ Total gas-phase mole concentrations

$Y_k$ Gas-phase species mass fractions

$z_k$ Number of charges of $k$ th defect

Greek letters

$\alpha$ Channel aspect ratio

${\beta }_{\mathrm{a}}$ Anodic symmetric factor

${\beta }_{\mathrm{c}}$ Cathodic symmetric factor

$\mathrm{\Gamma }$ Surface site density

$\mathrm{\Delta }{H}^{\circ }$ Standard enthalpies of defect reactions

$\mathrm{\Delta }{S}^{\circ }$ Standard entropies of defect reactions

${\eta }_{\mathrm{a}\mathrm{c}\mathrm{t}}$ Activation overpotential

${\eta }_{\mathrm{a}\mathrm{c}\mathrm{t},\mathrm{a}}$ Activation overpotential within the anode

${\eta }_{\mathrm{a}\mathrm{c}\mathrm{t},\mathrm{c}}$ Activation overpotential within the cathode

${\theta }_k$ Site fractions of surface-adsorbed species

$\lambda$ Gas-phase heat conductivity

${\lambda }_{\mathrm{s}}$ Solid-phase heat conductivity

${\mu }_k$ Species chemical potentials

${\mu }_k^{\circ }$ Species standard-state chemical potentials

${\mu }_{{\mathrm{e}}^{\prime }(\mathrm{e}\mathrm{d})}^{\circ }$ ${\mathrm{e}}^{\prime }(\mathrm{e}\mathrm{d})$ standard-state chemical potentials

${\mu }_{{\mathrm{O}}_{\mathrm{O}}^{\bullet }(\mathrm{e}\mathrm{l})}^{\circ }$ ${\mathrm{O}}_{\mathrm{O}}^{\bullet }(\mathrm{e}\mathrm{l})$ standard-state chemical potentials

${\mu }_{{\mathrm{O}}_{\mathrm{O}}^{\times }(\mathrm{e}\mathrm{l})}^{\circ }$ ${\mathrm{O}}_{\mathrm{O}}^{\times }(\mathrm{e}\mathrm{l})$ standard-state chemical potentials

${\rho }_{\mathrm{s}}$ Solid-phase density

${\tau }_{\mathrm{w}}$ Channel wall shear stress

$\mu$ Gas-phase viscosity

${\rho }_{\mathrm{g}}$ Gas-phase mass density

${\rho }_{\mathrm{s}}$ Solid-phase mass density

${\sigma }_{\mathrm{e}\mathrm{d}}$ Electric conductivity in the electronic-conducting phase

${\sigma }_{\mathrm{e}\mathrm{l}}$ Electric conductivity in the ionic-conducting phase

${\mathrm{\Phi }}_{\mathrm{e}\mathrm{d}}$ Electric potential in the electronic-conducting phase

${\mathrm{\Phi }}_{\mathrm{e}\mathrm{l}}$ Electric potential in the ionic-conducting phase

${\mathrm{\Phi }}_{\mathrm{e}\mathrm{d}}^{\mathrm{e}\mathrm{q}}$ Equilibrium electric potential in the electronic-conducting phase

${\mathrm{\Phi }}_{\mathrm{e}\mathrm{l}}^{\mathrm{e}\mathrm{q}}$ Equilibrium electric potential in the ionic-conducting phase

${\varphi }_{\mathrm{g}}$ Porosity

${\varphi }_m$ Volume fraction of phase $m$

${\varphi }_{\mathrm{N}\mathrm{i}}$ Ni volume fraction

${\mathrm{\Phi }}_{\mathrm{a},\mathrm{a}\mathrm{c}}$ Electric potential at the anode-current collector interface

${\mathrm{\Phi }}_{\mathrm{c},\mathrm{c}\mathrm{c}}$ Electric potential at the cathode-current collector interface