Multiphysics Modeling and Simulation of a Solid Oxide Electrolysis Cell D. Grondin*,1, J. Deseure1, A. Brisse2, M. Zahid2 and P. Ozil1 1Laboratoire dlectrochimie et de Physico-chimie des Matriaux et des Interfaces (LEPMI), UMR 5631 CNRS-INPG-UJF, 2European Institute for Energy Research (EIFER) *Corresponding author: LEPMI, BP 75, 38402 Saint Martin dHres, France, [email protected] Abstract: Based on solid oxide fuel cell (SOFC) technology, solid oxide electrolysis cell (SOEC) offers an interesting solution for mass hydrogen production. This study proposes a multiphysics model to predict the SOEC behavior, based on similar charge, mass and heat transport phenomena as for SOFC. However the mechanism of water steam reduction on Nickel/Yttria Stabilized Zirconia (YSZ) cermet is not yet clearly identified. Therefore a global approach and several electrochemical kinetic equations were used for modeling. The simulated results demonstrated that a Butler-Volmers equation including concentration overpotential provides an acceptable estimation of the experimental electric performance. These simulations highlighted three thermal operating modes of SOEC and showed that temperature distribution depends on gas feeding configurations. Keywords: hydrogen production, solid oxide electrolysis cell, multiphysics modeling, diffusion phenomena, electrochemical kinetic description 1. Introduction
Recently, significant research efforts are achieved to develop hydrogen economy. Hydrogen is a promising energy carrier due to its abundance, mainly in water, the high value of released energy (120 MJ/kg) and the absence of greenhouse gas emissions after combustion. Contrary to fossil fuels, hydrogen does not exist in a native state and so its use requires its production. Nowadays, the industrial mass production of hydrogen is mainly based on hydrocarbons reforming. However water electrolysis could be the most convenient production process if it uses a clean renewable energy source. From a thermodynamical point of view, water electrolysis is more interesting at higher temperature because of a lower electricity demand. Based on the Solid Oxide Fuel Cell
(SOFC) technology, a Solid Oxide Electrolysis Cell (SOEC) is a device that allows electrochemical water splitting at high temperature (700 900C). The cell consists on the assembly of a three-layer region involving two ceramic electrodes separated by a dense ceramic electrolyte made in the same materials as for a SOFC (Fig. 1).
Figure 1. Schematic view of a SOEC
The hydrogen electrode is usually composed
of nickel and yttrium stabilized zirconia (YSZ) cermet. The electrolyte is made of YSZ and the oxygen electrode is based on perovskite-type oxides, which is usually strontium-doped lanthanum manganite La1-xSrxMnO3 (LSM). The electrochemical reactions in SOEC electrodes are as it follows: Cathode: H2O + 2e- H2 + O2- (1) Anode: O2- O2 + 2e- (2) At cathode, water steam is reduced and oxygen ions are produced (1). Then, oxygen ions migrate through the electrolyte to the anode where oxygen molecules and electrons are released (2). So, the ionic and electronic currents produced and consumed at electrodes cross the whole SOEC and generate heat sources due to the internal cell resistance. If the cell voltage value is H/nF, the heat source exactly provides the heat removed by the steam electrolysis process
Excerpt from the Proceedings of the COMSOL Conference 2008 Hannover
(thermo neutral voltage). For upper and lower cell potential values, the operating modes are respectively endothermic and exothermic ones.
The first works devoted to SOEC were mainly experimental ones and were carried out in the 80s in a context of a relevant decline in oil production. However these studies have been suspended until the recent development of SOFC and the investigation of reversible SOFC. Many computing studies showed a great relevance for understanding and optimizing SOFC [1]. Computation fluid dynamics model is a quite recent method to investigate the SOEC stack behavior. Most of SOEC models are based on models previously developed for SOFC. Indeed, a 3-D SOEC model was already developed in order to investigate the effects of operating conditions on current densities and temperature distributions. Nevertheless, few works are available by literature regarding the water reduction kinetic on Nickel/YSZ cermet. Some experimental studies were carried out and corresponding reaction mechanisms were suggested but no further studies confirmed these proposals.
More recently, two electrochemical models were developed for an electrolyte supported cell and simulations were compared to experimental data. Both models seem to provide quite accurate predictions although there are different. Only one theoretical study was proposed for a cathode-supported SOEC, but without any comparison with experimental data. The major part of available models uses a Butler-Volmers law for activation overpotential calculation. However this approach seems to be not precise enough since some earlier studies demonstrate that several chemical and electrochemical steps should occur.
This study proposes a multiphysics model of a single SOEC. Several electrochemical kinetic laws are used to predict the electric behavior of the cell under study. The Butler-Volmer law pertinence is discussed for different operating conditions. Finally, the effect of feeding configuration on temperature distribution is presented. 2. Nomenclature A Specific surface area (m/m3) b Tafel slope (V) c Concentration (mol/m3)
Cp Heat capacity (J/mol) d Mean diameter (m) D Diffusion coefficient (m/s) F Faraday constant (96485 C/mol) j Electrochemical current density (A/m) J Total current density (A/m) j0 Exchange current density (A/m) K Permeability (m) M Molecular weight (kg/mol) p Pressure (Pa) R Universal gas constant (8.314 J/mol/K) S Current source (A/m3) V Potential (V) T Temperature (K) u Gas velocity (m/s) y Molar fraction (-) Greeks letters Charge transfer coefficient (-) Reaction rate (mol/m3/s) S Water entropy formation (J/mol/K) Porosity (-) Overpotential (V) Thermal conductivity (W/m/K) Gas viscosity (Pa.s) Gas density (kg/m3) Conductivity (S/m) Tortuosity (-) Heat source (W/m3) Subscripts a Anode atm Atmospheric c Cathode d Darcy e Electrolyte el Electric eq Equivalent g Grain H2 Hydrogen H2O Water i,j Binary coefficient of species i,j i,k Knudsen coefficient of species i io Ionic i,0 Bulk concentration of species i N2 Nitrogen o Operating temperature ox Oxidant species O2 Oxygen p Pore red Reductive species TBP Triple Phase Boundary 0 Inlet condition Superscripts eff Effective
3. Governing equations
The physical phenomena taking place within a SOEC were separately studied. Model accuracy depends on the selected mathematical description. SOFC and SOEC are roughly similar system. As a first step, the mathematical model developed for SOFC can be used for SOEC because of the similitude of both systems. The multiphysics approach takes into account dependence between phenomena. The main assumptions concern gas velocities along the gas channels, electrodes ionic conductivities and material thermal conductivities that are all supposed to stay constant. 3.1 Charge balance
SOEC electrodes are mixed electronic-ionic conductors. The transport of each type of charge particle (e-, O2-) is described by an Ohmics law expressed as:
( ) i,a,cii SV. = (3) S being the current source term defined by relation (4).
ca,TPBca,i, jAS = (4) The electrochemical reaction is assumed to
take place at the triple phase boundary (TPB) i.e. the contact area between gas, electric and ionic conductors. The specific surface area (ATPB) is the surface generated by these contact areas in the electrode volume. TPBs are assumed to be uniformly distributed in the electrode volume. For simulations, ATPB will be included in the exchange current density value. In the same electrode, current source related to anion consumption/production is the opposite of that for electron (5). (5) ioel -SS =
In the electrolyte, no current source term is considered and a pure ionic conductivity is assumed. Electrodes electric and electrolyte ionic conductivies are considered as temperature dependent. 3.2 Mass balance
Mass transport is mainly driven by diffusion convection in the whole cell and can be described by:
( ) += cu.cD. (6) this expression differing according to the considered part of the cell.
3.2.1 Hydrogen side
In the case under study, water steam is
provided with hydrogen and nitrogen at cathode side. Stefan-Maxwell diffusion model is used regarding the significant difference between molecular weight of species. Moreover, Knudsen diffusion should be considered in the electrode that is a porous media. Thus, the dusty-gas model (DGM) is used at cathode. Such model seems to provide the most accurate description of mass transport for SOFC anode [2]. The DGM may be summarized in the following equivalent effective diffusion coefficient [2]:
effHO,H
OH
effNO,H
effHO,H
NeffNO,HkO,H
effeq
22
2
2222
2
222
Dy
D1
D1)y(1
D1
D1D
++=
(7)
with 21
H
OH
2
2
MM
1
= (8)
The Knudsen diffusion coefficient of the species i (Di,k) is calculated from relation (9)
ipki, M
8RT3dD = (9)
while the mean pore diameter is determined considering electrode characteristics (10).
gp d1
32d
= (10)
Where the effective diffusion coefficient is the diffusion coefficient in a porous
