Mathematical modeling of mass and charge transport and reaction in a solid oxide fuel cell with mixed ionic conduction
Highlights
► IDEAL-Cell is an SOFC concept experimentally proven operating in the range 600–700 °C. ► A model for the central membrane, the innovative part of the IDEAL-Cell, is presented. ► Model of transport phenomena and reactions under steady-state in continuum approach. ► Simulations show the strong dependence of results from parameters a priori unknown. ► Optimal porosity, particles radius and cell dimensions obtained by design analysis.
Introduction
Fuel cells are electrochemical devices which convert the chemical energy of a combustible and a combustive agent (e.g., hydrogen and air, respectively) directly into electric energy, without passing through a Carnot thermodynamic cycle, thus increasing the energetic efficiency of the process and reducing pollution levels in exhaust gases (Larminie and Dicks, 2003). Among various types of fuel cells, Solid Oxide Fuel Cells (SOFCs) and Proton Conducting Solid Oxide Fuel Cells (PCFCs) have attracted research and technology interest due to high expected performance and efficiency.
The Innovative Dual mEmbrAne fueL Cell (IDEAL-Cell) is a new SOFC concept operating in the temperature range of 600–700 °C (Thorel et al., 2009). It consists in the junction between the anodic part of a PCFC (i.e., anode and dense protonic electrolyte) and the cathodic part of an SOFC (i.e., cathode and dense anionic electrolyte) through a porous composite layer (called central membrane, CM), made of proton-conducting and anion-conducting phase. At the anode, hydrogen is converted into protons while at the cathode molecular oxygen is converted into oxygen ions. Protons and oxygen ions migrate through their respective electrolytes towards the CM wherein they react to produce water vapor (Fig. 1).
The water recombination reaction occurs in the CM rather than at one of electrodes as in common SOFC and PCFC configurations. As a consequence, the generation of corrosive mixtures of water with hydrogen or oxygen is avoided, safeguarding the interconnect materials. At electrodes water vapor does not dilute reactants, thus they can be recycled to the electrodes without any treatment, while pure water and heat can be recovered from the CM. In principle, the IDEAL-Cell performance can be improved beyond either SOFC and PCFC performance since anode, cathode and CM are independent and can therefore be fully optimized for their individual purposes, that is, the delivery and conversion of reactants into ions at the electrodes and production and discharge of water vapor in the CM.
The CM represents the main innovative component of the IDEAL-Cell since electrodes are similar (though optimized) to those used in SOFC and PCFC configurations. The CM shows mixed conduction of oxygen ions and protons. Within the layer, ions react at the active sites to produce water vapor, which leaves the CM through the pores. The CM is an electrochemical system in which mixed ionic conduction, mass transport in the gas phase and reaction simultaneously occur.
Mixed ionic conduction and water recombination from protons and oxygen ions are the peculiar features of the IDEAL-Cell. They occur neither in SOFC nor in PCFC, and for this reason they have not attracted attention before.
Due to mixed ionic–protonic conduction in the CM, the IDEAL-Cell is an original concept of a fuel cell with three chambers for separately feeding fuel (at the anode) and air (at the cathode) and removing produced water (at the CM). This cell concept was demonstrated by a set of dedicated experiments (Thorel et al., 2009). Being the objective of these experiments the proof of concept of the IDEAL-Cell, the cell design was not optimized, resulting in thick layers for different compartments and poor electrochemical performance. Much effort is currently being dedicated to the shaping of performing cells, and the objective of the model presented in this paper is, besides allowing more fundamental interpretation of the experimental findings, providing a tool to support material and cell design. To this end, a mathematical model for the description of simultaneous mixed ionic conduction and electrochemical reaction in a porous composite layer was developed. The model is based on charge and mass balances in a continuum approach, which describes the porous composite structure as a continuum characterized by effective transport and kinetic parameters (conductivities, reaction constants, gas diffusivities, etc.). Despite its simplifications, this approach has been employed in several modeling studies of composite electrodes yielding valuable results (Costamagna et al., 1998, Kenney and Karan, 2007, Zhu and Kee, 2008, Nicolella et al., 2009, Ho et al., 2009, Bessler et al., 2010). The continuum model is then a mechanistic model, that is, based on the physical and chemical representation of the phenomena involved in the cell, which describes the reacting system by local partial-differential balance equations for species participating to the reactions.
The presented model is the extension and the refinement of a previous model of the CM (Ou et al., 2009). In particular, the current model is able to reproduce the experimental behavior of the IDEAL-Cell and to elucidate the key factors (e.g., structural and geometrical parameters, operating conditions, etc.) governing the cell performance. Hence, this refined model has been developed in order to reach a better physical description of the system, to focus on sensitive parameters, to perform design analyses for the improvement of cell performances, and finally to extend the results of the existing model (specifically tailored on the CM of the IDEAL-Cell) for description of a general porous composite system showing simultaneous mixed ionic conduction and electrochemical reaction.
Section snippets
General aspects
The CM is a composite layer made of proton-conducting and anion-conducting particles randomly distributed and sintered to give enough porosity for water vapor transport towards the surrounding gas phase. The recombination reaction between protons, coming from the anodic compartment and carried by the proton-conducting phase (PCP), and oxygen ions, coming from the cathodic compartment and carried by the anion-conducting phase (ACP), occurs at the three-phase boundary (TPB) among PCP, ACP and gas
Results and discussion
The model of the CM, that is, the system of Eqs. (27), (28), (29), (30), (31) coupled with relationships of fluxes and kinetics, is implemented and solved by using COMSOL Multiphysics 3.5 (based on the finite element method) in 2D due to the symmetry of the geometry. The main model outcome is itot, that is, the total current density passed through the axial direction of the CM referred to either electrode or cell area. Cell and CM polarization resistances (Rpcell and RpCM), that is, the main
Conclusions
A mathematical model of the central membrane (CM) of the IDEAL-Cell was developed in this paper. The CM was modeled using a continuum approach describing a mixed ionic conduction layer where chemical and electrochemical reactions, coupled with charge and mass transports of reacting species, occur. The model consists of a system of local charge and mass balance differential equations under steady-state conditions. Geometrical parameters were obtained using morphological models based on
Nomenclature
- ai(K)
activity of species i in phase K (dimensionless)
- avPCP
PCP surface area exposed to gas phase per unit volume (m−1)
- B
permeability coefficient (m2 s−1)
- cO
molar ratio of oxygen ions to perovskite cells (dimensionless)
- cOH
molar ratio of protonic defects to perovskite cells (dimensionless)
- cVO
molar ratio of oxygen vacancies to perovskite cells (dimensionless)
- Cw,PCP
volume concentration of incorporated water in PCP (mol m−3)
- DiK
Knudsen diffusion for species i (water vapor or carrier gas) (m2 s−1)
- dp
mean
Acknowledgements
This research has received funding from the European Community's FP7 Program under grant agreement No 213389.
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