Mathematical modeling of mass and charge transport and reaction in a solid oxide fuel cell with mixed ionic conduction

A mathematical model for the description of transport phenomena and reactions in an innovative solid oxide fuel cell (called IDEAL-Cell) under steady-state conditions is presented. This cell is characterized by an intermediate porous composite layer (called central membrane) between cathodic and anodic compartments, which shows mixed conduction of protons and oxygen ions and offers active sites for their recombination to form water vapor. This paper presents an original model of charge transport and reaction in the central membrane. The model, based on local mass and charge balances, accounts for mixed conduction in the solid phase, diffusion and convection in the gas phase and reaction at the solid/gas interface. The model domain is resolved in a continuum approach by using effective properties related to morphology and material properties through percolation theory. The model predictions are successfully compared with experimental data, which provide an estimate of the kinetic parameter of the water recombination reaction. Simulations show a strong dependence of predicted results on the kinetic constant of the water incorporation reaction and the effective conductivities. A design analysis on porosity, thickness, particle dimension, composition of central membrane and cell radius is performed and an optimal membrane design is obtained.