On Modeling Multi-Component Diffusion Inside the Porous Anode of Solid Oxide Fuel Cells Using Fick’s Model

Stefan-Maxwell Model (SMM) and simple Fick’s Model (FM) type of relations both including Knudsen diffusion for the calculation of species mole fraction distribution inside the porous anode of a solid oxide fuel cell (SOFC) were compared and it was found that at low current densities the models agree well but as current increases the differences also increase. Based on the findings an empirical correction is proposed for the effective diffusivity used in Fick’s Model. The corrected diffusivity coefficient gave better agreement with the Stefan-Maxwell model and even at higher current densities the error is less than 5%. This correction was implemented via a three-dimensional, in-house SOFC simulation code (DREAM-SOFC) which uses Fick’s Model type relations for diffusion flux calculations. The code also takes into account methane steam reforming (MSR) and water gas shift (WGS) reactions and the electrochemical oxidation of both H₂ and CO. As an application, a SOFC button cell which is being tested at West Virginia University was simulated. The results with and without the proposed correction for effective diffusivity are compared.