Multi-scale mathematical modeling of methane-fueled SOFCs: Predicting limiting current density using a modified Fick's model

Highlights: • Effect of limiting current density is captured for methane contained syngas fuel. • A multi-scale modeling framework by taking into account the limiting current density. • Extent of H₂ oxidation is obtained by fuel utilization for carbon formation analysis. • Due to shortcoming of dusty gas model in predicting limiting current density a modified Fick's model is adopted. - Abstract: In this work, a direct internal reforming methane-fed solid oxide fuel cell based on a multi-physics channel-level mathematical model considering the effect of limiting current density, is studied. A modified Fick's model is adopted to refine the gas species concentration at the triple phase boundary. The model assumes competitive absorption of reactants followed by surface diffusion to the reactive sites. The percolation theory is employed to model the micro-scale behavior of the cell. Safe operations of the cell in terms of carbon deposition boundaries for different operating conditions by obtaining the extent of hydrogen oxidation based on fuel utilization are also discussed. A quantitative analysis is presented to show the effects of critical system parameters on the output variables of interest. Porosity and particles size from the micro-model as well as fuel utilization, temperature and pre-reforming rate from the macro-model are some of those estimated parameters. The obtained results show that the suggested rate limiting mechanism based on Fick's model more accurately predict the effect of limiting current density compared to those of dusty gas model. Further analysis illustrate that the limiting current density increases in both cases of higher inlet fuel concentrations and lower fuel utilizations. In addition, increasing pre-reforming rate and current density causes the system efficiency to diminish while power density is improved.