Sensitivity Based Order Reduction of a Chemical Membrane Degradation Model for Low-Temperature Proton Exchange Membrane Fuel Cells

The chemical degradation of the perfluorinated sulfonic acid (PFSA) ion-exchange membrane as a result of an attack from a radical species, originating as a by-product of the oxygen reduction reaction, represents a significant limiting factor in a wider adoption of low-temperature proton exchange membrane fuel cells (LT-PEMFCs). The efficient mathematical modeling of these processes is therefore a crucial step in the further development of proton exchange membrane fuel cells. Starting with an extensive kinetic modeling framework, describing the whole range of chemical processes leading to the membrane degradation, we use the mathematical method of sensitivity analysis to systematically reduce the number of both chemical species and reactions needed to efficiently and accurately describe the chemical degradation of the membrane. The analysis suggests the elimination of chemical reactions among the radical species, which is supported by the physicochemical consideration of the modeled reactions, while the degradation of Nafion backbone can be significantly simplified by lumping several individual species concentrations. The resulting reduced model features only 12 species coupled by 8 chemical reactions, compared to 19 species coupled by 23 reactions in the original model. The time complexity of the model, analyzed on the basis of its stiffness, however, is not significantly improved in the process. Nevertheless, the significant reduction in the model system size and number of parameters represents an important step in the development of a computationally efficient coupled model of various fuel cell degradation processes. Additionally, the demonstrated application of sensitivity analysis method shows a great potential for further use in the optimization of models of operation and degradation of fuel cell components.