Analytical calculation of electrolyte water content of a Proton Exchange Membrane Fuel Cell for on-board modelling applications

This paper proposes an analytical model of the water content of the electrolyte of a Proton Exchange Membrane Fuel Cell. The model is designed by accounting for several simplifying assumptions, which make the model suitable for on-board/online water management applications, while ensuring a good accuracy of the considered phenomena, with respect to advanced numerical solutions. The achieved analytical solution, expressing electrolyte water content, is compared with that obtained by means of a complex numerical approach, used to solve the same mathematical problem. The achieved results show that the mean error is below 5% for electrodes water content values ranging from 2 to 15 (given as boundary conditions), and it does not overcome 0.26% for electrodes water content above 5. These results prove the capability of the solution to correctly model electrolyte water content at any operating condition, aiming at embodiment into more complex frameworks (e.g., cell or stack models), related to fuel cell simulation, monitoring, control, diagnosis and prognosis.