Improvement of the Process Model for the Ohmic Loss of the Proton Exchange Membrane Fuel Cell

The process model is defined as an analytical solution for the governing equations of an electrochemical system which is used to predict the impedance characteristics of the system and identify the relation between different parts of the measured impedances and physicochemical properties and operating conditions [1, 2]. Despite various attempts made towards presenting a process model for proton exchange membrane (PEM) fuel cells, no complete process model is introduced yet [1, 3]. We have focused on developing such a process model by separately modeling the three losses: ohmic, activation, and mass transport. Our first process model of the ohmic loss [3] required an estimation of the water concentration in the catalyst layer which cannot be readily determined experimentally. Moreover, while the water transport in the catalyst layer was considered in the governing equations of the membrane, the water flux from the membrane towards the catalyst layer was not considered in the water flux equation of the catalyst layer. In this study, the ohmic-loss model presented before is improved by calculating the water concentration in the catalyst layer from other inputs as well as considering the water flux from the membrane in the catalyst layer equation. In the new model, the equivalent circuit extracted from the theoretical relation determined for the impedance of the ohmic loss still has the same format as the model presented before [3] (see Figure 1). However, the elements of the equivalent circuit have different theoretical definitions.

In the following equations, subscripts m, cl, and GDL represent the membrane, catalyst layer and cathode gas diffusion layer properties, respectively. l, D, M, F, T and j denote the thickness, diffusion coefficient, molecular mass, Faraday’s constant, temperature and current density, respectively. ρ, σ and λpresent the density, electrical conductivity and water content, respectively. Also,

a = 0.5193 exp(1268(1/303-1/T))

 b = 0.326 exp(1268(1/303-1/T))

 α = 2.5/(22F)

 β = ρ_mD_m/M_m

The model is compared against the measured impedances obtained for a 7.98-cm²cell operated at the 90% relative humidities for the anode and cathode, three different temperatures (65 °C, 70 °C and 75 °C), and two potentials (0.7 V and 0.75 V). The measured impedances are reported in the frequency span of 10-0.01 Hz as the ohmic loss is dominant in this range [3]. The results in Figure 2 show an excellent agreement between the theoretical predictions and the measured impedances.

References

1. S.M. Rezaei Niya, M. Hoorfar, J. Power Sources, 240, 281 (2013).
2. P. Agarwal, M. Orazem, J. Electrochem. Soc., 139, 1917 (1992)
3. S.M. Rezaei Niya, M. Hoorfar, Electrochimica Acta, 120, 193 (2014).