High Efficiency Operation Conditions in Polymer Electrolyte Fuel Cell System with Hydrogen Circulation
Authors: Ma Yulei , Yamaguchi Kazuhiro , Kageyama Miho , Kawase Motoaki 
Published: December 2020

Introduction
Water management is an essential problem to achieve PEFC’s maximum performance. Hydrogen circulation is one of methods to humidify the cell with water produced in oxygen reduction reaction (ORR), while the overall hydrogen utilization can be 100 %. Additionally, by controlling the operation conditions such as gas flow direction, one-pass conversion and humidifying temperature, the cell performance can be improved. The purpose of this study is to investigate the effects of these parameters, and to optimize the cell performance. Water transport in the PEFC system is analyzed in the through-plane direction at steady state, when the dry hydrogen and humidified air are supplied to an 80 oC isothermal system, and the molar flowrate ratio of hydrogen to oxygen at cell inlet is 2.
Numerical Simulation
Gas channels were regarded as straight lines and the gas flow inside was plug flow. The water permeation flux through PEM, which is determined by electroosmosis and back diffusion, was calculated by Eq. (1) [1]. The properties of PEM were assumed as constants, and the equilibrium moisture content λ was assumed and calculated by Springer’s equation [1].
Local current density i was calculated by Eq. (2) [2], where k
vcm
represents 1st-order cathode reaction rate constant per layer volume, which is the function of IR-corrected cell voltage E
cm
expressed by Eq. (3), p
Oc
represents partial pressure of oxygen at cathode catalyst layer (CCL) - gas diffusion layer (GDL) boundary and F
e is effectiveness factor of CCL, represents the ratio of observed rate to intrinsic rate. According to our previous work, F
eis only determined by 4 dimensionless moduli M
Om
, M
pm
, P
Om
and y
Oc

[2]. M
Om
represents the ratio of oxygen diffusion resistance to ORR resistance (Thiele modulus). M
pm
represents the ratio of proton transport resistance to ORR resistance (our modulus). P
Om
represents the ratio of convection to oxygen diffusion (Péclet mumber).
Results and Discussion
Fig. 1 shows the distribution of relative humidity (RH) along gas channels, and water permeation flux through PEM in cases of co-current and countercurrent at the fixed one-pass conversion and current density. The total water permeation rate is 0 since the make-up H2 supplied into the system is dry and no water leaves the cell at steady state. The RH in cathode gas channel increases monotonically in case of countercurrent; the RH has a maximum value in case of co-current, since the water permeation flux varies in a greater region than co-current.
The effect of one-pass conversion on performance is the competition of mass transport and reaction. As shown in Figs. 2 and 3, when the one-pass conversion increases at the fixed cell voltage, the average RH in gas channels increase, due to the decrease in gas flowrate in the gas channels. However, the inflection points in Fig. 2 exist around x
H = 0.3, which indicates when the one-pass conversion is lower than 0.3, the gas flowrate is too high for water produced in ORR to humidify anode gas sufficiently. As the RH increasing, the average proton conductivity of PEM increases and average oxygen partial pressure in cathode gas channel decreases, as shown in Figs. 4 and 5, which indicates the proton transport is enhanced due to the humidification by water produced in ORR, and the reaction rate is reduced since the concentration of reactant decreases. As the result, by increasing the one-pass conversion, the current density firstly increases and then decreases, as shown in Fig. 6.
In addition, when the one-pass conversion is high enough, the RH in gas channel will reach 1, and flooding will happen more likely inside the cell than at the exit in case of countercurrent, since RH has a maximum value in gas channel. To prevent flooding, the maximum operation conversion should be lower than the value calculated by Eq. (4), according to the material balance, where the RH2
[C] represents the cathode outlet RH, which is 1 for co-current and lower than 1 for countercurrent.
Conclusions
The optimized one-pass conversion is determined by the competition of mass transfer and reaction. As the one-pass conversion increases, the proton transfer resistance decreases due to the humidification by water produced in ORR, and reaction rate decreases due to the consumption of oxygen. The optimized one-pass conversion should be higher than 0.3 to ensure the sufficient humidification, and lower than the value calculated from Eq. (4) to prevent flooding.
References
[1] E. Springer et al., J. Electrochem. Soc., 138, 8 (1991)
[2] M. Kawase et al., AIChE J. 63(1), 249-256 (2017)

Figure 1