Two-Phase Modeling of a PEMFC with CO Poisoning Effect

In this chapter, we extended our previous study to a one-dimensional, two-phase mathematical model to analyze the poisoning effect of anode CO kinetics on the performance of a PEM fuel cell using dilute hydrogen feed. Both vapor and liquid water transport are examined inside the cell. Figure 3.1 illustrates the presented simulation model of the PEM fuel cell, including the anode catalyst layer, the membrane and the cathode catalyst layer. Some basic assumptions were made as following:

1. Steady state.

2. One dimensional Cartesian coordinate system.

3. Isothermal and isobaric.

4. Ideal gas.

5. Catalyst layer and membrane are isotropic.

6. Only diffusion mechanism is considered.

7. Permeability is constant

8. Physical domain includes anode catalyst layer, membrane and cathode catalyst layer.

3.1 Theoretical Model

The two-phase theoretical CO poisoning behavior is investigated. Table 3.1 presents the governing equations which were used in the theoretical model where gaseous hydrogen concentration CH2; the gaseous oxygen concentration CO2; the

gaseous carbon monoxide concentration CCO; the vapor concentration Cwg; the concentration of liquid water in the Nafion phase Cwn; the saturation of liquid water s and the ionic potential φ. The variables must be solved for simultaneously. The steady state hydrogen coverage θ_H and carbon monoxide coverage θ_CO are expressed as

( )

in which φs is the phase potential of solid phase of electrode. The transport of fuel, oxidant and vapor water are expressed as

( )

[

_CL

]

_i

i

i D s C

N =− ε 1− ^1.5∇ (3-3)

where N is the flux for fuel, oxidant and vapor water and ε_CLis the gaseous porosity.

The water transfer rate between the gas and liquid interfacial phase used by He et al.

[21] and Lin et al. [27] and is used herein. The first and second term on the right hand side represents the condensation and

evaporation rates, respectively. The transport of liquid water in the membrane is driven by the combined effect of diffusion and electro-osmotic drag [80]:

d catalytic layer is described by the simplified correlation K_w

( )

s equals a constant value [21]. Equation (3-6) describes the liquid water transport in the cathode catalyst layer.

in which ρw is the density of liquid water, μw is the viscosity, Kw is the permeability, Mw is the molecular weight, n_d,CL is the coefficient of electro-osmotic drag, RO2is the reaction rate of oxygen and Pc is the capillary pressure. In the present theoretical study

(

−dP_c ds

)

is treated as a constant and Rw is calculated from Eq. (3-4).

Protons were produced from hydrogen oxidation reactions at the anode catalyst layer and then transported toward fuel cell cathode through membrane. The current density at the membrane can be expressed as [27]:

φ

∇

−

= k_n

i (3-7)

Where kn is the membrane conductivity. In the anode catalyst layer, the distributions of the current densities of hydrogen and carbon monoxide are

( )

where k and _eH k_eCO are the hydrogen and CO electro-oxidation rate constants [53];

φ represents the electrolytic phase potential and U is the thermodynamic ₀ equilibrium potential [81]. The reaction rates of hydrogen, CO and oxygen within in the catalytic layers are

( )

_⎟^⎟

where θ_CO is the average value of CO coverage which was calculated from the anode CO coverage θ_CO. Table 3.2 lists all of the boundary conditions used in this

simulation model.

3.2 Numerical Method

In this chapter, the governing equations in table 3.1 are second order ordinary differential equations. Central difference scheme is applied to solve the dependent variables. The transport equations for hydrogen and carbon monoxide can be rewritten as: The dependent variables must be solved simultaneously. Other variables such as oxygen, proton, vapor and liquid water can be treated by using the same finite difference method.

3.3 Results and Discussion

A one-dimensional, two-phase mathematical model under various CO concentrations and hydrogen dilutions are employed to simulate hydrogen fuels from the reformer, and thus elucidate the poisoning effect on the performance of the fuel cell. The reactant gas distribution, the coverage and the liquid water distribution are investigated under the CO poisoning. The feed streams were fully saturated with

parameters used in this work.

Figure 3.2 plots the hydrogen coverage across the anode catalyst layer with various CO concentrations and hydrogen dilutions. The hydrogen coverage, θH2, decreases with CO concentration increases because increasing the CO concentration increases the rate of adsorption of CO onto the sites of the catalyst. When the anode inlet flow contains hydrogen dilution, θH also falls with increasing the dilute of hydrogen.

Further, reduces the number of catalytic sites available for the electro-oxidation of hydrogen. From the figure hydrogen dilution significantly affects the hydrogen coverage, especially at low ppm CO. During poisoning, adding pure hydrogen fuel increase more reaction sites for hydrogen, especially at low CO concentration. Figure 3.3 shows opposite trend of CO coverage on the catalytic sites, because the Pt catalyst has a strong affinity for CO. The accumulation of CO at the catalytic sites is sustained, inhibiting the electro-oxidation of hydrogen.

Figure 3.4 shows the liquid water saturation profiles across the anode catalyst layer.

The effect of the electro-osmotic drag is proportional to the cell current density, which was generated by the electro-chemical reaction of fuel gas. The coverage of hydrogen falls, so the current density was reduced, weakening the effect of electro-osmotic drag.

However, the oxygen reduction reactions are also suppressed, reducing the diffusion of water from the cathode to the anode. Therefore, the saturation level of liquid water across the anode catalyst layer decreases with amount of CO and hydrogen dilution increase. The distribution of liquid water saturation level depends more strongly on the CO concentration than on dilution of hydrogen.

Figure 3.5 plots the liquid water distribution across the membrane. The gradient of the liquid water distribution declines with CO contents, because, as the amount of CO increases, the rate of the reaction decreases on both the anode and the cathode sides.

The effect of electro-osmotic drag and the diffusion of liquid water from the cathode

to the anode are also weakened, reducing the slope of the liquid water distribution across the membrane. At 100 ppm CO, 40%H2, the effect of the electro-osmotic drag is small and less liquid water is generated at the cathode catalyst layer, causing the liquid water distribution to have a smallest slop. Consequently, the CO concentration significantly influences the distribution of liquid water across the membrane.

Figure 3.6 reveals that the amount of liquid water saturation level of the cathode catalyst layer greatly exceeds that on the anodic side of the catalyst. The small electro-osmotic drag and the generation of less liquid water cause the drops of liquid saturation level. Figure 3.7 presents the ionic potential profile across the MEA. In the catalytic layers, the ionic potential distribution is nonlinear, because chemical reactions consume fuel gas. Under poisoning, the ionic potential loss decreases, because CO poisoning reduces the output current density. As discussed above, increasing the CO level or diluting the hydrogen seriously reduces the saturation level of liquid water and the loss of ionic potential.

Figure 3.8 compares the present simulation results with experimental data reported by Bhatia and Wang [58] or four gas compositions fed into the anode. The simulation results show that the cell performance and durability depends strongly on the dilution of hydrogen and CO concentration. Increasing hydrogen dilution and CO concentration degrades the performance of the cell. The predicted CO poisoning results agree closely with the experimental values. Increasing the amount of pure hydrogen drastically increases cell current density for a wide range of CO contents, promoting the tolerance for CO. Figure 3.9 plots the effect of various hydrogen dilutions and CO contents on the performance of the fuel cell. As shown in the polarization curve, the theoretical results indicate that a higher CO concentration and hydrogen dilution results in large drop in the cell performance. The presence of CO in

performance of the fuel cell depends more strongly on the CO concentration than on dilution of hydrogen. Increasing hydrogen dilution and CO concentration further degrades the performance of the fuel cell. In order to promote the tolerance for CO, increasing the amount of pure hydrogen drastically increases current density for a wide range of CO contents.

Table 3.1. Governing equations

Table 3.2. Boundary Conditions

Variables x=0 ACL /MEM MEM /CCL x=L

H2

C CH₂ =CHⁱⁿ₂ N_H2 =0 N/A N/A

O2

C N/A N/A 0

2 =

NO C_O2 =C_Oⁱⁿ₂

CCO C_CO =C_COⁱⁿ N_CO =0 N/A N/A

Cwg C_wg =C_wgⁱⁿ N_wg =0 N_wg =0 C_wg =C_wgⁱⁿ Cwn N/A σ

(

^C_a^−C_wn

)

^=N_w

(

^C_c ^C_wn

)

^N_w

F

i +σ − =−

2 N/A

s s=0 N_s =N_w N_w =N_s s=₀

φ φ=0 k_n,eff∇φ=k_n∇φ k_n,eff∇φ=k_n∇φ ∇φ=0

Table 3.3 The parameters used in the present model [57,58,81].

Temperature T 353 K Pressure P 1 atm Diffusion coefficient of hydrogen in gas phase D _H2 1.1028 (cm² s^-1) Diffusion coefficient of oxygen in gas phase

O2

D 0.1775×(T/273.15)^1.823 (cm² s^-1) Diffusion coefficient of vapor in gas phase D _wg 0.256×(T/307.15)^2.334 (cm² s^-1) Thickness of catalyst layer δ_{CL 16 (μm)} Thickness of membrane δ_MEM 50 (μm) Gas porosity in catalyst layer ε_CL 0.4 Volumetric fraction of Nafion in membrane ε_MEM 0.4 Membrane conductivity k _n 0.17 (mho cm^-1)

Fig. 3.1 A schematic model of MEA of the PEM fuel cell.

Membrane CCL ACL

x

0 4 8 12 16

Anode Catalyst Layer, μm

0 0.1 0.2 0.3

H

2

Cove rage θ

H2

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.2 The effect of various CO concentrations and hydrogen dilutions on the distribution of hydrogen coverage across the anode catalyst layer at 0.6 V.

0 4 8 12 16

Anode Catalyst Layer, μm

0.5 0.6 0.7 0.8 0.9 1

CO Co verag e θ

CO

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.3 The effect of various CO concentrations and hydrogen dilutions on the distribution of CO coverage across the anode catalyst layer at 0.6 V.

0 4 8 12 16

Anode Catalyst Layer, μm

0 0.02 0.04 0.06 0.08

Sat u rati o n

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.4 The effect of various CO concentrations and hydrogen dilutions on the distribution of liquid water saturation across the anode catalyst layer at 0.6 V.

16 26 36 46 56 66

Membrane, μm

13.6 13.8 14 14.2 14.4 14.6

Wa te r C o nte n t λ

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.5 The effect of various CO concentrations and hydrogen dilutions on the distribution of water content across the membrane at 0.6 V.

66 70 74 78 82

Cathode Catalyst Layer, μm

0 0.04 0.08 0.12 0.16

Sat u rati o n

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.6 The effect of various CO concentrations and hydrogen dilutions on the distribution of liquid water saturation across the cathode catalyst layer at 0.6 V.

0 41 82

Distance, μm

-0.03 -0.02 -0.01 0

Ionic Potential, V 10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.7 The effect of various CO concentrations and hydrogen dilutions on the distribution of ionic potential across the MEA at 0.6 V.

0 20 40 60 80 100 120

CO Concentration, ppm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cu rr en t Den s it y, A /cm

2

Experiments [58]

100% H

2

40% H

2

Present Results 100% H

2

40% H

2

Fig. 3.8 The present simulation results compare with experimental data at 0.6 V.

0 0.2 0.4 0.6 0.8 1

Current Density, A/cm

²

0.5 0.6 0.7 0.8 0.9

C e ll V o lt a ge , V

pure H

2

10 ppm, 100% H

2

10 ppm, 40% H

2

100 ppm, 100% H

2

100 ppm, 40% H

2

Fig. 3.9 The effect of various hydrogen dilutions and CO contents on the performance of the fuel cell.

4. Transient Analysis of Multicomponent Transport with

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