1. INTRODUCTION
1.3 Literature Survey
Zero-Dimensional Models
The simplest method use only a single equation to describe the cell polarization is the zero-dimensional models. The models can not realize the fundamental understanding of the transport phenomena but are worth for determining the kinetic parameters and are relatively simple for use. A typical expression of the 0-D model is used by Kim et al. [7] which incorporated the gas-phase mass transport limitations
( )
i b( )
i Ri m( )
ni bU
V = + log 0 − log − − exp (1-9)
in which V is the cell potential, U is the reversible potential, io is the exchange current density, b is the Tafel slope, R represents the total resistance, and m and n are fitting parameters, respectively. Sena et al. [8] used similar approach describing the water transport in the membrane. For Nafion 115 and 117 membranes, liquid water flooded is the limiting effect at high current density. For Nafion 112 membrane, oxygen diffusion effects dominate the cell behavior. Pisani et al. [9] and Passalacqua et al. [10]
change the concentration overpotential to be a more complicate function with more fitting parameters. Pisani et al. [9] derived a semi-empirical equation to describe the performance of the fuel cell. The Ohmic overpotential is used to be the only one empirical term in the performance equation. The modeling results showed a quantitative depiction of the voltage drop at high current density. Passalacqua et al.
[10] proposed a equation that described the relation between the current density and potential. The results indicated that cell performance is affected by the Nafion content.
An optimal content of Nafion was found about 33 wt% of ionomer.
Fuel Cell Modeling
The fuel cell sandwich model shows the cross section of the fuel cell which
includes flow field, diffusion media, catalyst layer and membrane. Fuels are fed through the flow field at the anode and cathode side. The fuels flow through the diffusion media and react at the catalyst layers. At the anode catalyst layer, electrons and ions are generated by hydrogen oxidation-reactions. At the cathode catalyst layer, the oxygen reduction reactions produce either liquid or vapor water. Energy and mass transport along with electrochemical kinetics occur through various sandwich layers.
Various parts of the fuel cell modeling equations are presented as follows
Membrane Modeling
For polymer electrolyte fuel cells, electrolyte is a proton-conducting membrane.
Figure 1.9 shows the structure of the membrane as a function of water content [11].
The first type of membrane modeling treating the membrane system as a single phase is the diffusive model which corresponds to the vapor equilibrated membrane (panel c of figure 1.9). The model assumes that the proton and water dissolve and move by diffusion. The simplest method for use to treat the proton movement is the Ohm’s law
φ
∇
−
= k
i (1-10)
where k is the membrane conductivity. The above equation is the simplified result of using dilute theory. Only the interaction between each dissolved species and the solvent is considered. If water transportation is considered in the membrane, the electro osmotic flow can be added to the overall flux of water.
C F D
Nw =ξ i − w∇ (1-11)
in which ξ is the electro-osmotic coefficient. The effect of electro-osmotic drag is proportional to the current density. Kulikovsky [12] and Siegel et al. [13] used this method successfully to treat the membrane as a single phase. Kulikovsky study the nonlinear distribution of water content through the membrane. Water diffusion
coefficient drops rapidly blow certain λ value which causes a region with large gradient of water. The model also shows the increase of membrane resistance with current density. Siegel et al. used agglomerate catalyst geometry to analyze the fuel cell behavior. As a result, the optimal void fraction of 0.4 was found for the electro-chemical reactions. Cell performance decreased with the size of the catalyst agglomerate.
One another approach is the hydraulic model that assumes the membrane system as two phases (water and membrane). The membrane is treated as having pores that are filled with liquid water. The water content of the membrane is assumed to be constant shown in panel d of Fig. 1.9. The gas pores of the membrane are filled with liquid water. Bernardi and Verbrugge [14,15] first treated the membrane using above fashion. The Schlogl’s equation is used to define the liquid water velocity in the pores of the membrane phase which is related to the pressure gradient and potential gradient. Murgia et al. [16] used the same approach to model the liquid water transport in fuel cells. The study modified the model of Bernardi and Verbrugge (BV model). The MBV model integrated the Bulter-Volmer equation in the catalyst layer to get more stable numerical calculation. The results show indistinguishable between these two models and extend the range of the current density.
Rowe and Li [17] combined both diffusive and hydraulic model to treat the liquid water transport in the membrane. The model investigated temperature distribution and water management in the fuel cell. As a result, the temperature difference becomes larger and low operation temperature and partial humidified streams. At high operating pressure, membrane hydration decrease due to the decrease of water vapor concentration within in the anode electrode.
k P C C F D
Nw = i − w∇ − ∇
ξ μ (1-12)
The problem with the above approach is the use of a gas pressure gradient. This means that the gas-phase is exist within the membrane, but does not agree with experiments.
Diffusion Media Modeling
The diffusion media are placed between the catalyst layer and gas channel which is generally made either a carbon paper or a carbon cloth material. The diffusion media provide a structure support and a pathway for reactants, water and electrons. The transportations of the species are discussed as follows
For the gas-phase transport, if the mean free path of the gas molecule is less than 0.01 times the pore radius, the Stefan-Maxwell equation is used to illustrate the gas transport in the fuel cell.
where xis the molar fraction, Dieff,j is the effective binary diffusion coefficient. As the pore size is comparable to the gas mean free path, Knudsen diffusion becomes more significant. Kulikovsky et al. [18] combined both Stefan-Maxwell and Knudsen diffusion to treat both diffusion medium and catalyst layer of a PEM fuel cell cathode.
Two different values of the carbon conductivity is considered to investigated oxygen concentration distribution, potential of carbon phase, electron flow and current density distribution. The simulation results indicate that a dead zone in front of the gas channel within in the catalyst layer is formed with low carbon conductivity. Reduction of the catalyst loading leads only an insignificant effect on the cell performance.
Kulikovsky [12] also assumed that vapor water transport by Knudsen diffusion in the catalyst layer. In this work, the Knudsen diffusion coefficient is a function of pore
size. The diffusion coefficient of water drops significantly below certain value of water content which cause the high nonlinear distribution of liquid water across the membrane. Membrane resistance and gradient of liquid water distribution increase with current density due to nonlinear drying at the anode side of the membrane.
Bulk diffusion dominates when the pore size is 100 times to the molecule mean free path, and Knudsen diffusion dominates when the pore size 0.1 times to the molecule mean free path. Weber and Newman [11] indicated that Knudsen diffusion become a significant effect when the pore radius is less then about 0.5 μm. Typically, pore size is often 0.5~20 μm in the diffusion media, and 0.05~2 μm. in the Microporous layer.
Thus, only microporous layer should be accounted using Knudsen diffusion.
The simplest method to treat the liquid water inside the cells is to neglect it. The liquid water transport is not considered and the effect is to decrease the effective diffusion coefficient of gas species. Gurau et al. [19] developed an analytical solution of a half-cell mode. The parallel composite structure of the diffusion medium with different porosity was applied to mimic the flooding effect. Chu et al. [20] further developed a one-dimensional model to consider the non-uniform porosity of the diffusion medium. In this work, various functions of the porosity are considered to simulate liquid water across the gas diffusion medium.
Gas and liquid are actually coexistence in a porous medium of the fuel cells. The interaction between gas and liquid is expressed as
P r P
Pc = l − g =−2γ cosθ (1-14)
in which γ is the surface tension of water, θ is the contact angle, r is the pore radius.
The most significant aspect of the two-phase model is the prediction of the liquid saturation s which is defined as liquid fraction of pore volume. The liquid water saturation greatly influences the gas diffusion coefficient and represents the flooding
effect. He et al. [21] used two-phase model to investigate the interdigitated flow fields of the PEM fuel cells. The simulation results indicate that high pressure gradient between the inlet and outlet channel produce higher performance of the fuel cell. An optimal thickness of the electrode (0.08 cm) is obtained. The higher the channel/shoulder ratio also yields better cell performance. Natarajan and Nguyen [22]
developed a three-dimensional model the study the liquid water flooding in the fuel cell cathode. As a result, higher stoichiometric rate and temperature result in higher current density. The cell performance increase with decreasing inlet stream humidity You and Liu [23] developed a multiple-phase mixture model to examine the two-phase distribution in the fuel cell cathode. The liquid water saturation increases with current density. In addition, high humidification temperature at both anode and cathode inlet increase the liquid water saturation but decrease the limiting current density. Pasaogullari and Wang [24] applied the commercial CFD software, Fluent, to study the effect of humidification level and flow rate of reactants on the cell performance and liquid saturation profile. Liquid saturation increased with humidification level along the flow channel. In the fully humidified situation, the membrane are well hydrated which results high current density.
Catalyst Layer Modeling
The simplest type of catalyst layer modeling is the zero-dimensional or interface models. The catalyst layers are treated as an interface between the diffusion media and the membrane. The thickness and the structure of the catalyst layer are assumed to be ignored. Kulikovsky [12] and Natarajan [20] used Faraday’s law as a generation/consumption term at the boundary between the membrane and the diffusion medium. More rigorous modeling (porous-electrode model) treat the catalyst layer with finite thickness [16,17]. The characteristic length is the thickness of the
catalyst layer. This model is concerned about the chemical-reaction distribution across the catalyst layer. Siegel [13] described a mathematical PEMFC model base on agglomerate catalyst geometry. The model describes that gas flow through pores and then diffuses into agglomerate catalyst, as shown in Fig 1.10. In this approach, the characteristic length is the agglomerate size and the agglomerates are assumed to be uniform. Pisani et al [25] considered cylindrical gas pores of fixed radius through the catalyst layer. Both longitudinal and transverse oxygen diffusion are solved in gas phase and liquid phase, respectively. Pisani [26] further compared five different porous structure of the catalyst layer. Lin et al [27] used thin-film agglomerate model to simulate the catalyst layer structure. For the agglomerate model analysis, an effectiveness factor is used to describe the ORR as follows
E ai i= h
⋅
∇ (1-15)
where E is the effectiveness factor. In spherical agglomerate, an analytic expression is shown as [28,29]
where ζ is the characteristic length of the agglomerate, Ragg/3 for spheres, Ragg/2 for cylinders, and δagg for slabs, and Κ is a rate constant given by
The governing equation for the agglomerate model without external mass-transfer limitation is expressed as
Poisoning Effects by Impurity Ions and CO
Many researchers have focused their interest to investigate the effects of the impurities ions from both hydrogen fuel and air on the cell performance. Okada et al.
[30-37] experimentally examined the water transport in the membrane of the fuel cell with the effects of various impurity ions. Water content, membrane conductivity, ionic transference coefficient, and diffusion coefficient of water decrease with an increase in the impurity ions. Okada [38,39] and Chen et al.[40] theoretically discussed the effect by impurity cations in membranes of PEM fuel cells. Okada [38,39]
investigated the poisoning effect of impurity ions at the anode and cathode side, respectively. Operating current density and membrane thickness significantly affect the membrane performance. The most severe effects on the cell performance by the contaminant ions occur at the membrane-cathode interface. Chen [40] combined the theoretical model by Okada [38,39] to study the transient behavior of water transport in the membrane. The results show that contaminant ions enhance the electro-osmotic effect but decrease the diffusion of water from cathode. The steady state time tss
decrease with the initial current density increase.
The most efficient fuel for use in a PEM fuel cell is pure hydrogen. However, this is difficult to store and has a high cost of production. Reforming from hydrocarbons, including gasoline and alcohol is the most extensively used technique for generating hydrogen fuel, which contain 45% hydrogen, 10ppm CO, 15% CO2 and 1% CH4 [1].
CO at a concentration even as low as 5-10 ppm effectively blocks Pt reaction sites for
the electro-oxidation of hydrogen [2-3]. The affinity between CO and Pt is such that even at this low concentration of CO, the consequent loss of performance is severe [4-5]. Lee et al. [4] investigated the tolerance of PtSn/C, Pt/C and PtRu/C alloy electrocatalysts for CO. Depending on the nature of the electrode material, the CO oxidation occurs at different potentials. The improvement of CO tolerance is contributed by the changes in the thermodynamics and the CO adsorption process.
Murthy et al. [5] presented the steady-state and transient performance of a fuel cell with relatively high concentrations of CO, for two types of gas diffusion media.
Recently, many efforts have been made to increase the tolerance of the PEM fuel cell to CO [41-46]. Schmidt et al. [41] and Divisek et al. [42] presented two methods for improving the cell performance using H2/CO as a fuel. First, the use of Pt-Ru electrocatalysts at the anode can considerably enhance the tolerance to CO. Second, the addition of liquid hydrogen peroxide to the humidification water in the cell leads to the formation of active oxygen by the decomposition of H2O2. Complete recovery can be achieved for H2/100 ppm CO. Si et al. studied the CO tolerance of the Pt-Ru/C catalyst at elevated temperature and atmospheric pressure in a PEM fuel cell [43].
They demonstrated that the anodic polarization fell dramatically as the temperature increased, because the CO coverage was lower. Improving the activity of the catalyst with a high CO tolerance increases the rates of reaction of CO and hydrogen. Zhang et al. [44] found that CO poisoning process can be accelerated at high anode flow rate.
The performance decreases substantially as the anode flow rate increases, because CO is adsorbed on the catalyst site. However, increasing the anode overpotential promotes the oxidation of CO, maintaining desired cell performance. Yu et al. [45] and Santiago et al. [46] adopted the Pt-Ru/C electrocatalyst for different electrode structures to improve the tolerance of PEMFC to CO. Water sufficiently activates the Ru surface to
Pt–Ru–P/C catalyst. The results show that Pt–Ru–P/C catalyst shows high activity for the methanol electro-oxidation. The greater oxidation of carbon monoxide also obtains compared with Pt–Ru/C catalyst. A PtRuIr/C catalyst was prepared by Liang et al [48] to exhibit excellent CO tolerance for PEM fuel cells. Ir in the PtRu electrocatalyst produces excellent activity of CO electro-oxidations. The superior performance is attributed by the interaction between RuO2 and IrO2.
To avoid the use of precious metal, some researchers adopted some methods to restore the cell performance during the operation process, including the oxidant-bleeding [49,50], self-oxidation [2,51], and current-pulsing [51,52]. Qi et al.
[49] used cyclic voltammetry method to detect the CO adsorption on the cathode catalyst layer. The results show poisoning and recovering process is quickly within in 15 minutes. CO can pass through the membrane and poison the cathode catalyst. The potential drop at the cathode side is sometimes larger than anode. Well hydrated membrane can prevent CO crossover the membrane and increase the tolerance of CO.
Adock et al. [50] used reconfigured anode (RCA) to enhance the air-bleed effectiveness for increase the CO tolerance of the fuel cell. A nonprecious-metal is place on the anode side adjacent to the flow field in order to perform preferential oxidations. Thomason et al. [51] compared both self-oxidation and current pulsing method for increasing the tolerance of CO. From the experimental results, current pulsing is more effective than self-oxidation in creasing the tolerance of CO. Carrette et al. [52] also used pulsing technique for determining the optimized operating conditions. Under various CO concentration, pulsing frequency need to be adjusted without significant performance loss.
Other researches have been developed to investigate the effect of hydrogen dilution in the anode feed [53, 54]. The effect of hydrogen dilution without CO containing fuel has been studied [53]. The predicted polarization curves showed a strong effect on cell
performance. Gu [54] studied the dilution effect of N2 and CO2 individually. As a result of RWGS, CO2/H2 mixture has significantly larger polarization than N2/H2
mixture at the same concentration. Wee and Lee [55] established an overview of the development of CO tolerant electrocatalysts.
In theoretical studies, Springer et al. [56] derived a mathematical model to describe CO poisoning on the catalytic sites. Chan et al. [57] combined the theoretical models developed by Springer et al. [56] and Bernardi et al. [14,15] to examine the CO kinetics. Bhatia and Wang [58] treated the characteristics of the anode catalyst layer as a boundary condition in analyzing the transient CO poisoning behaviors for various levels of CO. Baschuk and Li [59] developed a mathematical model to simulate both CO poisoning and oxygen bleeding.
Recently, high temperature polybenzimidazole (PBI) membrane fuel cells have received great attentions. Wainright et al. [60] applied acid-doped PBI membrane for fuel cells. PBI is a basic polymer and exhibits high conductivity through doping with various acids or bases. Sulphuric acid and phosphoric acid are the most widely used doping matter to perform high conductivity. Wang et al. [61] demonstrated that the PBI membrane fuel cells performed well at 150oC under atmosphere. After 200 hour operating, no membrane dehydration occurred. Li et al. [62] investigated phosphoric acid doped PBI membrane fuel cell in a various doping range. Acid doping level, water uptake, water drag coefficient and mechanical strength were all investigated.
Proton conductivity of PBI and PBI composite membranes was measured by He et al.
[63]. The conductivity could be influence by temperature, acid doping level and humidity. Li et al. [64] studied the influence of doping level and water uptake of PBI membrane fuel cells. Methanol permeation and proton conductivity of poly(N-methylbenzimidazole) (PNMBI), poly(N-ethylbenzimidazole) (PNEBI) and
membrane conductivity under various humidity, temperature and acid doping level.
Liu et al. [67,68] investigated the O2 reduction at a Pt-polymer electrolyte interface.
The operating temperature of acid-doped PBI membrane fuel cells is much higher than PFSA polymer membrane fuel cells. Several advantages make it superior to low temperature PEMFC. Firstly, operating temperature up to 200oC can tolerate up to 3%
The operating temperature of acid-doped PBI membrane fuel cells is much higher than PFSA polymer membrane fuel cells. Several advantages make it superior to low temperature PEMFC. Firstly, operating temperature up to 200oC can tolerate up to 3%