Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

Abstract

Fuel cells are electrochemical devices that can convert the chemical energy of fuels and oxidants into electrical power via electrochemical reactions in an efficient, quiet, and clean manner. Common fuel cells include proton exchange membrane fuel cells (PEMFCs), direct methanol fuel cells, direct alcohol fuel cells, alkaline fuel cells, phosphoric acid fuel cells, molten carbonate fuel cells, and solid oxide fuel cells. Among all types of fuel cells, PEMFC is the most promising technology for automotive applications, due to its high power density and fast start-up. The operation of PEMFCs can be reversed for H2 and O2 production by water electrolysis (the cell is called PEM electrolyzer cell: PEMEC). The reversible operation of PEMFC provides a good option for excess renewable power storage: when the renewable power generation is higher than electricity demand, excess renewable power can drive a PEMEC to generate H2 (Figure 1), which can be converted back to electricity by a PEMFC when the renewable power is insufficient. Therefore, PEMFCs capable of working in both fuel cell mode and electrolysis mode are very promising for advanced energy conversion and storage. However, extensive research efforts are still needed to improve the performance, durability, and reversibility, as well as to reduce the cost of PEMFCs. Extensive experimental studies have been conducted to reduce the loading of Pt catalyst without significantly sacrificing the cell performance, to develop alternatives to precious Pt catalyst for PEMFCs, and to understand the degradation behaviours of PEMFCs. Apart from experimental investigation, mathematical modelling serves as a powerful tool in exploring the complicated physical and chemical processes in PEMFCs, especially the coupled transport and reaction processes, which are critical for design optimization and practical applications of PEMFCs but are difficult to study by experiments. The mathematical modelling of PEMFCs has been reported extensively in the past 2 decades, from atomic level to understand the fundamental reaction processes on the catalyst surface, to stack level to understand the multi-phase transport and reaction in the complicated geometries. Although significant progress has been made, there are still challenges in modelling of PEM cells. The objective of this perspective is to identify and discuss the challenges and the directions for modelling PEMFCs. Like other types of fuel cells, a single PEMFC consists of a porous anode, a porous cathode, and a polymer electrolyte membrane capable of conducting protons (Figure 2). In operation, H2 fuel and air are supplied to the anode and cathode, respectively. H2 molecules flow from the anode channel to the gas diffusion layer (GDL), then to the catalyst layer (CL), where hydrogen oxidation reaction takes place to produce protons and electrons. The protons are conducted through the electrolyte to the porous cathode while the electrons are transported through the external circuit to produce electrical power. In cathode, oxygen reduction reaction takes place in the CL to form H2O. Water management has been regarded as the hot research area for PEMFC development for the last 2 decades. To maintain acceptable proton conductivity of the electrolyte membrane (eg, Nafion), it is critical to completely hydrate the membrane and external humidification is usually needed. On the other hand, the relatively low working temperature of PEMFC (about 80°C) causes the produced water to condense on the cathode side. The amount of liquid H2O could flood the electrode pore regions, preventing the reactant gas to reach the reaction sites, leading to reduced fuel cell performance. Even worse, the electro-osmotic drag effect causing water flow from the anode to the cathode is more significant at high current density, which in turn leads to dehydration of the electrolyte membrane (thus a lower proton conductivity) on the anode side and more significant flooding in the cathode. Thus, it is critical yet challenging to completely hydrate the electrolyte membrane while to efficiently remove the produced water from the cell. A fundamental understanding of the liquid water-gas multiphase flow is critical to achieve this target, as shown in Figure 3. In the literature, extensive efforts have been made to model the multiphase flow in PEMFCs at different scales. Volume of fluid (VOF) method has been employed for simulating the gas-water transport in PEMFC flow channel and GDL, but it is still very challenging to apply it to the CL due to the very small length scale of CL.1-5 Moreover, it is challenging to model the dynamic contact angle change by VOF method, which is critical in simulating the droplet transport. For large PEMFC stacks with high power density, the demand in reactant gas supply, especially for air in cathode, can be significantly high, possibly leading to two-phase turbulent flow in channel. The traditional turbulent models, such as the Reynolds averaged Navier-Stokes equations model, cannot capture the detailed turbulent fluctuation effect on two-phase flow when coupled with VOF. The direct numerical simulation method, computationally demanding but solving all the turbulent scales, has been recently used together with VOF to capture the detailed turbulent two-phase flow in channel.6, 7 To more accurately capture the droplet dynamics at pore scale, lattice boltzmann method (LBM) is effective, thus it is employed for multiphase flow simulation in the nanostructured CL.8 Based on the single relaxation time Bhatnagar-Gross-Krook evolution and Shan-Chan model, the LBM model could capture the dynamics of water transport in the porous electrodes of PEMFC. It is found that the liquid water transport is strongly affected by the microstructure of the porous layer and the liquid water tends to flow through the large pores. Liquid water in small pores may retract and transport to the neighbouring larger pores. The results clearly demonstrated the importance of local liquid transport at pore scale, which could substantially impact the PEMFC performance at cell scale. Over the past decade, the molecular dynamics and quantum mechanics methods have been well developed and widely used for PEMFC to investigate the transfer behaviour at microscopic level.9-13 However, there are quite a few issues for these modelling methods: (1) The small time step of the simulation results in the low computation efficiency; (2) these numerical methods are mainly used to capture the transfer behaviour of the existing water and droplet, and the combination of multiphase phase flow, chemical reaction, and phase change is currently considered to be a main direction for modelling the water transport behaviour in PEMFC; (3) the ice formation process and morphology in the porous medium, especially in the GDL, MPL, and CL, also remains to be an important issue to be further investigated. In a word, the combination of the multi-scale methods will be the future trend for the modelling research of PEMFC. Numerical studies on PEMFC at stack level also confirmed the importance of multiphase transport in the flow channels and under the land of the bipolar plate.3 However, the water transport at pore scale and at cell/stack scale is studied separately and their interaction remains to be investigated. It should be noticed that at the whole cell and stack level, for the models coupling multiphase transport and electrochemical reaction/charge transport, due to the limitation of the VOF and LBM methods in terms of time/length scales mentioned previously, only the two-fluid and mixture models were used to describe the multiphase transport, in which the detailed liquid/gas interface cannot be tracked. For such multiphase full cell models, by assuming that the liquid water concentration is continuous, the liquid phase continuity equation was commonly solved.14 However, at the interface of different layers (eg GDL and MPL), there exists sudden change of porous structure and wettability, leading to the fact that the concentration is discontinuous but the force (pressure) should be. For this reason, recently, the liquid and gas pressure continuity method was adopted, in which the liquid saturation jump at the interfaces of the neighbouring porous layers can be described.15-17 The water management problem becomes more significant for cold start of PEMFC. The freezing of water (ice formation) may cover the catalyst surface, hinder the transport of reactant, and even damage the structure of the PEMFC component. In general, several forms of water may exist during the cold start process of PEMFC, including water vapour, liquid water (supercooled water), ice, membrane water, and frozen membrane water, leading to more critical water management strategy.3 Due to the complexity of water phase change process in PEMFC during cold start, the freezing/melting dynamics need to be solved at both pore scale and cell/stack scale. Future research is needed to develop multiscale models capable of capturing the local water dynamics as well as the macro-behaviours of the PEMFC at cell or even stack level. As mentioned above, the operation of PEMFC can be reversed for H2 production by H2O electrolysis.18 However, compared to PEMFCs, the development of the modelling studies for PEM electrolyzer cell (PEMEC) is still in its early stage. Most of the existing modelling studies on PEMEC focus on the PEMEC system analysis and dynamic control with simplified descriptions of the coupled transport and reaction phenomena in the PEMEC components. It should be noted that the transport process in PEMEC is different from that of PEMFC as the transport of gas bubbles in the porous electrodes and flow channel become important in PEMEC. More research efforts should be made in the modelling of PEMEC at both pore scale and stack scale to understand the complicated transport process for performance improvement. The Nafion membrane used for PEMFC or PEMEC limits its operating temperature to be below 100°C as its proton conductivity significantly decrease with a further increase in temperature. For comparison, the phosphoric acid-doped polybenzimidazole (PBI)-based membranes show excellent proton conductivity at a temperature range of 160°C to 180°C; thus, it is widely used as an electrolyte membrane for high temperature PEMFC (HT-PEMFC). Compared with low temperature PEMFC based on Nafion electrolyte, the HT-PEMFC shows the following advantages: (1) faster reaction kinetics at the electrode at a higher temperature leading to lower activation loss and potentially higher performance; (2) the alternative nonprecious catalyst to replace Pt catalyst is possible at high operating temperature leading to potentially lower cost; (3) the CO tolerance is significantly improved at a high temperature; (4) the critical water management for low temperature PEMFC is no longer a main issue for HT-PEMFC as all reactants and products are in gaseous form; (5) the high operating temperature make HT-PEMFC suitable for combined heat and power (CHP) co-generation to achieve higher system efficiency. Due to the above-mentioned advantages, HT-PEMFC has received great attention in the past few decades. Mathematical models from single-cell level to stack level have been developed for HT-PEMFC.19, 20 As the operating temperature is about 160°C to180°C, the degradation of the membrane electrolyte remains a problem for HT-PEMFC. Although some preliminary modelling studies have been conducted on HT-PEMFC degradation, the models are usually simplified and more efforts are needed to understand the degradation behaviour and to hinder the degradation process. Although water management is no longer a problem for HT-PEMFC, the thermal management is still an important issue, especially during start-up and shut down, which may cause significant temperature gradient and thermal stress in the HT-PEMFC stack.21 More research should be carried out to develop more comprehensive dynamic models to simulate the transient behaviour of HT-PEMFC, especially during start-up. Unlike low temperature PEMFC (LT-PEMFC) that has been modelled at various levels, the pore-scale modelling and multiscale modelling of HT-PEMFC are still lacking. In addition, the system-level model also remains to be an important subject for the HT-PEMFC, as well as the LT-PEMFC.22 The operation of HT-PEMFC can also be reversed as a high temperature PEM electrolyzer cell (HT-PEMEC). A few experimental studies have demonstrated the feasibility of HT-PEMEC for H2 production.23 Compared with low temperature PEM electrolyzer cell, the electrical energy requirement by HT-PEMEC (working at about 160°C) is reduced as part of the energy input is in the form of heat, making HT-PEMEC suitable for utilizing waste heat from the industry. Although the higher temperature solid oxide electrolyzer cell usually operates at 800°C and requires more thermal energy input,24 its high operating temperature requires very high grade waste heat, which limits its application for waste heat utilization. For comparison, HT-PEMEC can utilize wider range of waste heat from the industry. Therefore, HT-PEMEC represents a promising technology for H2 production, especially when HT-PEMEC is driven by excess nuclear power or renewable solar/wind power. In the literature, there is only one modelling study on HT-PEMEC for hydrogen production on the effect of flow configuration on cell performance.25 The coupled transport and reaction process in the HT-PEMEC at pore scale remains to be studied. Modelling study on the effect of operating conditions on HT-PEMEC for performance improvement is also lacking. There are plenty of research opportunities in HT-PEMEC modelling. Various platforms are available for PEMFC modelling. Commercial software, open-source code, or in-house codes have been developed for PEMFCs. The most frequently used commercial software for PEMFC modelling include FLUENT, STAR-CD, COMSOL, and CFD-ACE+, which have good documentation and good pre-processing and post-processing. The commercial software is relatively easy to use and thus widely adopted for PEMFC modelling. However, as the codes are not available to the public, it is hard to compare the results from different models for model evaluation. In addition, the understanding of the PEMFC physics is evolving and there is a need to incorporate the latest development and understanding into PEMFC model. However, the commercial software cannot be readily extended and each group needs to add additional code (such as user defined functions: UDF in FLUENT). Despite these disadvantages, commercial software is still popular in PEMFC simulation due to the good documentation, convenient pre- and post-processing. For comparison, open-source software: Open FOAM with pre-developed modules are gaining popularity for simulating complex multiphysics fields. The advantage of Open FOAM is that the users can easily extend the code by incorporating new features and share the new features with other scientists. Therefore, different groups can share their new developments and the repeating work can be avoided. Due to this big advantage, a few research groups are developing Open FOAM platform for PEMFC and solid oxide fuel cell modelling. Compared with commercial software, the open-source code has the following advantages: (1) the incorporation of new features or new development can be easily shared with other scientists; (2) easy to integrate with other model for simulating more complicated systems; (3) easy for comparison with different models; (4) transparent and easy for model validation. However, there are quite a few challenges and/or difficulties for the open-source platforms to be widely used: (1) Currently, the available programs and codes for LT-PEMFC are still lacking; (2) compared to the commercial CFD software, the open-source platform is less friendly to the researchers, due to the complicated program structure, leading to the low efficiency of coding and computation; (3) maintenance of the open-source platform remains a challenge due to the lack of funding; (4) the users still need to use other software for pre-processing (mesh generation for example) and post-processing; (5) the open-source code usually does not have good documentation, thus it is difficult for new users to learn and start; (6) development of the open-source code require a certain level of programming skills, making it difficult to use for researchers not good at computer programming; (7) in the development of open-source code, researchers may work on different versions, which may not be compatible with different operation system and make it inconvenient for code sharing. Despite these disadvantages, several research groups in Canada and European countries are actively developing fuel cell modelling using the open-source code.26, 27 The open-source code (eg, Open FOAM) is still needed to be further developed. To make the open-source code more impactful and popular, extensive efforts should be made to address the above-mentioned challenges. This work is supported by a Humboldt Research Fellowship (for experienced researcher, grant number: CHN—1186510—HFST-E) from Alexander von Humboldt Foundation, Germany.