Proton Exchange Membrane Fuel Cell Modeling

Several complex and interrelated phenomena occur during the operation of proton exchange mebrane fuel cell (PEMFC). These processes include mass and heat transfer, electrochemical reactions, and ionic and electronic transport. Real phenomena occuring in PEMFC can only be understood through a robust fundamental model based on the physical models. These physical models are derivatives of experimental observations.

A number of issues need to be resolved before fuel cells can be commercially viable. Proton exchange membranes require precise water management, which is difficult under the variable load associated with several applications (e.g. automobile driving). Deyhdration of the membrane results in lower ionic conductivity as well as the risk of de-adhesion of the membrane, whereas excessive water production (at high current densities) results in mass transport limitations on the cathode side. Sluggish electrode kinetics is also a serious problem during the course of operation. The rate of oxygen reduction at the cathode is much slower than hydrogen oxidation at the anode, and this limits the performance of the cell. Besides these, trace amounts of CO in the hydrogen feed have severe effect on platinum based catalyst typically used in PEMFCs.

Parametric models allow predicting the performance of the fuel cell given geometric parameters, material properties and operating conditions, such as temperature, pressure and humidity. Such models are advantageous because experimentation is limited to designs, thus does not facilitate innovative design. Considering highly reactive environment within the fuel cell, it is often improbable to measure critical parameters, such as temperature, pressure and potential gradients, or species concentration within the cell. For this reason, detailed transport models, which accurately predict the flux and concentration of multiple species, are required.

A fuel cell model may fall into one of three categories: analytic, semi-empirical, or mechanistic (theoretical). Analytical models are only approximate and do not give an accurate picture of transport processes occuring within the cell. They are limited to predicting voltage losses and water managament requirements for simple designs. On the other hand, semi-empirical modeling combines theoretically derived differential and algebraic equations with empirically determined relationships. Empirical relationships are employed when the physical phenomena are difficult to model or the theory governing the phenomena is not well understood. Semi-empirical models are, however, limited to a narrow range of operating conditions. They cannot accurately predict performance outside of that range. They are very useful for making quick predictions for designs that already exists. They cannot be used to predict the response of the fuel cell to parameter changes outside of the conditions under which the empirical relationships were developed. Empirical relationships also do not provide an adequate physical understanding of the phenomena inside the cell. They only correlate output with input.

Early in 1990s, simple modeling efforts started as the experimental studies on PEMFC performance accelerated. First 0-D models were used to analyze the data and these models generally fit the experimental data with a single equation. Although these models well agree with some experimental data and quick and easy to model, models fail to predict real phenomena for a wide range of operating conditions and these models are less reliable. From these models, the two main fundamental models were derived. Bernardi and Verbrugge [4, 5] and Springer et al. [3] treat the fuel cell sandwich, composed of membrane, diffusion media, and catalyst layers, and are isothermal and 1-D. Bernardi and Verbrugge model assumes a fully hydrated membrane and incorporates porous-electrode equations and Stefan-Maxwell diffusion in the diffusion media and catalyst layers. The model of Springer et al. does not use porous-electrode equations but does consider changing water content in the membrane. This allows for variable properties in the membrane such as conductivity and the water diffusion coefficient. Most models trace their roots back to these models.

There are several fuel cell models in the literature considering various transport mechanisms within the different parts of fuel cells. Some of these researches investigate specific phenomena like water managament, thermal management or flooding of fuel cells. No matter which phenomenon is investigated, modeling of the fuel cells could be classified in two groups: partial cell models and complete cell models. As the name implies, partial cell models examines only a few components of the fuell cell (membrane, gas diffuser, etc.), whereas complete cell models includes almost all of the components of the fuel cell. Partial cell models can give quick estimates (short computation time) of certain transport charecteristics of the components that are under investigation. However, a detailed understanding of the fuel cell performance and more accurate simulation can only be achieved by complete cell models. Knowledge of detailed analysis comes with the cost of increased solution time and the complexity of the model [2].

Researches of Springer et al. [3] and Bernardi et al. [4,5] could be considered as pioneer works on fuel cell modeling. Springer et al. [1] investigated water transport mechanism in the polymer membrane and for this purpose they set up a PEMFC model that includes GDL and the membrane (partial cell model). Catalyst layers are treated as interfaces and source terms are applied at the interfaces. Water content of the membrane is given as a function of local vapor activity and ionic conductivity and diffusion coefficient of water are expressed in terms of water content and temperature. Model in itself gives a good understanding of water transport in the membrane. Since it is a one dimensional model and do not include catalyst layers, it is not very informative on the total fuel cell performance.

1. Cheddie D., Munroe N., “Review and comparison of approaches to proton exchange membrane fuel cell modeling”, Journal of Power Sources, 147, 72-84, 2005

2. Weber A. Z., Newman J., “Modeling transport in polymer electrolyte fuel cells”, Chem. Rev., 104, 4679-4726, 2004

3. Springer T. E., Zawodzinski T. A., Gottesfeld S., “Polymer Electrolyte Fuel Cell Model”, J. Electrochem. Soc., 138, 2334-2341, 1991

4. Bernardi D. M., Verbrugge M. W., “A Mathematical Model of the Solid-Polymer-Electrolyte Fuel Cell”, J. Electrochem. Soc., 139, 2477-2490,1992