A two-dimensional steady-state model for phosphoric acid fuel cells (PAFC)

doi:10.1016/S0378-7753(02)00369-5

Journal of Power Sources

Volume 112, Issue 1, 24 October 2002, Pages 137-152

https://doi.org/10.1016/S0378-7753(02)00369-5 Get rights and content

Abstract

A two-dimensional steady-state model for a phosphoric acid fuel cell (PAFC) is developed. While most of the published literature deals with one-dimensional models for PAFC, a two-dimensional model is necessitated in cases where the oxygen concentration changes substantially in the flow direction due to depletion of oxygen and back diffusion of product water. The proposed modeling strategy was validated by: (i) testing in one-dimensional mode for verification of the basic parameters through a micro setup known as “unit cell”, and (ii) evaluation of the two-dimensional model through an experimental setup of a PAFC stack with four cells. Further, the utility of the model in design and humidity management, and parametric sensitivity studies are presented.

Introduction

The need for highly efficient and low emission energy conversion devices has attracted attention towards fuel cells world over. A fuel cell is an electrochemical device which converts chemical energy to electrical energy directly. Out of several families of fuel cells, hydrogen–oxygen fuel cells are an important class of fuel cells for which the technology is mature enough for practical usage. Fuel cells have been used in the past in space applications. Other possible applications include small to medium sized stationary power generation plants, vehicle propulsion, various types of power sources for military use and so on. Of the hydrogen–oxygen fuel cell systems, the most mature is phosphoric acid fuel cell (PAFC). It operates at 150–190 °C and pressures ranging from ambient to 5 atm. PAFC systems primarily use Pt as a catalyst, both for hydrogen and oxygen electrodes. Operating temperature range of PAFC allows it to take up hydrogen directly from hydrogen sources like reformer gases. CO (less than 1%) present in the reformer gases are not adsorbed on Pt sites owing to the high operating temperature. The other components used in PAFC are mainly made of graphite and carbon. All these make PAFC a versatile member of the hydrogen–oxygen fuel cell family.

As a part of the PAFC research program in Naval Materials Research Laboratory (NMRL), India, modeling of PAFC stacks of various capacities and configurations are being developed. Numerous parameters like electrode characteristics, gas flow fields, acid concentration, temperature, inlet partial pressures of the reactants and so on have significant effect on the performance of a PAFC stack. It is, therefore, difficult to analyze the effect of each parameter through experimentation in order to design PAFC components optimally. A comprehensive model allows in depth study of the system at various operating conditions with several possible combinations of the component parameters. Another advantage of a good representative model is easy development of diagnostic tools [1] for determining possible malfunctions inside large sized, higher capacity stacks. Stable operation of medium to high capacity PAFC stacks require balancing of several operational parameters like flow rates, humidity and temperature. The output electrical potential of a PAFC stack is a function of its energy conversion efficiency. Thus, under variable load, it is important to maintain the potential at the maximum possible value in order to maximize energy conversion efficiency. In this paper, we develop a two-dimensional steady-state model for PAFC to study and understand the relationship between the performance of the fuel cell and various design options.

Section snippets

Phosphoric acid fuel cell (PAFC)—principle of operation

A phosphoric acid fuel cell is composed of two porous gas diffusion electrodes namely anode and cathode (see Fig. 1) [2] juxtaposed against a porous electrolyte matrix. The gas diffusion electrodes comprise a porous substrate that faces the gaseous feed. This substrate is a porous carbon paper or cloth. On the other side of this substrate, which faces the electrolyte (phosphoric acid), platinised fine carbon powder electrocatalyst is roll coated with poly-tetra-fluro-ethylene (PTFE) as a

Background of model development

Modeling of a phosphoric acid fuel cell requires the representation of the following factors in the model: (i) temperature, (ii) operating pressure, (iii) humidity, (iv) electrical load, and (v) phosphoric acid management inside PAFC.

PAFC electrodes are basically porous gas diffusion electrodes (GDE), which are difficult to characterize on a microscopic level. One approach to this problem is to employ a macroscopic model like “porous electrode theory” [1], [4] that accounts for the essential

Development of steady state model for PAFC cathode (oxygen electrode)

Diffusion of Oxygen and back diffusion of water vapor in the porous substrate, where no reaction takes place, can be defined by the following governing equation: $D_{d} RT ∂^{2} p_{i} ∂x^{2} + D_{d} RT ∂^{2} p_{i} ∂y^{2} =0, i=1,2$

Modeling of the reaction layer can be done by using the flooded agglomerate model [1], [4] coupled with gas diffusion equations.

Fig. 3 depicts the concept of flooded electrolyte model [1]. It is considered that the carbon particles containing catalyst (Pt) formed small agglomerates. These agglomerate

Conclusions

The model developed helps in analyzing the distribution pattern of oxygen partial pressure at various points of a composite porous gas diffusion cathode of a PAFC. Current generation at various points of a PAFC cathode depends upon local oxygen concentration. This model helps in determining the area(s) of low oxygen concentration and, thus, is helpful for designing various components of PAFC stacks. The model has been extensively used in NMRL for designing of groove pattern for the oxygen flow

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