Elsevier

Journal of Power Sources

Volume 162, Issue 1, 8 November 2006, Pages 316-326
Journal of Power Sources

Parameter setting and analysis of a dynamic tubular SOFC model

https://doi.org/10.1016/j.jpowsour.2006.06.086Get rights and content

Abstract

An improved one-dimensional dynamic model of a tubular SOFC stack capable of system simulation in the virtual test bed (VTB) simulation environment is presented in this paper. This model is based on the electrochemical and thermal modeling, accounting for the voltage losses and temperature dynamics. The modeling of an external reformer is also included in this study. A detailed parametric analysis of working conditions and cell configuration of the solid oxide fuel cell (SOFC) stack is the main focus of this paper. The following operating parameters are investigated: pressure ratio, temperature, mass flow rate, external reforming degree and stream to carbon (S/C) ratio. The cell geometric parameters studied include cell diameter and cell length. Elevated operating pressure improves the cell performance. Whereas, higher operating temperature decreases both the Nernst potential and the irreversible losses, resulting in an initial increase then a decrease in cell efficiency. It was found that a higher S/C ratio yields a lower H2 concentration and partial pressure, which has a negative effect on the Nernst potential. Increased cell diameter is found to increase the power due to a larger activation area at the same time and due to longer current path length there is an increase in the ohmic loss. Increased length of the cell has the undesired affect of an increased pressure drop.

Introduction

The high temperature solid oxide fuel cell (SOFC), with the advantages of its high efficiency, environmental friendliness and flexibility of usable fuel types, has been considered as one of the most promising technologies for electric energy generation. Many variations of SOFC fuel cell design are possible: such as tubular, planar and monolithic. The tubular SOFC power system (Siemens-Westinghouse Power Corporation), integrated with a gas turbine, has achieved an overall 55% efficiency [1]. The planar and monolithic SOFC technologies are frequently analyzed in the literature. The current paper focuses on an improved dynamic model for a tubular SOFC stack, and a detailed parameter analysis of operating conditions and cell geometric configurations. Parameter analysis not only shows the influence of the parameters’ variance on the SOFC performance, but also identifies areas of the largest possible impact with the least effort.

In the past couple of years, several models have been developed and tested to study the design and operating conditions of SOFC stack. Most models, however, are steady state models [2], [3], [4] and are valid for only the specific operating points. Padulles et al. [5] developed a SOFC model with focus on electrochemistry and species dynamics, but temperature and heat transfer dynamics were not considered in their model. A dynamic transient SOFC model has been developed by Sedghisigarchi [6], however, their model is based on lumped capacitance model where the spatial distributions of temperature, current density and species concentration are not investigated. In addition, few studies have evaluated the effect of length of current pathway, which has significant influence on the cell diameter.

In this paper, a one-dimensional dynamic model of a tubular SOFC is presented with external reforming and system integration capabilities. Based on the electrical behavior, chemical reaction equilibrium and energy balance, the proposed model can predict the SOFC characteristics in steady states and also in transient operating states. The accuracy and reliability of the model is demonstrated by comparisons with experimental data from the literature. The distinctive feature of the current model is that the model takes into consideration the variation of variables in the axial direction, as a result it can predict the cell performance more accurately. Another important feature of the proposed model is that, the concentration loss is modeled by introducing partial pressure related to limiting current and an equivalent circuit has been built to evaluate how the length of the current pathway affects the ohmic loss of a tubular SOFC. In addition, the simulation results of the model, which is dynamic in nature, can be used for performance evaluation and cell design optimization under variable operating conditions and geometric conditions.

The virtual test bed (VTB) platform provides an effective computational environment to simulate the dynamic performance of the SOFC stack [7], [8]. The non-linear model equations based on electrochemistry and thermodynamics are discretized in resistive companion (RC) form for effective implementation in the VTB platform.

The paper is organized as follows. In Section 2, the system configurations, operating conditions and important assumptions of SOFC stack are presented. The model description is presented in details in Section 3. The parameter analysis of operating conditions and cell configuration are presented in Section 4. Conclusions are drawn in Section 5.

Section snippets

System configuration

Fig. 1 illustrates the system configurations of a SOFC stack implemented in the VTB simulation environment. The system consists of one SOFC stack, an external reformer, two valves, one electrical load and two thermal sinks. A methane–steam mixture is supplied to the external reformer before being delivered to the SOFC stack. The inlet pressure and temperature of fuel and air are assumed as constant and defined as user input parameters. The fuel from the external reformer and the air are

Model description

A one-dimensional dynamic model of a SOFC stack, based on the earlier work [20], has been developed. The stack model has been improved significantly by introduction of an external reformer, appropriate modeling of concentration loss by introducing partial pressure related to limiting current, and most importantly, an equivalent circuit has been built to evaluate how the length of current pathway affects the ohmic loss of tubular SOFC. The following important assumptions are made in developing

Parameter analysis

The parameter analysis of tubular SOFC, based on the design point listed in Table 1 and system shown in Fig. 1, will be presented in this section. The following operating parameters are investigated:

  • Stack pressure ratio (operation pressure to atmosphere pressure).

  • Temperature, including stack mean temperature, air inlet temperature and fuel inlet temperature.

  • Mass flow rate, including air flow rate and fuel flow rate.

  • Degree of external reforming.

  • Stream to carbon (S/C) ratio.

The cell geometric

Conclusions

A one-dimensional dynamic SOFC model, based on the electrochemical and thermal modeling, has been successfully developed and simulated in the VTB simulation environment. Comparisons between the simulation results and the experimental data, under different operating pressures and temperatures, demonstrate the accuracy and reliability of the model. A detailed parameter analysis of stack working condition and cell configurations of the SOFC stack is presented in this study. Listed below are the

Acknowledgements

The authors would like to acknowledge Office of Naval Research (ONR) and the ESRDC consortium for their financial support.

References (21)

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