質子交換膜燃料電池陰極反應之電腦模擬

Modeling and Simulation on the Cathode Reaction of PEM Fuel Cell

譚金鴻(Gin-Hong Tan)

指導教授 ： 尋孝國

元智大學/工程學院/化學工程與材料科學學系/碩士(2001年)

摘要

本研究以推導數學模組的方式來調查質子交換膜燃料電池(proton exchange membrane fuel cell)陰極之結構與參數對於傳遞現象以及反應之影響，藉以了解如何能夠獲得較佳的電池效能。與一般文獻不同的部份，是我們採用二維模式來進行討論，考慮雙極板之溝槽結構，造成僅有氣體可以直接擴散的氣體通道與僅有電子可以傳導之電極板部位，亦即導電區與氣體通道並不是相互重疊而是相互間隔。
首先我們討論在陰極觸媒層(cathode catalyst layer)中反應物(氧氣、氫離子與電子)之傳遞與反應現象，其中氫離子在高分子離子體(ionomer)中的傳遞現象是以Nernst-Planck equation來描述，而在陰極觸媒層中反應生成電流的動力學模式則是以Butler-Volmer equation來計算。接下來，我們使用Stefan-Maxwell equation來描述多成份氣體(氧氣、氮氣與飽和水蒸汽)由氣體擴散層(gas diffusion layer)朝著觸媒層進行傳遞的現象。
經由以B-spline為基底函數之有限元素配點法求取數學模式的數值解。計算結果顯示以二維模式計算與一般模擬時將導電區與氣體通道重疊計算之一維模式計算結果會有一些差異。一維模式計算結果因為忽略了電極平面方向的濃度梯度及電位梯度，而較為偏離真實情況。結果顯示，由於氣體擴散層的存在，可以幫助氣體較均勻地擴散至觸媒層，而減小一維模式與二維模式計算結果之差異。當溝槽寬度越大時，會造成氣體擴散較不平均，使得一維模式計算結果偏離二維模式計算之結果。而過薄或孔隙度過低的氣體擴散層也會降低氣體平均擴散至觸媒層的機會，而造成電池效能的下降。另外，也比較了其他參數如電解值在觸媒層中所佔比例、氧氣使用分壓等對於電池效能的影響。

關鍵字

質子交換膜 ； 燃料電池 ； 數學模組 ； 陰極反應

並列摘要

A mathematical model is developed to investigate transport phenomena as well as electrochemical reaction occurring in the cathode of a proton exchange membrane fuel cell (PEMFC). The main goal of the present research is to explore the two-dimensional effects that have been ignored by most previous investigators. Restriction of the access of oxygen to the catalyst layer of the cathode by the ribs of bipolar plates is taken into account in the model presently studied.
In the catalyst layer, Nernst-Planck equation is used to describe the mass transport of proton in the ionomer, and the electrochemical reaction is assumed to follow the Butler-Volmer equation. In addition, the Stefan-Maxwell equation is applied to calculate the local mole fraction of gaseous species in the diffusion layer.
A method of collocation on finite elements based on B-spline interpolation is employed for the numerical solution of the coupled nonlinear differential equations. The computational results reveal that the one-dimensional model would overestimate the cathode performance since it ignores the concentration and potential gradients along the plane direction. The two-dimensional model is likely to yield more accurate presentation of the cathode performance due to its realistic considerations. Though the existence of diffusion layer could obviously reduce the differences between the one-dimensional model and the two-dimensional model, an inappropriate thickness or porosity may also adversely affect the performance of the fuel cell. The effects of percentage of Nafion in catalyst layer, oxygen pressure and other parameters are also discussed.

並列關鍵字

pem ； fuel cell ； modeling ； Cathode Reaction

參考文獻

1. Hassmann, K., and R. Rippel, “A new approach to fuel cell investment strategy”, J. Power Sources 71, 75(1998).

2. Teagan, W. P., J. Bentley, and B. Barnett, “ Cost reductions of fuel cells for transport applications：fuel processing options”, J. Power Sources 71, 80(1998).

3. Barbir, F., and T. Gomez, “Efficiency and economics of proton exchange membrane(PEM) fuel cells”, Int. J. Hydrogen Energy 22, 1027(1997).

4. Donitz, W., ”Fuel cells for mobile applications, status, requirements and future application potential”, Int. J. Hydrogen Energy 23, 611(1998).

5. Xue, D., and Z. Dong, “Optimal fuel cell system design considering functional performance and production costs”, J. Power Sources 76, 69(1998).