主要对碳基固体氧化物燃料电池（SOFC）中三传二反的控制方程、不同尺度的不同物理场理论模型以及碳基燃料的重整、催化和硫化等方面进行概括总结。SOFC有可使用氢气、一氧化碳、甲烷和其他的碳氢化合物作为燃料进行电化学反应的燃料灵活性，但使用碳氢燃料需要解决诸如碳基燃料的重整、电极的催化、积碳和硫化等问题。电池内部反应气体的物质输运、电荷输运、能量输运、动量输运和化学及电化学反应状态均可以用偏微分方程来描述。运用这些电化学反应和输运的偏微分方程，结合材料的微观性质，可以建立SOFC的多尺度多物理场模型。通过理论模型研究材料微结构与性质、工作条件、几何构型等参数对电池性能的影响，对SOFC材料组成与电池堆结构进行定量分析和优化设计，可以加速SOFC技术的更快发展。

This paper summarizes the governing equations and multi-scale modeling methods for the thermal, electrical and mass transports, reformation, catalytic and sulfurization reactions in SOFCs. SOFCs have the advantage of fuel flexibility by converting a broad range of fuels such as hydrogen, carbon monoxide, methane and other hydrocarbons into electricity, but require in depth understanding of the processes of reformation, catalysis， coke and vulcanization. The transports of fuel and oxidant, heat and electricity, chemical and electrochemical reactions may be described by solving their coupled partial differential equations. The multiscale model based on these equations and the material microstructures are used to study the effects of operating conditions, material properties and geometrical configurations on the SOFC performance. Quantitative analysis and design optimization of the material compositions and the stack configurations are helpful for accelerating the development of SOFC technology.