The ionic conductivity is essential to the performance of a solid oxide fuel cell (SOFC). While the effective conductivity of a porous electrode is frequently involved in SOFC models, the concept of the real (in situ) conductivity in a working electrode is yet to be clarified. To model the in situ ionic and electronic conductivity, the microstructure/geometry and the associated spatial property distribution, as well as the chemical reactions have to be explicitly considered. Here we present a theoretical framework together with phase field modeling to approach this issue. In addition, a recently developed spectral method is used to solve the transport problem in media with complex microstructure.