Porous structures are naturally involved in electrochemical processes. The specific architectures of the available porous materials, as well as their physical properties, crucially affect their applications, e.g., their use in fuel cells, batteries, or electrolysers. A key point is the correlation of transport properties (mass, heat, and charges) in the spatially—and in certain cases also temporally—distributed pore structure. In this paper, we use mathematical modeling to investigate the impact of the pore structure on the distribution of wetting and non-wetting phases in porous transport layers used in water electrolysis. We present and discuss the potential of pore network models and an upscaling strategy for the simulation of the saturation of the pore space with liquid and gas, as well as the computation of the relative permeabilities and oxygen dissolution and diffusion. It is studied how a change of structure, i.e., the spatial grading of the pore size distribution and porosity, change the transport properties. Several situations are investigated, including a vertical gradient ranging from small to large pore sizes and vice versa, as well as a dual-porosity network. The simulation results indicate that the specific porous structure has a significant impact on the spatial distribution of species and their respective relative permeabilities. In more detail, it is found that the continuous increase of pore sizes from the catalyst layer side towards the water inlet interface yields the best transport properties among the investigated pore networks. This outcome could be useful for the development of grading strategies, specifically for material optimization for improved transport kinetics in water electrolyser applications and for electrochemical processes in general.