The understanding of the structure–performance relationship of porous media and the optimization of the microstructure is the key to the improvement of its performance applied in various engineering applications involving gas diffusion layers, catalyst support layers, and capillary wicks. The transport property is strongly impacted by the pore phase morphology. Considering the application of fibrous porous material as catalyst support layers, a small pore size attributed to a larger specific surface area leads to an enhanced catalyst loading and reaction, while a larger pore size or specially processed structures, such as grooved microchannels, can provide a highway for flow so that the reactants can be removed in time. In a word, the presence of different pore sizes results in an ideal solution satisfying both properties dominated at different length scales. Nowadays, effects in developing such a multiscale, or in other words, a hierarchy structure for optimized engineered material, has gained considerable attention [1]. For example, P. Trogadas et al. [2] proposed lung-inspired fractal microchannel flow fields applied in polymer electrolyte fuel cells (PEFC) and outperformed the conventional serpentine flow field due to the more uniform reactant distribution. Alternatively, Y. Zhang et al. [3] achieved the desired uniformity in current density by tailoring the porosity variation in the gas diffusion layer (GDL) using a gradient configuration. Briefly, the microchannels [4,5,6] and pore structures [7,8,9,10] demonstrate significant influences on the mass transport properties and have been extensively explored.

These works further inspire the idea of the combination of microchannels and pore structures (Figure 1). Fabricating microchannels on porous structures was proposed [11,12,13] and applied in a methanol steam reforming (MSR) as catalyst support layers, and enhanced hydrogen production was obtained comparing the ones without microchannels. However, on the one hand, experimental measurements for obtaining physical properties could be hard to conduct due to a small pore size. On the other hand, numerical modeling is also difficult since the computational capacity is insufficient to handle a heterogeneous structure. Fortunately, we can apply pore networking as an alternate. Pore network modeling [14] is a kind of pore-scale model that accounts for the true geometrical heterogeneity but simplified geometrical details of the porous material at the pore scale. Despite the simplification, its validation is testified through a comparison with the Lattice Boltzmann method in our earlier efforts [15,16]. The pore network can be extracted from 3D images [17,18] using imaging processing, but the extraction process is nontrivial, let alone hierarchical materials with multi-scale structures. To this end, Sadeghi et al. [19] constructed a 2D regular lattice network consisting of nanopores and macropores were later added into it with its overlapping nanopores removed. This hierarchical pore network architecture was further extended to 3D cases by Moghaddam et al. [20] However, both of the pore networks [19,20] are constructed on regular 2D or 3D lattices, which deviates from the extracted ones in nature. Jiang et al. [21] proposed an approach to generate from an extracted network a stochastic network of arbitrary size. Pores were randomly located in the given network domain and connected by throats according to their correlations. The flow properties involving capillary pressure, absolute and relative permeability were preserved in the stochastic network.