The transport efficiency of anisotropic functional membranes is largely dictated by the geometry and orientation of their internal pores. In this study, a numerical finite-volume framework was developed to evaluate how elliptical pore eccentricity ($\epsilon cc$) and orientation influence charge transport and effective conductivity ($e_k$) within two-dimensional porous membrane microstructures. Canonical stochastic domains with controlled porosity were generated, considering parallel and perpendicular aligned configurations of the major pore axis relative to the imposed potential gradient. Results demonstrated a strong orientation dependence: under perpendicular alignment, the effective conductivity decreased by up to 70% as εcc increased from 0.5 to 0.999, while parallel alignment maintained at $e_k$ > 0.8 even for highly elongated pores. The aspect ratio $(b/a)$ was identified as a secondary geometric modulator producing opposite conductivity trends depending on orientation. Through isotropy-error analysis, a critical morphological threshold at $\epsilon cc$ ≈ 0.9 was found, indicating the onset of structural anisotropy and loss of isotropic transport. These results establish a quantitative structure–property relationship linking pore geometry to macroscopic transport performance. The proposed stochastic FVM-based approach provides a generalizable and computationally efficient tool for the design and optimization of anisotropic porous membranes used in electrochemical and energy-conversion devices.

The electrochemical performance of hydrogen compressors (EHCs) depends critically on the hierarchical microstructure of their catalyst layers (CLs), where platinum, carbon, and ionomer phases govern coupled charge and mass transport across nanometric (Nano) and mesoporous (Meso) scales, the latter characterized by agglomerate and pore phases. This work presents an experimental–computational framework to establish quantitative microstructure–transport–performance relationships in EHC CLs. CLs were fabricated by electrospray deposition on Nafion^® 117 membranes and characterized by scanning electron microscopy, from which 33 representative Meso MCs were extracted and used to assemble an EHC cell for experimental polarization curves. Statistically equivalent Nano MCs resolved phase connectivity within the agglomerate phase and determined the effective catalyst area from neighboring phase configurations. Effective transport coefficients for electronic conductivity, protonic conductivity, and H₂ diffusivity were computed via the finite volume method and multiscale-coupled into an analytical polarization model. Electronic and protonic conductivities are controlled by conductive-phase connectivity at the Nano scale, while H₂ diffusivity is governed by the pore fraction and spatial distribution at the Meso scale, with variations exceeding three orders of magnitude. Multiscale transport coupling factors obtained via inverse calibration reduced model–experiment discrepancies to 0.05 V, validating the framework for EHC electrode design.