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Although engineers can control the internal geometry of materials down to the micro-scale, it is unclear what configuration is ideal for a given transport process. We explore the use of mazes as abstract representations of two-phase systems. Mazes can be easily generated using many different algorithms and then represented as graphs for analysis. The three, dimensionless graph parameters of effective tortuous resistance, average tortuosity, and minimum-cut-size were derived and then correlated to the maze’s effective transport property (e.g., permeability), average residence time, and robustness, respectively. It was shown that by tuning the settings of the maze algorithm, one can obtain desired maze performance. Finally, a composite maze was constructed and shown to mimic the geometry and permeability of a real commercial membrane. In principle, a surrogate maze geometry can be optimized/tuned for a given transport process and then used to guide the rational design of the engineered system it represents.