Modern technological advances have enabled one to manufacture nanoporous materials with a prescribed pore structure. This raises a possibility of using controllable pore-scale parameters (e.g., pore size and connectivity) to design materials with desired macroscopic properties (e.g., diffusion coefficient and adsorption capacity). By relating these two scales, the homogenization theory (or other upscaling techniques) provides a means of guiding the experimental design. To demonstrate this approach, we consider a class of nanoporous materials whose pore space consists of nanotunnels interconnected by nanotube bridges. Such hierarchical nanoporous carbons with mesopores and micropores have shown high specific electric double layer capacitances and high rate capability in an organic electrolyte. We express the anisotropic diffusion coefficient and adsorption coefficient of such materials in terms of the tunnels’ properties (pore radius and inter-pore throat width) and their connectivity (spacing between the adjacent tunnels and nanotube-bridge density) Our analysis is applicable for solutes that undergo a non-equilibrium Langmuir adsorption reaction on the surfaces of fluid-filled pores, but other homogeneous and heterogeneous reactions can be handled in a similar fashion. The presented results can be used to guide the design of nanoporous materials with optimal permeability and sorption capacity.