Three-dimensional computations of coupled gas and surface diffusion in periodic arrays of solid spheres and spherical cavities are undertaken to assess the role of pore size, void fraction, and pore geometry on permeability. With nano-dimensioned pores, gas-phase diffusion is hindered by the small mean-free path, so the overall permeability hinges on surface diffusion. We prescribe the intrinsic gas-phase diffusivity to be self-consistent with the Knudsen diffusivity obtained from molecular-kinetic simulations reported in the literature. The continuum model of Albaalbaki and Hill then couples the gas and surface phases via an equilibrium adsorption isotherm and kinetic-exchange parameters. Solving these equations in complex pore-scale geometries provides new insights into the coupling. To interpret the results, we decompose the net flux into (i) gas and surface contributions that can be calculated without knowledge of the concentration perturbations to equilibrium, but which depend on the pore geometry, and (ii) counterparts that must be evaluated from integrals of the concentration perturbations to equilibrium. These measures are directly related to the familiar, but less precise, gas and surface tortuosity parameters, which are often used to interpret experiments. The results highlight (i) discontinuous variations in the fluxes when passing through void and solid percolation thresholds, (ii) how the surface flux depends on the specific surface area, and (iii) the pore sizes at which surface transport compares with void transport. (C) 2016 Elsevier Ltd. All rights reserved.