Porous materials such as rocks, soils, and peats are typically complex mixtures built up of more than one component, with intrinsic permeabilities that depend on factors such as pore shape and surface area, tortuosity, and connectivity. In such media, the macroscopic permeability is an integrated combination of the permeabilities of the individual components. In this study, we numerically simulated fluid flow in binary mixtures of low- and high-permeability components constructed of spheres and ellipsoids using the lattice-Boltzmann (LB) method to model permeability in porous media. We then applied the effective-medium approximation (EMA) to predict permeability in the simulated binary mixtures. Our results indicate a very good match between predicted permeabilities by EMA and those simulated by LB in simple and body-centered cubic packs as long as the permeability of the high-permeability component Kh is not substantially different than that of the low-permeability component Kl. The upper limit of Kh/Kl for which the EMA approach results in very accurate permeability predictions depends on several factors, such as packing arrangement, grain shape, and porosity. Including all data, we found the EMA permeability predictions still within a factor of two of the LB simulations.