The volume averaging method (VAM) is widely used for estimating the effective diffusivity for solute transport in constrained geometries (e.g., porous media). Comparisons with experimental results for different geometric configurations have indicated that the VAM can provide accurate results over a wide range of porous media configurations. This work uses Brownian dynamics simulations (BDS) to estimate effective diffusivities for constrained geometries and to assess the accuracy of estimations from the VAM. For simple microscale geometric configurations, both isotropic and non-isotropic, it was found that the results predictions of effective diffusivity from VAM agree well with results from the BDS for high porosity values. However, some discrepancies are found for low porosity values, which were attributed to a smoothing effect of the VAM closure problem in the vicinity of very small apertures. (C) 2012 Elsevier Ltd. All rights reserved.