Advances in computational and image acquisition capabilities have made direct simulation of multiphase fluid flow through porous media possible. An example is application of volume of fluid modeling on images produced using the X-ray computed micro-tomography technique. Analysis of such high-resolution (both temporal and spatial) data sets provides new insights into pore-scale dynamics of previously less well-known processes. We present the outcomes of a high-resolution direct-simulation two-phase fluid displacement study performed on a series of five two-dimensional images of sandy porous media produced using erosion and dilation algorithms. This has enabled us to study the pore-scale dynamics systematically in models that are similar in connectivity but different in the morphology (pore sizes and aspect ratio). Our results show that the drainage and imbibition processes result in very distinct fluid displacement patterns in these models at the pore scale. As a result of drainage, the more open (eroded grains) models accommodate large oil clusters, while the tighter (dilated grains) models trap smaller oil clusters. The imbibition process is dominated by oil trapping in two ways: (i) bypassing larger oil clusters in the eroded models and (ii) local trapping of smaller clusters in the dilated models. This behavior is shown to arise from the relatively larger average aspect ratios of the dilated models compared to those of the eroded models. This promotes snap-off at pore throats (in competition with piston-like displacement), resulting in local trapping of the non-wetting phase. Both of these pore-scale trapping regimes seen here allow trapping of oil in as much as 50% of the pore space. Through the use of erosion and dilation operations, we show that a power–law relationship exists between the average pore size and the average grain size for these sandy media. This relationship is useful in designing engineered porous materials where pore sizes need to be estimated based on grain sizes.