Understanding multi-phase fluid flow and transport processes within aquifers, candidate reservoirs for CO2 sequestration, and petroleum reservoirs requires understanding a diverse set of geologic properties of the aquifer or reservoir, over a wide range of spatial and temporal scales. We focus on multi-phase flow dynamics with wetting (e.g., water) and non-wetting (e.g., gas or oil) fluids, with one invading another. This problem is of general interest in a number of fields and is illustrated here by considering the sweep efficiency of oil during a waterflood. Using a relatively fine-resolution grid throughout a relatively large domain in these simulations and probing the results with advanced scientific visualization tools (Reservoir Visualization Analysis [RVA]/ParaView software) promote a better understanding of how smaller-scale features affect the aggregate behavior at larger scales. We studied the effects on oil-sweep efficiency of the proportion, hierarchical organization, and connectivity of high-permeability open-framework conglomerate (OFC) cross-sets within the multi-scale stratal architecture found in fluvial deposits. We analyzed oil production rate, water breakthrough time, and spatial and temporal distribution of residual oil saturation. As expected, the effective permeability of the reservoir exhibits large-scale anisotropy created by the organization of OFC cross-sets within unit bars, and the organization of unit bars within compound-bars. As a result, oil-sweep efficiency critically depends on the direction of the pressure gradient. However, contrary to expectations, the total amount of trapped oil due to the effect of capillary trapping does not depend on the magnitude of the pressure gradient within the examined range. Hence the pressure difference between production and injection wells does not affect sweep efficiency; although the spatial distribution of oil remaining in the reservoir depends on this value. Whether or not clusters of connected OFC span the domain affects only the absolute rate of oil production—not sweep efficiency.