Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the context of modeling of flow and transport. In this work, we address this challenge with emphasis on the representation of the displacement efficiency in coarse-scale modeling. We propose a dual-porosity upscaling approach to handle displacement calculations in high resolution and highly heterogeneous formations. In this approach, the pore space is arranged into two levels of porosity based on flow contribution, and a dual-porosity dual-permeability flow model is adapted for coarse-scale flow simulation. The approach uses fine-scale streamline information to transform a heterogeneous geomodel into a coarse dual-continuum model that preserves the global flow pathways adequately. The performance of the proposed technique is demonstrated for two heterogeneous reservoirs using both black oil (waterflooding) and compositional (gas injection) modeling approaches. We demonstrate that the coarse dual-porosity models predict the breakthrough times accurately and reproduce the post-breakthrough responses adequately. This is in contrast to conventional single-porosity upscaling techniques that overestimate breakthrough times and displacement efficiencies (sweep). By preserving large-scale heterogeneities, coarse dual-porosity models are demonstrated to be significantly less sensitive to the level of upscaling, when compared to conventional single-porosity upscaling. Accordingly, the proposed upscaling approach is a relevant and suitable technique for upscaling of highly heterogeneous geomodels.