Improved and enhanced oil recovery (IOR/EOR) processes, such gas injection and waterflooding, are difficult to model accurately in fractured reservoirs due to complicated multiphase physics and the strong property contrast between permeable natural fractures and tight matrix rock. Traditionally, fractured reservoirs are modeled using coarse dual-porosity (DP) simulation models that idealize the fracture system. Consequently, important recovery physics can be missed, causing misleading flow predictions. We present an unstructured discrete-fracture-matrix (DFM) approach for three-phase, fully compositional simulations of IOR/EOR processes. We generate detailed DFM grids that represent several thousand realistic discrete fractures and different well configurations. These grids are then discretized for IOR/EOR flow simulations. We apply the flow-based multiple subregion (MSR) technique with two subregions to generate unstructured coarse-scale fracture models that are directly based on the DFM sector models. We next employ MSR upscaling to create corresponding structured DFM-based dual-porosity, dual-permeability (DPDK) models, computing parameters like shape factors and effective fracture permeabilities. We lastly generate conventional DPDK models by invoking simplifying assumptions and analytical equations. Using DFM results as reference solutions, we find the following order of decreasing accuracy: MSR, DFM-based DPDK, and conventional DPDK models. The DPDK models result in significant inaccuracies at individual wells when important fluid movement (e.g., gas breakthrough) is missed. The errors at sector scale are lower due to cancellation of errors at wells. The simulation results indicate that oil recovery and injected fluid breakthrough behavior are a complicated function of the reservoir heterogeneity, well configurations, and phase behavior. Large modeling errors can potentially lead to the selection of a sub-optimal injectant. One to two orders of computational speedup are achieved from the upscaling. These findings point to the need for systematic upscaling of realistic DFM representations to generate fast and accurate coarse fracture models for the assessment of field-development IOR/EOR schemes.