Abstract Accurate evaluation of recovery mechanisms in fractured reservoirs is challenging due to the large permeability contrast at the matrix-fracture interface. Dual Porosity-Dual Permeability (DPDK) models are typically used in field-scale simulations but can be biased by their use of idealized fracture networks and matrix-fracture interactions. Unstructured Discrete Fracture Models (USDFMs) are able to capture the complex physics accurately but can be computationally demanding. Embedded Discrete Fracture Models (EDFMs) integrate discrete fracture networks with a structured matrix grid and are the focus of this study. Our study considers dense and sparse fracture networks extracted from a field-scale fracture carbonate reservoir model. EDFMs are constructed for different matrix grid resolutions, and simulations are performed to evaluate gravity drainage, spontaneous imbibition, viscous displacement. In each case, EDFM results are compared with highly refined USDFM reference solutions and equivalent DPDK simulations. We improve the EDFM single phase matrix-fracture transfer function to account for pseudo-steady state and fracture interactions. In the cases of gravity drainage, EDFM simulations converge to the fine scale reference solutions with matrix grid refinement. For the coarser grids, the new matrix fracture function gives much better results than the ones reported in the literature. For spontaneous imbibition, both EDFM and USDFM overpredict the rate of spontaneous imbibition with coarse matrix grids, but the overestimation is less severe than with DPDK. In viscous displacements, EDFM overestimates recovery with coarse grids and displacement efficiency diminishes with refinement. DPDK underpredicts recovery from viscous displacement at all resolutions.