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The drainage areas (and volumes) near hydraulically fractured wells, computed and visualized in our study at high resolution, may be critically affected by the presence of natural fractures. Using a recently developed algorithm based on complex analysis methods (CAMs), the drained rock volume (DRV) is visualized for a range of synthetic constellations of natural fractures near hydraulic fractures. First, flow interference effects near a single hydraulic fracture are systematically investigated for a variety of natural fracture sets. The permeability contrast between the matrix and the natural fractures is increased stepwise in order to better understand the effect on the DRV. Next, a larger-scale model investigates flow interference for a full hydraulically fractured well with a variety of natural fracture sets. The time of flight contours (TOFCs) outlining the DRV are for all cases with natural fractures compared to a base case without any natural fractures. Discrete natural fractures, with different orientations, hydraulic conductivity, and fracture density, may shift the TOFC patterns in the reservoir region drained by the hydraulically fractured well, essentially shifting the location of the well’s drainage area. The CAM-based models provide a computationally efficient method to quantify and visualize the drainage in both naturally and hydraulically fractured reservoirs.