The objective of this study is to visualize the drained rock volume (DRV) and pressure depletion in hydraulically and naturally fractured reservoirs, using a high-resolution simulator to plot streamlines and time-of-flight contours that outline the DRV, based on computationally efficient complex potentials. A recently developed expression based on fast, grid-less Complex Analysis Methods (CAM) is applied to model the flow through discrete natural fractures with variable hydraulic conductivity. The impact of natural fractures on the local development of DRV contours and streamline patterns is analyzed. A sensitivity analysis of various permeability contrasts between natural fractures and the matrix is included. The results show that the DRV near hydraulic fractures is significantly affected by the presence of nearby natural fractures. The DRV location shifts according to the orientations, permeability and the density of the natural fractures. Reservoirs with numerous natural fractures result in highly distorted DRV shapes as compared to reservoirs without any discernable natural fractures. Additionally, the DRV shift due to natural fractures may contribute to enhanced well-interference by flow channeling via the natural fractures, as well as the creation of undrained rock volumes between the natural fractures. Complementary pressure depletion plots for each case show how the local pressure field changes, in a heterogeneous reservoir, due to the presence of natural fractures. The results from this study offer insights on how natural fractures affect the DRV and pressure contour plots. This study uses a fast grid-less and meshless high-resolution flow simulation tool based on CAM to simulate the flow in heterogeneous naturally fractured porous media. The CAM tool provides a practical/efficient simulation platform, complementary to grid-based reservoir simulators.