The studied 25 by 30 km site of Porto Alegre Southern Brazil fractured granites, accounts for surface lineaments assumed to mimic its fractures. Observations address the lineaments spatial characteristics, significant deviations between stationary groundwater levels condensed at part of the domain while sparse at most of the area, and no pumping/injection rates. Fractured media feature, e.g., dead end pathways, lack of flow interconnections, and preferential infiltration paths. These characteristics are not in line with the implementation of continuum-based macroscopic balance equations. Subject to such data and the inherent features, the objective was to verify if with lumped parameter modeling (LPM) following a flow directed graph approach we can assess a groundwater flow pattern. We at first addressed the site lineaments layout for which the evaluation of the hydraulic heads revealed the existence of isolated lineament clusters, leading to flow or no-flow zones. Aiming at better spatial distribution of flow distributions and based on the site surface lineaments, we established a virtual fracture network (VFN) for which the domain was subdivided into representative elementary area (REA) cells. Each REA was chosen so that the ratio of all its lineament lengths over that of the cell area remained practically unchanged between two consecutive subdivisions. Within each REA, lineaments with similar geometrical characteristics were considered as segment groups. The VFN was established upon elongating segments that created intersection points with other stretched segments from cells at the circumference of a considered REA. The evaluated steady state hydraulic head was compared between two LPM solutions: (1) Referring to flow along the VFN branches between intersection points, and (2) Using a flux interconnected network (FIN) for which each REA was replaced by a pole communicating flow to other poles. Computation of the FIN approach was significantly less intense. Both of these approaches resolved with hydraulic head isolines consistently similar to those obtained by interpolation between the observed groundwater levels. One reported event of a Nitrate polluted well and its plausible contaminating source within the study domain, show that it is in line with the predicted resultant flow direction following the FIN map.