The flow toward hydraulic fractures is visualized at high resolution using a newly developed analytical streamline simulator that is based on complex potentials. Drainage contours show progressive fluid recovery from the stimulated rock volume (SRV). The method plots streamlines, time-of-flight contours, velocity-field contours, and pressure distribution around fractured wells. Independent simulations with a commercial reservoir simulator confirm that visualizations with complex potentials are accurate, and that the latter method provides high-resolution images of the pressure and flow fields around individual fractures. Contours for the drained rock volume (DRV) that are based on particle-velocity tracking outline the actual region drained by a well through its fractures. First, matrix drainage by two-fracture and three-fracture clusters is studied in detail. Flow-separation surfaces between two clustered fractures (with equal length and flux) are always straight, creating planes of symmetry between adjacent drainage regions. Clusters of three fractures develop curved-flow-separation surfaces, convex toward the inner fracture. For fracture spacing less than four times total fracture length, drainage of the central region of the three-fracture clusters slows down because of flow interference, which confirms earlier findings that production gains become insignificant above certain fracture length/spacing ratios. Next, the analysis shows the flow field, drainage contours, velocity contours, and pressure distribution for a horizontal, synthetic well with 11 transversal, kinked fractures. A final section shows a brief example of application to a field case.

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