Complex analytical solutions for flow in hydraulically fractured hydrocarbon reservoirs with and without natural fractures

Reservoir drainage towards producer wells in a hydraulically and naturally fractured reservoir is visualized by using an analytical streamline simulator that plots streamlines, time-of-flight contours and drainage contours based on complex potentials. A new analytical expression is derived to model the flow through natural fractures with enhanced hydraulic conductivity. Synthetic examples show that in an otherwise homogeneous reservoir even a small number of natural fractures may severely affect streamline patterns and distort the drainage contours. Multiple parallel natural fractures result in a drainage region that is narrower in the direction normal to the natural fractures while the drainage reach is larger in the natural fracture direction. Reservoirs with numerous natural fractures are shown to be characterized by more tortuous drainage patterns than reservoirs without natural fractures. Finally, the analytical flow model for naturally fractured reservoirs is applied to a natural analog of flow into hydraulic fractures. The tendency of the injected fluid to stay confined to the fracture network as opposed to matrix flow is entirely controlled by the hydraulic conductivity contrast between the fracture network and the matrix.