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A semi-analytical model for transient flow behavior of hydraulic fracture networks
JIA Pin, CHENG Linsong, HUANG Shijun, LI Quan
(College of Petroleum Engineering in China University of Petroleum, Beijing 102249, China)
Abstract:
Comparing with the flow in single and multiple fractures, the flow behaviors in hydraulic fractured networks that consist of interconnected fractures are featured of flow redirection and flux redistibution at fracture intersections. In this paper, the flow behavior in fractured networks was modeled and the numerical solution was given by combining star-delta transformation and finite difference methods. An analytical solution for the flow in reservoir matrix was obtained based on source functions in Laplace domain and superposition principles. A semi-analytical model for the transient flow in hydraulic fractured networks was derived by dynamically coupling these two flow processes. The model was verified with a field case study. The results show that the semi-analytical model can be applied to fracture networks with arbitrary geometry and variable fracture conductivity. The transient bottomhole pressure and production rate can be solved along with reservoir pressure distribution during different production periods. In an infinite slabed reservoir, the flow in hydraulic fractured networks can be classified into five flow regimes, including the fracture linear flow, bilinear flow, formation linear flow, transient flow and pseudo-radial flow. The afterflow caused by wellbore storage effect may overshadow the fracture linear flow. For the reservoirs with permeability of 1×10-7 μm2, the fluid drainage occurs primarily in the vicinity of the fractures with large density and higher conductivity at the early-middle production periods. However, the ultimate depletion (e.g. after 30-50 years of production) is still limited to the region of the stimulated reservoir volume and the fluid flow beyond the stimulated region makes little contribution to the total production.
Key words:  hydraulic fracture networks  star-delta transformation  finite difference method  point source function  transient responses