Transient behavior of complex fracture networks

Interacting with the pre-existing natural fractures, multi-stage hydraulic fracturing along horizontal wells creates complex fracture networks in the reservoirs. The flow behavior of these created networks is significantly different from that of traditional single or multiple planar fractures due to complex interplay of flow caused by the interconnected fractures. Therefore, modelling the flow behavior of such fracture networks is essential if one intends to evaluate well performance or characterize fracture properties. In this paper, we present a semi-analytical model for the transient behavior of complex fracture networks in which hydraulic and natural fractures can interconnect with arbitrary angles. To model the flow behavior more rigorously, the fractures within the network are represented explicitly rather than idealized as dual-porosity media with the matrix around them. This approach allows us to concentrate on the details of network properties, especially for the complex geometry and varying conductivity within the fracture. In the model, the transient responses are obtained from coupling a reservoir flow model and a fracture network flow model dynamically. Source functions in Laplace domain and superposition principle are adopted to model the flow behavior in reservoir analytically and the transient flow equation in the network is solved by finite difference method numerically. Furthermore, Star-Delta transformation commonly used in discrete fracture network simulation (DFN) is adopted to solve the interplay of flow between the interconnected fractures. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator for orthogonal network. The parameter analysis indicates that the planar penetration coefficient of natural fractures and the varying fracture conductivity have a great effect on the transient responses and drainage pattern for orthogonal networks. Finally, a field example from the Barnett Shale shows the capacity and practical use of the semi-analytical model to evaluate well performance and stimulation effectiveness of complex fracture networks in unconventional reservoirs.