Multiple hydraulic fracture treatments in reservoirs with natural fractures create complex fracture networks. Predicting well performance in such a complex fracture network system is an extreme challenge. The statistical nature of natural fracture networks changes the flow characteristics from that of a single linear fracture. Simply using single linear fracture models for individual fractures, and then summing the flow from each fracture as the total flow rate for the network could introduce significant error. In this paper we present a semi-analytical model by a source method to estimate well performance in a complex fracture network system. The method simulates complex fracture systems in a more reasonable approach. We statistically assigned a fracture network of natural fractures, based on the spacing between fractures and fracture geometry. We then added multiple dominating hydraulic fractures to the natural fracture system. Each of the hydraulic fractures is connected to the horizontal wellbore, and some of the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying the superposition principle to all of the fractures. The fluid inside the natural fractures flows into the hydraulic fractures, and the fluid of the hydraulic fracture from both the reservoir and the natural fractures flows to the wellbore. The finite conductivity of hydraulic fractures is modeled by additional pressure drop inside the fracture, but it is neglected in natural fractures. This paper also shows that non-Darcy flow effects have an impact on the performance of fractured horizontal wells. In hydraulic fracture calculation, non-Darcy flow can be treated as the reduction of permeability in the fracture to a considerably smaller effective permeability. The reduction is about 2% to 20%, due to non- Darcy flow that can result in a low rate.

The semi-analytical solution presented can be used to efficiently calculate the flow rate of multistage-fractured wells. Examples are used to illustrate the application of the model to evaluate well performance in reservoirs that contain complex fracture networks.