In this work, a mathematical model is developed for production data analysis (PDA) in complex fracture-network horizontal wells, and the PDA is mainly based on the log-log plots of rate-normalized pressure (RNP) versus material-balance time. Stimulated region (Inner Region) and non-stimulated region (Outer Region) with different permeability caused by stimulated reservoir volume (SRV) effects are also considered in the mathematical model. The mathematical model is solved by semi-analytical approach with discretization of fracture networks and region boundaries. With the model solutions, verifications based on a numerical model and sensitivity analysis based on the proposed model are all performed
The comparison results show that the proposed model matches well with the numerical simulator. For the well productivity, it increases with the increases in outer radius and inner radius, while it decreases with the increases in mobility ratio and capacity ratio. Like pressure difference and its derivative, the flow regimes of production behaviors are identified based on RNP and RNP’. According to their special features, it is learnt that the production behaviors of horizontal wells with complex fracture networks can be divided into eight stages. Similar to conventional composite formation, the mobility ratio mainly affects the transitional flow, flow in Outer Region, and boundary-dominated flow. The horizontal value of RNP derivative in Outer Region is 0.5M. The larger the capacity ratio is, the steeper the RNP curves in late stages go up. With the increase in capacity ratio, the boundary-dominated flow appears earlier as the elastic energy of Outer Region is smaller. In addition, with the increase of inner radius, the pseudo radial flow in Inner Region lasts longer, and the appearances of transition flow and flow in Outer Region are later. The starting time of boundary-dominated flow is completely controlled by dimensionless outer radius.