Flow model of a multi-stage hydraulic fractured horizontal well based on tree-shaped fractal fracture networks

Multi-stage hydraulic fractured horizontal wells (MHFHWs) are used to develop low permeability reservoirs. A flow model of the MHFHW is proposed based on tree-shaped fractal fracture networks (TFFNs) considering the tree-shaped fractal network and the hydraulic theory of fracture. Then, a physical model of the MHFHW is established by several TFFNs, including the physical model, generating rules, and numbering rules of the TFFN. A coupling mathematical model is presented by combining the flow and seepage models for the TFFN of the MHFHW. The iterative method is used to solve the mathematical model, and the distributions of pressure, flow rate, and seepage rate in the MHFHW are obtained. The proposed model provides a new method to simulate the flow of the MHFHW considering the tree shape and the fractal characteristics of fractures in the MHFHW.