A Fast Simulation Method for Predicting the Production Behavior of Artificial Fractures Based on Diffusive Time of Flight

Multi-stage hydraulic fracturing is a widely used technology in the development of shale oil and gas reservoirs that creates artificial fractures and forms fracture networks that enhance fluid flow within reservoirs. A well-designed fracture network can significantly enhance the production performance of oil and gas wells, thereby improving the recovery of shale oil and gas reservoirs. To achieve this, understanding the gas production performance of individual artificial fractures is crucial, as it provides valuable insights for refining subsequent fracturing designs, ultimately leading to an optimized fracture network design. At present, numerical simulations are commonly used to study the production performance of individual artificial fractures by modeling the production process of the entire shale oil and gas reservoir. However, due to the heterogeneity of reservoirs and the presence of numerous natural fractures, traditional numerical simulations require high-resolution grids to model the production process, making them computationally expensive and time-consuming. To address this issue, in this work, based on the concept of diffusive time of flight (DTOF), the authors propose a fast simulation method to efficiently simulate the production behavior of individual artificial fractures throughout the shale oil and gas reservoir production process. The DTOF can be obtained by solving the Eikonal equation using the fast marching method (FMM), which is then used to calculate the drainage volume of individual artificial fractures. Subsequently, a geometric approximation of the drainage volume is used to efficiently compute the production rates of individual artificial fractures. Unlike traditional numerical simulations, this method uses a single non-iterative calculation to determine the drainage volume of individual artificial fractures, followed by a geometric approximation to compute the production rates. This eliminates the need for high-resolution grids, significantly reducing computational cost and time, which allows the proposed method to provide faster simulations compared to traditional numerical methods while maintaining sufficient accuracy.