An Efficient Method for Simulating High-Velocity Non-Darcy Gas Flow in Fractured Reservoirs Based on Diffusive Time of Flight

In gas reservoirs, high gas velocity causes significant inertial effects, leading to a nonlinear relationship between pressure gradient and velocity, especially near wellbores or fractures. In such cases, Darcy’s law is inadequate, and the Forchheimer equation is commonly used to model nonlinear flow behavior. Although the Forchheimer equation improves simulation accuracy for high-velocity flow in porous media, incorporating it into conventional numerical simulations greatly increases computational time, as nonlinear flow equations must be solved over the entire reservoir. This difficulty is exacerbated in heterogeneous fractured reservoirs, where complex fracture–matrix interactions and localized high-velocity flow complicate solving nonlinear equations. To address this, this work proposes a fast numerical simulation method based on diffusive time of flight (DTOF). By using DTOF as a spatial coordinate, the original three-dimensional flow equations incorporating the Forchheimer equation are reduced to a one-dimensional form, enhancing computational efficiency. DTOF represents the diffusive time for a pressure disturbance from a well to reach a specific reservoir location and can be efficiently computed by solving the Eikonal equation via the fast marching method (FMM). Once the DTOF field is obtained, the three-dimensional problem is transformed into a one-dimensional problem. This dimensionality reduction enables fast and reliable modeling of nonlinear high-velocity gas transport in complex reservoirs. The proposed method’s results show good agreement with those from COMSOL Multiphysics, confirming its accuracy in capturing nonlinear gas flow behavior.