Modeling the flow characteristics of high-velocity non-Darcy flow in gas reservoirs with heterogeneously distributed fractures

In naturally fractured gas reservoirs with highly heterogeneous fracture distributions, high-velocity non-Darcy (HVND) flow tends to occur near the wellbore, especially in fracture-intensive zones. As flow velocity increases, inertial and nonlinear effects become significant, causing deviation from linear Darcy behavior. The conventional Darcy flow equation neglects these nonlinear factors and thus fails to represent the actual flow conditions accurately. To address this, a dual-porosity, dual-permeability two-region composite model is developed, applying Izbash’s equation to the inner HVND zone and Darcy flow to the outer zone. The model incorporates porosity and permeability contrasts between matrix and fractures, along with wellbore storage and skin effects. A semi-analytical solution is obtained using line source function, linearization, Laplace transform, and Stehfest inversion. Bottomhole pressure and derivative curves reveal seven flow stages, including non-Darcy crossflow, transition flow, and Darcy crossflow. The non-Darcy index quantifies HVND intensity; lower values indicate stronger nonlinearity. More intensive fractures enhance interregional transmissibility and storage, amplifying transition-stage responses. The proposed model effectively characterizes HVND behavior in gas reservoirs with spatially heterogeneous fractures, providing a theoretical basis for analyzing complex well test responses.