Study on Seepage Model of Staged-Fractured Horizontal Well in Low Permeability Reservoir

This study addresses the coupled influence of the threshold pressure gradient and stress sensitivity during the seepage process in low-permeability reservoirs. By integrating Laplace transform, perturbation transform, the image principle, and the superposition principle, a non-steady-state seepage model for segmented-fractured horizontal wells considering both effects is established for the first time. The analytical solution of the point source function including the threshold pressure gradient (λ) and stress sensitivity effect (permeability modulus α) is innovatively derived and extended to closed-boundary reservoirs. The model accuracy is verified by CMG numerical simulation (with an error of only 1.02%). Based on this, the seepage process is divided into four stages: I linear flow (pressure derivative slope of 0.5), II fracture radial flow (slope of 0), III dual radial flow (slope of 0.36), and IV pseudo-radial flow (slope of 0). Sensitivity analysis indicates the following: (1) The threshold pressure gradient significantly increases the seepage resistance in the late stage (the pressure curve shows a significant upward curvature when λ = 0.1 MPa/m); (2) Stress sensitivity dominates the energy dissipation in the middle and late stages (a closed-boundary-like feature is presented when α > 0.1 MPa−1); (3) The half-length of fractures dominates the early flow (a 100 m fracture reduces the pressure drop by 40% compared to a 20 m fracture). This model resolves the accuracy deficiency of traditional single-effect models and provides theoretical support for the development effect evaluation and well test interpretation of fractured horizontal wells in low-permeability reservoirs.