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Low-velocity non-linear flow is the basic form of fluid movement in low-permeability reservoirs; however, most of the current well-test methodologies are developed based on Darcy's flow, which leads to inaccurate interpretation results. In addition, water-injection development and hydraulic fracturing technology are considered the most effective methods for the development of low-permeability reservoirs, whereas the traditional single-well testing model ignores the interference effect of adjacent wells on observation wells, leading to a deviation between the interpretation results and actual reservoir properties. Therefore, research on interference well-testing models based on non-linear flow for vertical fractured wells (VFW) is necessary. In this paper, a new interference well-test model is proposed to study the transient pressure behaviour of a VFW surrounded by multiple adjacent injection wells. The fluid in the matrix system moves in the form of a non-linear flow, but it conforms to Darcy's flow in the fracture system. Hydraulic fractures are unique channels wherein fluid flows from the matrix system into the wellbore. The simulation results reveal that non-linear flow exhibits 20–30% slower pressure propagation and 15–25% lower bottomhole pressure (BHP) during unsteady flow compared with Darcy flow. In steady-state flow, it generates low-pressure zones that are 30–50% broader and requires up to 3.1 MPa greater pressure drops. Typical curves identify four distinct flow regimes (wellbore storage, fracture flow, pore flow and interference flow), with non-linear flow elevating pressure derivatives by 30% in the pore flow and interference stages. Sensitivity analyses demonstrate that increasing the fracture half-length (0–90 m) or fracture count (one–four) reduces the BHP by 15–25%. Higher production rates (4–10 m3/day) intensify drawdown and suppress interference effects. Expanding well spacing (150–300 m) delays interference onset by 40% and halves its amplitude.
These findings demonstrate that neglecting non-linear effects in low-permeability reservoirs systematically underestimates permeability and overpredicts energy replenishment efficiency. For practical applications, the model advocates optimizing fracture parameters and production strategies to achieve rational field development.