Rate Transient Analysis for Fractured Wells in Inter-Salt Shale Oil Reservoirs Considering Threshold Pressure Gradient

The low-velocity non-Darcy effect within the shale matrix significantly influences the well production performance of shale reservoirs, primarily caused by the threshold pressure gradient identified by various researchers. Moreover, in inter-salt shale reservoirs, salt minerals dissolve and diffuse when they encounter water-based working fluids, resulting in substantial alterations in pore structure. This paper introduces a transient pressure model for inter-salt shale oil reservoirs that accounts for oil flow from formation to the wellbore, considering all of the aforementioned mechanisms. The partial differential equations of this dual-porosity model, which incorporate salt dissolution and the low-velocity non-Darcy effect in the shale matrix, are derived. An accurate solution is achieved through the application of Laplace transformation and Green’s functions. We derive the analytical solutions for transient pressure and production in real space by employing the Stehfest numerical inversion method and obtain the bi-logarithmic type curves. Six distinct flow regimes are identified, and the impacts of salt dissolution, the threshold pressure gradient, the cross-flow coefficient, and the storativity ratio are discussed. This analysis holds significant importance for evaluating fluid flow and transport in inter-salt shale oil reservoirs.