Asymptotic-Poroelastic Model for Reservoir Compaction Damage Management in Fractured Oil Wells with Stress-Dependent Permeability

The adequate management of the damage caused by effective permeability loss in stress-sensitive reservoirs becomes essential to productivity maintenance. This paper proposes a new unsteady-state poroelastic solution for the nonlinear hydraulic diffusivity equation in Biot’s effective stress-sensitive reservoirs fully penetrated by fractured oil wells. The hydraulic fracture in the proposed mathematical modeling is finite with tip effects and crosses the whole reservoir net pay. The NHDE is expanded in a first-order asymptotic series, and a poroelastic integro-differential solution coupled with a Green’s function (GF) is used to represent the source/sink term. A set of pore pressure and permeability data is used from geomechanical literature and transformed into effective stress through Biot’s equation. The effect of the Biot’s coefficient, overburden stress, oil flow rate, fracture’s tip, and proppant porosity arrangements is simulated. The results show that these parameters are essential to minimize formation damage. The accuracy, ease of implementation, and low computational costs constitute the main advantages of the model addressed in this paper. Hence, it may be a valuable and attractive mathematical tool to identify flow regimes, providing permeability loss control and supporting well–reservoir management. Hence, the proposed modeling becomes a useful and attractive tool for forecasting and monitoring permeability loss, oil flow rate specification, and reservoir history matching.