Analytical Model to Effective Permeability Loss Prediction and Formation Mechanical Damage Control in Fractured Oil Wells

Abstract

AbstractThis work presents a new analytical model to evaluate the effective permeability response during the oil’s production through a fractured vertical well fully penetrating a pressure-sensitive reservoir. The nonlinear hydraulic diffusivity equation (NHDE) is solved analytically through an integro-differential model coupled to Green’s function (GF) related to a semi-infinite oil source plan that represents a hydraulic fracture. The NHDE is perturbed using a first-order asymptotic series expansion method and the solution is derived in terms of a new effective permeability pseudo-pressure function, considering the matrix and fracture permeability roles. A new hydraulic diffusivity deviator factor is also derived to represent the effective permeability loss as a function of the pore pressure throughout the well-reservoir life-cycle. For this modeling, the general solution is expressed by the sum of the linear solution (constant permeability) plus a corrective term given by the combination of the exponential function and the complementary error function erfc(yD,tD). The model calibration is performed through a porous media numerical oil flow simulator, named IMEX® and the results presented high accuracy.