Analytical Model to Effective Permeability Loss Prediction and Formation Mechanical Damage Control in Fractured Oil Wells
Fernando Bastos Fernandes, Arthur M. B. Braga, A. L. S. de Souza, Antônio Cláudio Soares
Abstract
Abstract This 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.