Mechanical formation damage management in oil wells with finite extent hydraulic fractures and source effects using an asymptotic-perturbation method

Abstract

The petroleum industry has used hydraulic fracturing technology to solve various problems and provide an understanding of many complex issues. This work presents a new analytical model to evaluate the effective permeability response during the oil’s production through a vertical well fully penetrating a pressure-sensitive reservoir with a finite extent hydraulic fracture. The nonlinear hydraulic diffusivity equation (NHDE) is solved analytically through an integro-differential model coupled with Green’s function (GF) related to an oil source plan representing a finite extent hydraulic fracture. A new effective hydraulic diffusivity deviator factor is also derived to represent the permeability loss as a function of the pore pressure throughout the well-reservoir life cycle. For this oil flow 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 Ei(xD,yD,tD) and the complementary error function erfc(xD,yD,tD). The proposed model is implemented in Matlab software to evaluate the effect of the effective deviator factor in the permeability response over the oil’s production period. The model calibration is performed through a numerical oil flow simulator, widely used in the petroleum industry, and the results were accurate.