Analytical Model to Effective Permeability Loss Monitoring and Boundary Effects Identification in Oil Wells with Finite Hydraulic Fractures

Abstract

ABSTRACT: Hydraulic fracturing technology has been used by petroleum industry to solve a variety of problems and providing the understanding for many of difficult 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 to Green’s function (GF) related to an oil source plan that represents the finite hydraulic fracture. A new effective hydraulic diffusivity deviator factor is also derived to represent the permeability loss as 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’s period. The model calibration is performed through a numerical oil flow simulator, widely used in the petroleum industry and scientific works and the results were accurate. 1 INTRODUCTION Reservoir stimulation techniques e.g. acidizing, acid and hydraulic fracturing are used to make the production’s curve economically attractive (Fernandes, 2021a,b; Fernandes et al., 2021a). These techniques are also used to improve the oil production curve when the reservoir permeability drops and the minimum viable oil flow rate is reached. Hydraulically fractured petroleum reservoirs may increase significantly the oil production’s curve and make many projects more attractive economically (Almisned and Al-Awad, 2017; Miskimins, 2019). Various works related to proppant transport and hydraulic fractures behavior in conventional and unconventional pressure-sensitive oil reservoirs have been published to reach the maximum stimulated reservoir volume to improve the oil recovery (Miskimins, 2019; Miskimins and Alotaibi, 2019). There-with, hydraulic fracturing is a continuously evolving well stimulation method to enhance, accelerate and restore production by reducing the oil flow-path resistance from the porous media to the well (Howard and Fast, 1957; Zoback and Haimson, 1982; Warpinski et al., 1981a,b, 1982a,b, 1985, 1993, 1998; Gringarten, 2008; Economides and Noltes, 2000; Miskimins, 2019; Miskimins and Alotaibi, 2019).