Analytical solution of stress field on elliptical borehole and its hydraulic fracturing characteristics

Subsurface reservoir rocks have been in the state of in-situ stress prior to drilling.The borehole is performed under confined pressure, which results in stress redistribution around the borehole.Thereby, the borehole shape may change from a circular borehole to an elliptical borehole under in-situ stress.Therefore, the pressurized water caused by hydraulic fracturing technology may act on the elliptical borehole wall.The analytical solution of stress filed around elliptical boreholes under far-field stress and borehole internal pressure (local symmetric stress on both ends of the elliptical long axis) is obtained by using complex variable function under reasonable physical assumptions.The analytical solution can be degenerated into the uniform stress on the elliptical or circular borehole wall.Assuming that the shape of the borehole and stress field are given, the horizontal stress differences and the borehole shapes jointly affect the breakdown pressure and the initiation of the main hydraulic crack based on the maximum circumferential stress criterion.When the horizontal stress difference is large, the flatter the elliptical borehole is, the higher the water pressure is needed to form the main hydraulic crack.When there is no horizontal stress difference, the water pressure needed to form the main fracture is lower.When the horizontal stress difference is small and the borehole is flatter, the maximum circumferential stress may appear in the direction parallel to the major horizontal stress, which makes it possible for the hydraulic main fractures to crack in the direction parallel to the minor principal stress.In addition, due to the limitations of physical assumptions, the analytical solution may be more suitable for sandstones with better homogeneity or shale with transversely isotropic properties.The breakdown pressure properties and hydraulic crack propagation of elliptical boreholes formed by in-situ stress in different reservoir rocks (sandstone, shale and raw coal) under uniform load need to be further verified by experiments and operations.