3D numerical analysis of stability and onset of hydraulic fracture in the vertical-oblique-horizontal wells under wide range of in situ stresses

Influence of the depth and location of perforation, direction and magnitudes of in situ stresses, wellbore angle, and pumping pressure is investigated numerically for the hydraulic fracture. 3D models of rock formation with vertical, inclined or horizontal wells containing semi-circular crack are analyzed to obtain both KI and the minimum pumping pressure. By computing the magnitude and sign of the T-stress it is demonstrated that hydraulic fracture path is generally stable except for a very limited situations in which the vertical well is subjected to the lowest in situ stresses. The minimum horizontal in situ stress has the most dominant role in controlling the hydraulic fracture. A direct relationship between KI and T was obtained for different ranges of in situ stresses and some relations were presented for estimating the critical stress intensity factor at the onset of hydraulic fracture and minimum injection pressure in terms of the applied in situ stresses.