A Study of Inclined Hydraulic Fractures

The results of a theoretical and experimental investigation of inclined hydraulic fractures, reported in this paper, indicate that such fractures do not generally initiate perpendicular to the maximum tensile stress induced on the borehole wall. Unlike axial or normal hydraulic fractures, a degree of shear failure seems to be associated with the initiation and extension of almost all inclined hydraulic fractures. These fractures often intersect the borehole along two diametrically opposite axial lines, thus giving it the appearance of an axial fracture. Inclined hydraulic fractures generally change their orientation as they extend away from the wellbore until they become perpendicular to the least compressive in-situ principal stress. Therefore, the borehole trace of such fractures cannot be used for their positive identification. Introduction The process of hydraulic fracturing of a formation essentially consists of injecting a fluid inside the borehole and pressurizing it until the induced stresses exceed the strength of the formation and cause failure. Failure is generally indicated by a sudden major drop in the variations of the borehole fluid pressure with time. In general in an isotropic medium, the over-all plane of a hydraulic fracture is either parallel, plane of a hydraulic fracture is either parallel, inclined, or perpendicular to the axis of the borehole from which it is extending. Accordingly, these fractures will be called axial, inclined or normal, respectively. This classification of hydraulic fractures refers them to the borehole where they are observed rather than the ground surface or the bedding planes. In case of vertical boreholes, axial and normal fractures become identical with vertical and horizontal fractures (which are the terms often used in petroleum industry). In the first comprehensive analysis of the mechanics of hydraulic fracturing, Hubbert and Willis proposed that axial or normal hydraulic fractures initiate when the maximum tensile stress induced around the borehole exceeds the tensile strength of the formation, and that such fractures extend in a plane perpendicular to the least compressive in - situ principal stress. The correctness of this proposal has since been verified by Haimson and Fairhurst, who conducted an extensive series of laboratory experiments on the subject. In their theoretical and experimental work, Haimson and Fairhurst assumed that one of the in-situ principal stresses is parallel to the borehole axis. Under such a condition, one can only create an axial or a normal hydraulic fracture in an isotropic medium. For the case when none of the in-situ principal stresses are parallel to the borehole, Fairhurst derived mathematical expressions for the stress components on the borehole wall, in isotropic and transversely isotropic media. Experimentally, von Schonfeldt and Daneshy independently observed that under such a condition the fracture orientation is influenced by the borehole in its vicinity. The trace of inclined hydraulic fractures at the wellbore was found to be misleading if used for the purpose of determining the over-all fracture orientation. The research reported here is an extension of a previous work on the subject of inclined hydraulic previous work on the subject of inclined hydraulic fractures. It includes the computation of the magnitude and the orientation of the maximum tensile stress induced at the borehole wall, for each experiment, and the resulting fracture shape. Such investigations can, in the course of time, provide means of determining the over-all fracture provide means of determining the over-all fracture type at great depth, which has significant importance in many fields, such as geophysics, petroleum, geological and civil engineering. STRESS DISTRIBUTION AT THE WALL OF THE BOREHOLE Let sigma1, sigma2 and sigma3 be the three in-situ total principal stresses whose values and directions are assumed to remain constant throughout the isotropic porous elastic formation under consideration. No porous elastic formation under consideration. No restriction is imposed upon the direction of any of the in-situ principal stresses, except the mathematical requirement that they should be mutually perpendicular. Consider a coordinate system ox1 x2 x3 perpendicular. Consider a coordinate system ox1 x2 x3 chosen such that ox3 is the borehole axis, and ox1, lies in the plane osigma1 sigma2, Fig. 1. SPEJ P. 61