True and Apparent Direction of Hydraulic Fractures
Authors: Daneshy Abbas Ali 
Published: December 2007

Abstract
The type of fracture (i.e., horizontal, vertical or inclined) obtained in a fracturing process is often determined by instruments such process is often determined by instruments such as Borehole Televiewers, impression packers, etc. Such instruments only determine the fracture appearance at the wellbore and give no information about the fracture geometry away from the wellbore.
At moderate depths (less than 15,000 ft), a fracture initiates when the maximum tensile stress induced at any point around the wellbore exceeds the tensile strength of the formation at that point. In this paper it will be shown that, theoretically, if none of the principal stresses are parallel to the borehole, the maximum tensile stress is attained at two diametrically opposite points along the circular periphery of the borehole. In three dimensions, periphery of the borehole. In three dimensions, the loci of these points are two straight lines parallel to the directrix of the borehole. parallel to the directrix of the borehole. If the smallest compressive principal stress is not the one which makes the least angle with the borehole, then these lines are likely directions for fracture propagation at the wellbore. Once the fracture extends sufficiently away from the borehole it becomes perpendicular to the least compressive principal perpendicular to the least compressive principal stress. At the wellbore this fracture may appear as vertical.
The theoretical findings of the paper are verified experimentally. The paper also includes a discussion of the effects of these findings on fracture geometry evaluations.

Introduction
For over two decades the petroleum industry has been using hydraulic fracturing for well stimulation. The first comprehensive analysis of the mechanics of hydraulic fracturing was made by Hubbert and Willis. Assuming the wellbore to be parallel to the vertical principal stress, they calculated the stress principal stress, they calculated the stress distribution around the borehole. It was suggested that a fracture is initiated when the maximum tensile stress induced around the wellbore exceeds the tensile strength of the rock and that it extends in a plane perpendicular to the least in-situ compressive perpendicular to the least in-situ compressive principal stress. Scheidegger was first to principal stress. Scheidegger was first to consider the effect of fluid penetration on fracture initiation. He also modified the Hubbert and Willis equations by allowing the tensile strength of the rock to have a nonzero value. Kehle has analyzed the effects of the packers on stress distribution and fracture initiation. The mechanics of hydraulic fracturing in a porous permeable rock has been discussed in a porous permeable rock has been discussed in a series of articles by Haimson, Fairhurst and Haimson and Fairhurst. The stress distribution for the case when the borehole is not parallel to one of the in-situ principal stresses has been calculated by Fairhurst in an isotropic or transversely isotropic medium.
Haimson conducted an extensive series of tests in the laboratory in order to investigate fracture initiation and orientation. He found that induced fractures are initiated when the maximum tensile stress exceeds the tensile strength of the formation and are oriented normal to the least compressive principal stress, as suggested by Hubbert and Willis. In Haimson's experiments the borehole was parallel to one of the principal stresses.
A number of experiments have been conducted in the field for determining the fracture direction. This has been achieved by using instruments such as impression packers (Anderson and Stahl, Fraser and Pettit) or Borehole Televiewers (Zemanek et al.), etc.