Hydraulic Fracture Propagation in the Presence of Planes of Weakness
Authors: Daneshy Abbas Ali 
Published: December 2007

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
A study is made of hydraulic fracturing of formations containing natural flaws. The three factors of importance are shown to be the strength of the weakness plane, its orientation with respect to the least compressive principal stress and the difference between the principal stress magnitudes.
Material flaws with dimensions that are small compared with the induced hydraulic fracture are shown to be unable to change the over-all orientation of the hydraulic fracture. The induced fracture can encircle such material defects and override their possible effect. Even if it does not, the influence of these flaws is local and insignificant on the results of the fracturing treatment. Large material flaws are shown unable to drastically change fracture orientation.
The analytical results presented in the paper are based on the principle of least paper are based on the principle of least resistance. The study does not include severely fractured, highly permeable formations.

Introduction
Rocks, in their natural state, contain many flaws of various forms. On a small scale these include small cracks, crystal and grain boundaries, etc. On a larger scale, joints, beddings, and faults are examples of strength flaws. Most theoretical and experimental investigations on rocks are performed on relatively isotropic, homogeneous, and brittle-elastic rocks. The reason is either mathematics or ease of data analysis. This paper considers a small deviation from the above assumptions. It discusses hydraulic fracturing of an essentially isotropic, homogeneous, brittle-elastic material weakened by a planar flaw.

CONCEPTS OF FRACTURE MECHANICS IN HYDRAULIC FRACTURING
The analysis of the cause and process of crack propagation is extremely difficult and subject of many investigations. Irwin has observed that there are three basic modes of crack propagation: opening, sliding, and tearing (Fig. 1). In the opening mode (cleavage), the two faces of the crack tend to separate symmetrically with respect to the plane occupied by the crack before fracturing. plane occupied by the crack before fracturing. Hydraulic fractures usually fall in this category. In the sliding mode, the two faces of the crack slide over each other in opposite directions, but in the same plane. In the tearing mode, the material points that were originally in the same plane will twist and consequently occupy different planes.