Laboratory Investigation of Fracture Initiation Pressure and Orientation
Authors: Medlin W.L. , Masse L. 
Published: December 2007

Abstract
The mechanics of hydraulic fracture initiation have been investigated by comparing laboratory experiments with theoretical predictions based on poro-elastic behavior. Experiments were conducted poro-elastic behavior. Experiments were conducted with 4-in. (10-cm) diameter cores containing spherical and cylindrical cavities and loaded in a triaxial cell under variable confining pressure, end load, and pore pressure. Experimental results agreed with theory for nonpenetrating fracturing fluid for limited ranges of hydrostatic confining stresses for four kinds of limestone rock. With penetrating fracturing fluids, the theory was penetrating fracturing fluids, the theory was confirmed only partially. Under nonhydrostatic stress conditions, reproducibility of measurements was too poor to evaluate the theory. Fracture orientation was controlled predominantly by stress conditions and cavity geometry. Notching of cylindrical cavities failed through notch extension only if the notch depth exceeded the value predicted approximately by a simple Griffith theory predicted approximately by a simple Griffith theory equation. Field applications of all results are discussed.

Introduction
This paper describes a combined theoretical/ experimental investigation of the mechanics of hydraulic fracture initiation. We considered fracture initiation pressure, fracture orientation, and mode of failure for various stress conditions and wellbore geometries. Our intention has been to consider theory applicable for both field and laboratory conditions, to test this theory with laboratory experiments, and to apply the results to interpretation of field data.
The laboratory experiments were designed not to duplicate field conditions so much as to provide a critical test of the theory. Some field data are examined, but it is impractical to learn much about fracture initiation from field experiments because of the limited number of quantities that can be measured.
The theory presented here is more a generalization of earlier work than a development of new theory. It provides a completely general treatment of fracture initiation in spherical and cylindrical cavities for poro-elastic materials. An extension of this theory poro-elastic materials. An extension of this theory to porous materials with nonelastic behavior already has been developed by Biot and will be referred to later.
We begin by presenting theory for fracture initiation in spherical and cylindrical cavities. The theoretical results are followed by descriptions of laboratory experiments that test the equations for failure pressure in these geometries under various stress conditions, using penetrating and nonpentrating fracturing fluids. The effects of notching in cylindrical cavities then are considered, and a simple model based on Griffith crack theory is developed to explain experimental results. Field applications of all results then are discussed in detail.

THEORY OF FRACTURE INITIATION
The theory of hydraulic fracture initiation in rock materials has been treated in successive degrees of refinement. Cases of interest are hollow sphere and long hollow cylinder geometry with penetrating and nonpenetrating fracturing fluids. penetrating and nonpenetrating fracturing fluids. Refs. 1 through 7 cover various parts of the overall picture; Rice and Cleary give the most complete picture; Rice and Cleary give the most complete analysis. We present here an independent analysis based on Biot's theory for fluid saturated porous solids. Our analysis adds little that is new to the basic literature of fracture initiation theory. It is presented mainly to provide a way to analyze presented mainly to provide a way to analyze scaling effects between field results and our laboratory experiments.
We start with Biot's stress-strain relations for a fluid saturated porous solid:
(1)
SPEJ
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