Hydraulic Fracturing in Porous-Permeable Materials
Authors: Haimson Bezalel , Fairhurst Charles 
Published: December 2007

Laboratory tests show that in porous-permeable rock both vertical and horizontal hydraulic fractures are possible, and that the breakdown pressure is lower than in an impermeable but otherwise identical pressure is lower than in an impermeable but otherwise identical formation. The direction of vertical fractures and the magnitude of breakdown pressures can be predicted from theoretical considerations.

Introduction
Hydraulic fracturing is a stimulation method used by the petroleum industry to boost oilwell production. In an open-hole completion, the method consists of searing off a section of the well, injecting it with pressurized fluid, and raising the pressure until the pressurized fluid, and raising the pressure until the well fractures. The fracture is then extended by pumping in high volumes of water or other fluids; the pumping in high volumes of water or other fluids; the permeability of the formation is thus improved, often permeability of the formation is thus improved, often resulting in a substantial increase in oil output. However, not all fracturing jobs have been successful. Even today, 20 years after the method was introduced, no certain predictions can be made as to what critical pressure will be required to initiate a fracture, whether pressure will be required to initiate a fracture, whether it will be horizontal, vertical or inclined, what will be its direction, its length, its height, etc.
Articles have been published on the theoretical relationship between the tectonic (in-situ) stresses and the hydraulic fracturing pressures, but no thorough attention has been paid to the stresses due to possible infiltration of the formation by the injected fluid. Haimson and, independently, Geertsma have pointed out that this fluid penetration may significantly affect the critical (breakdown) pressure. This paper presents the criteria for fracture initiation in porous-permeable materials by considering all the possible stress fields around the wellbore.
There has been very little laboratory experimenting on hydraulic fracturing, and only few reports have been published. This paper summarizes some laboratory tests on hydrostone performed at the U. of Minnesota as a part of an extensive research program in hydraulic fracturing. The experimental set-up allowed for the application of three mutually perpendicular, unequal compressive loads on a cubical sample having a central vertical hole, thus realistically simulating principal tectonic stresses in the earth. The pressurization of the central hole until fracture occurred provided the value of the critical pressure. This value and the direction of the crack were then related to the simulated in-situ stresses. The purpose of the tests was to verify some of the theoretical predictions regarding the relationship between critical pressures and fracture directions vs tectonic stresses in porous rock. porous rock. Theory
It is assumed that the rock is brittle, linearly elastic, homogeneous, isotropic and porous, and that the fluid flow through the pores obeys Darcy's law. It is also assumed that one of the principal tectonic stresses acts in a vertical direction, i.e., parallel with the axis of the wellbore. The total stresses around the wellbore can be found by superposing the three individual stress fields generated by:
the three principal tectonic stresses, the pressurization of the open hole of the wellbore, and the fluid flow from the pressurized hole into the formation. pressurized hole into the formation. JPT
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