Thermal Stresses Near A Heated Fracture in Transversely Isotropic Oil Shale
Authors: Closmann P.J. , Phocas D.M. 
Published: December 2007

Abstract
This study presents an analysis and related numerical calculations to ascertain the practicality of horizontally fracturing an oil shale formation by thermally biasing underground stresses. Results indicate that stresses induced by beating from a vertical fracture reduce the chances of forming horizontal fractures at the vertical fracture face, as long as the entire system is far from a free surface or pressurized cavity surface, With such surfaces, more favorable conditions for horizontal fracturing may be obtained. Other stress conditions more conducive to horizontal fracturing are suggested, such as those some distance away from the heated fracture and the more favorable stress conditions that result by beating from parallel vertical fractures. These results should be useful to engineers designing thermal recovery processes that require hydraulic fracturing, as well as engineers studying recovery techniques for oil shale.

Introduction
The use of fracturing to improve productivity of petroleum reservoirs is well established. In petroleum reservoirs is well established. In particular, fractures in thermal recovery operations particular, fractures in thermal recovery operations permit heat to be injected over a wide area into permit heat to be injected over a wide area into an oil-bearing formation. In many cases horizontal fractures are more desirable than vertical ones, since they allow communication between wells to be established more easily. If sufficiently controlled, horizontal fractures permit contact with specially chosen layers of a reservoir.
The studies of fracturing of underground formations by Hubbert and Willis indicated that fractures form in a direction normal to the least compressive principal stress. Since the least compressive principal stress. Since the least compressive principal stress is horizontal in most cases, principal stress is horizontal in most cases, fractures are usually vertical. This tendency applies particularly to deep reservoirs. The orientation of particularly to deep reservoirs. The orientation of fractures and the pressures required for fracturing also will be affected by tectonic stresses. Often a vertical stress is determined by the weight of the overburden, although there are exceptions.
The use of thermal stresses to modify fracturing pressure and to enhance formation of horizontal pressure and to enhance formation of horizontal fractures was suggested by Matthews et al. They concluded that heating from vertical fractures eventually will allow formation of horizontal fractures by generation of sufficient horizontal stress.
In view of the applicability of fracturing to thermal projects in general and the interest in oil shale development in particular, investigation of the stresses developed during heating by injection of hot fluid into a fracture is desirable. Such information will provide an indication of the type of behavior anticipated when heating and applying increasing pressure to a fracture system. This paper considers the stress conditions arising as a paper considers the stress conditions arising as a solution to a thermoelastic boundary value problem. Failure criteria were not considered and could be a subject for future research. McLamore presented some considerations of this nature.
Specific effects of the wellbore have not been included in this study. Certain considerations involving wellbore geometry could have a significant effect on the expected values for fracturing pressures. This aspect has been investigated by pressures. This aspect has been investigated by Haimson. In our mathematical solution, a negative stress will be compressive and a positive stress will be tensile.

THEORY

GENERAL DESCRIPTION
Assume that an infinitely long fracture of limited vertical extent is present in the formation initially and that fluid loss through the walls of the fracture is negligible (Fig. 1).
SPEJ
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