A THREE-DIMENSIONAL DISPLACEMENT DISCONTINUITY MODEL FOR THE ANALYSIS OF HYDRAULICALLY PROPAGATED FRACTURES

The success of hydraulic fracturing operations for secondary recovery of oil and gas or for geothermal energy production depends mainly on the ability to propagate a fracture of desired extent. Some important considerations in determining the geometry of such a man-made fracture are its behaviour upon intersection with preexisting joints, and the effects of changes in material properties or in-situ stresses. It is hoped that research in these areas will lead to new methods for containing the hydraulic fracture of the pay-zone.;In this thesis a fully three-dimensional model of the hydraulic fracture propagation process is described. The following aspects have been incorporated into the numerical model. (1) Fracture propagation takes place when the energy release rate at the crack tip reaches a value characteristic of the rock. Propagation occurs along the path exhibiting the maximum circumferential tensile stress evaluated at a characteristic distance from the crack tip. The stress/displacement analysis used to calculate the crack-tip stresses, as well as the fracture aperture, is based on a boundary element technique known as the displacement discontinuity method. Special crack-tip elements with a square-root displacement variation have been developed to predict the stresses in the vicinity of the crack tip to any specified tolerance. (2) The fluid pressure distribution resulting from the fluid-flow analysis must be consistent with that used for the stress/displacement analysis. A finite element scheme was adopted for the fluid-flow analysis, making use of the same mesh as the stress/displacement boundary element analysis. (3) The apertures determined from the stress/displacement analysis must agree with the apertures used in the fluid-flow analysis. (4) The total fluid losses (i.e., storage, spurt and leakoff) must be equal to the total quantity of fluid injected at the borehole. In contrast to other models, the propagating fracture does not have to be planar and the influence of joints, faults and nonhomogeneous in-situ stresses and material properties are incorporated. Three-dimensional examples of a fracture approaching a bimaterial interface and nonplanar crack propagation under various in-situ stress states are given.