Anisotropy effects on induced fractures

Hydraulic fracturing is used to create deep penetrating reservoir fractures that improve the productivity of a well. During fracture initiation, breaking down the rocks will result in several mini-fractures and it is common to line wells with concrete casing. The fluid pressure will then reach the rock through special perforations made at the location of the tension zone along the well perimeter. Since these initial fractures may not lie in the preferred fracture plan (perpendicular to the minimum in-situ stress), the fracture will reorient itself while propagating away from the wellbore. The effective pressure will drop to smaller values depending on the deviation angle of the wellbore. Then the fracture will propagate without being affected by the wellbore (effect comes only in the pressure loss due to friction in wellbore and in perforations). There are many codes in industry to simulate this fracture propagation stage. Due to the complexity of the problem, these codes tend to neglect the formation anisotropy.; In the first part of this research, the sensitivity of the breakdown and the propagation pressures to the rock and casing properties will be discussed. The fracture initiation from a deviated cased wellbore is examined by applying three-dimensional elasticity theory. Effects of the off-plane shear stress components on location and orientation of the initial fracture plane will also be studied. The critical energy release rate will be used as a fracture criterion to solve for the crack extension from initiated mini-cracks at the wellbore surface. The sensitivity of crack extension to elastic properties of the reservoir medium is examined.; A practical form for stress distribution over planar cracks embedded in a transversely isotropic medium is derived as an integral function of the crack opening displacement. The second order Green's traction tensor appears in this expression is derived from the Green's function solution given by Pan and Chau (1976) for a transversely isotropic medium. Two expressions for the stress boundary integral are derived for the cases when the planar crack is parallel and perpendicular to the plane of isotropy. The derived BIE converges to that obtained by Bui (1977) and Weaver (1977) when isotropic elastic medium is assumed.; Finite element analysis (FEA) is applied to the Boundary Integral Equations (BIE) that governs the opening displacement of a crack embedded in an anisotropic medium. The point collocation method is used to reduce the excessive numerical computation associated with applying the FEM to the BIE. Several numerical integration techniques are examined to carry out the numerical value of the singular boundary integrals which appear. Model accuracy and convergence characteristics are successfully demonstrated for penny-shaped and elliptical cracks. Anisotropy effect on the opening displacement of pressurized elliptical cracks are discussed. The anisotropy results differ by up to 37% in some cases when compared with the isotropic results.