2011 , Volume 16, № 6, p.13-26

A multizone boundary element method for solving the three dimensional linear elasticity equations for a piecewise homogeneous material is presented (external elasticity problem is considered). The idea of the method is to apply the single zone boundary elements method to each zone and then combine the obtained matrices to resulting pseudostiffness matrix. The method has been tested on problems with known analytical solution. The method was used to simulate the fracture initiation process from both perforated cased or uncased wellbores located in the rock. As a criterion for fracture initiation is when the maximum tensile stress exceeds the breaking strength of the rock. Depending on the mutual directions of perforation and principal stresses, we obtain the critical pumping pressure, which is necessary to initiate the process of hydraulic fracturing. It is determined that the presence of a casing column considerably increases pressure necessary for the fracture initiation.