Application of complex SIE method for the prediction of hydrofracture path

Abstract

This study is aimed at application of the method of complex singular integral equation (SIE) to the problem of crack propagation in non-uniform stress field. The paper examines one actual problem of oil and gas production: modeling of the hydrofracture trajectories in a reservoir subjected to non-uniform distributions of pore pressure. A modification of the method of mechanical quadratures is used to solve the SIE to simulate the hydro-fracture trajectory. The modification addresses discontinuities in the loads acting on the hydrofracture and provides quite accurate and fast solutions for the stress intensity factors. The crack path is modeled by a polygonal line such that the orientation of every subsequent leg is chosen by the criterion of maximum tensile stresses at the crack tip calculated for the current configuration. Different interposition the hydrofracture and the injection wells are examined.