Investigation of the effect of in situ stresses and porosity on crack propagation mechanism in hydraulic fracturing by displacement discontinuity method

Nowadays, hydraulic fracturing is used in various fields such as stimulation of oil reservoirs, measurement of in-situ stresses, extraction of geothermal energy and extraction of conventional and unconventional hydrocarbon resources.Meanwhile in-situ stresses and porosity are the most important factors that affecting the propagation, opening and extension of the crack. In this research, the above parameters have been investigated using analytical and numerical methods. For numerical modeling in this research, the numerical method of displacement discontinuity, has been used, which is one of the methods with high ability in modeling discontinuity and failure. The program used is a quadratic element based on solid mechanics and fracture mechanics. In this research, by addition of the fluid flow module, the fluid mechanics is included in the analysis. In the fluid mechanics module, the effect of fluid flow on crack opening displacement is investigated. This part of the program is created by finite difference method in mode of forward time central space. Finally, after validation of the program, the effects of in situ stress and porosity on crack propagation were investigated. In order to generalize the results, the studied parameters have been presented in dimensionless forms. It is concluded that the best direction for creating a hydraulic fracture is in the direction of maximum principal stress. As the in-situ stress difference increases, less injection pressure is required to propagate the crack. In the crack with a 45 degrees angle relative to the maximum stress, a lower injection pressure is required to propagate the crack; then this crack after several step of growth deviates to the maximum stress direction. Increasing the porosity of the formation reduces the amount of Young's modulus and Poisson's ratio, which leads to increases the crack opening at higher porosity values.