XFEM modeling of the effect of in-situ stresses on hydraulic fracture characteristics and comparison with KGD and PKN models

Increasing the permeability of hydrocarbon reservoirs by creating artificial cracks that are induced by injection of fluids under high pressure is called hydraulic fracturing (HF). This method is widely used in petroleum reservoir engineering. For design of Hydraulic Fracture operations, several analytical models have been developed. KGD and PKN are the first and most used analytical models in this area. Although number of advanced softwares are developed in recent years, KGD and PKN models are still popular and have even been used in a number of softwares. In both models the characteristics of the fracture namely: fracture length (L), fracture width (w), and fluid pressure at the crack mouth (p) are determined based on closed form relations using the reservoir rock shear stiffness, Poisson's ratio, fluid injection rate, and injection time. Despite their ease of use, KGD and PKN models do not consider some important geo-mechanical and hydro-mechanical parameters and this shortcoming makes their results to be approximate. The aim of this study is evaluating the effects of in-situ stress on the fracture length, width, and fluid pressure employing XFEM method. In this study, tensile fracture mode and cohesive zone model are used for creation and propagation of cracks. In this paper, by conducting a series of numerical simulations using XFEM and after verification of the results, the accuracy of the analytical formulas of KGD and PKN models are examined. The results show that due to some simplifying assumptions used in KGD and PKN analytical models and neglecting some hydraulic and geomechanical parameters such as in-situ stresses, the length, width, and fluid pressure of the crack obtained from analytical formulas differ from the results of the numerical simulations. In this paper, the effects of in-situ stresses on hydraulic fracture characteristics (width, length, and crack mouth fluid pressure) are investigated and presented in the form of a number of correction (modification) factors that can be used for improvement of the results of KGD and PKN models. The findings of this study can help for more accurate design of hydraulic fracture process in oil industry for increasing the production of hydrocarbon reservoirs.