Abstract
Hydraulic fracturing is an important technology to increase the amount of production extracted from unconventional hydro-carbon reservoirs. In spite of the recent proliferation of the stimulation technique, the technical understanding of how fractures initiate, propagate, and interact with material heterogeneity is not well established. The need for improved scientific understanding of this methodology has motivated this research, which seeks to develop probabilistic finite element software for modeling fracture propagations in random formations. The finite element development proposed herein will combine the eXtended Finite Element Method (XFEM) with random field theory to characterize fracture propagation within heterogeneous tight hydro-carbon reservoirs without any need for re-meshing. The XFEM not only has a potential for improved modeling accuracy, but also reduces computational costs that might be needed when using a standard finite element method. Stochastic modeling of hydraulic fracturing will be used to further account for randomly distributed formation properties of the tight formation and the resulting various hydraulic fracturing patterns. The new methodology from this research will be called eXtended Random Finite Element Method (XRFEM). When combined with a Monte-Carlo simulation approach, this methodology will lead to probabilistic information on the response of various formations and enable better technical and financial risk management of unconventional reservoir stimulation. Parameters used in the XRFEM modeling of well stimulation are subject to different types and levels of uncertainties caused by inherent spatial variability in geological formations.