| In this study, several efficient and accurate mathematical models and numerical solutions to unconventional reservoir development problems are developed. The first is the three-dimensional embedded discrete fracture method (3D-EDFM), which is able to simulate fluid flow with multiple 3D hydraulic fractures with arbitrary strike and dip angles, shapes, curvatures, conductivities and connections. The second is a multi-porosity and multi-physics fluid flow model, which can capture gas flow behaviors in shales, which is complicated by highly heterogeneous and hierarchical rock structures (ranging from organic nanopores, inorganic nanopores, less permeable micro-fractures, more permeable macro-fractures to hydraulic fractures). The third is an iterative numerical approach combining the extended finite element method (X-FEM) and the embedded discrete fracture method (EDFM), which is developed for simulating the fluid-driven fracture propagation process in porous media.;Physical explanations and mathematical equations behind these mathematical models and numerical approaches are described in detail. Their advantages over alternative numerical methods are discussed. These numerical methods are incorporated into an in-house program. A series of synthetic but realistic cases are simulated. Simulated results reveal physical understandings qualitatively and match with available analytical solutions quantitatively. These novel mathematical models and computational solutions provide numerical approaches to understand complicated physical phenomena in developing unconventional reservoirs, thus they help in the better management of unconventional reservoirs. |
