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Dissertation Defense
Simulating Growth and Proppant Transport in Non-Planar Hydraulic Fractures
2:30 pm
WRW 113
A computational model is developed to simulate the growth of non-planar hydraulic fractures. A Symmetric Galerkin Boundary Element Method (SGBEM) is used to simulate the fracture growth process. This involves only weakly singular kernels to be computed. Additionally special shape functions are utilized to capture the stress intensity factors, which are used to update the geometry through a mixed mode I/II growth law. Fluid flow equations are derived for the case of flow through a thin channel defined on an arbitrarily curved 2D surface embedded in 3D space. Two separate methods for fluid flow are used to solve these equations. A Galerkin Finite Element Method (GFEM) is implemented to calculate the pressure in the fluid. Alternatively the Mixed Hybrid Finite Element Method (MHFEM) gives accurate pressures and velocities simultaneously. The GFEM method is computationally cheaper, while the MHFEM is much more suitable for simulation of proppant transport. The proppant transport process is modeled with an upwind finite volume method, taking into account the gravitational settling. Several examples are presented to demonstrate the capabilities of the model and to investigate the effect of material properties on fracture profiles.
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