Improved algorithms for generalized finite element simulations of three-dimensional hydraulic fracture propagation |
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| Authors: | Nathan Shauer Carlos Armando Duarte |
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| Institution: | Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL, U.S.A. |
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| Abstract: | This paper reports improvements to algorithms for the simulation of 3-D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3-D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak-off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples. |
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| Keywords: | finite element method (FEM) generalized finite element method (GFEM) hydraulic fracturing high-performance computing |
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