Premium
Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation
Author(s) -
Shauer Nathan,
Duarte Carlos Armando
Publication year - 2019
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2977
Subject(s) - finite element method , robustness (evolution) , algorithm , stiffness , hydraulic fracturing , stiffness matrix , mathematics , linear elasticity , fracture mechanics , mathematical optimization , computer science , structural engineering , engineering , geotechnical engineering , biochemistry , chemistry , gene
Summary 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.