Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 43; no. 18; pp. 2707 - 2742
• Main Authors: Shauer, Nathan, Duarte, Carlos Armando
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.12.2019
• Subjects: Algorithms; Aquatic reptiles; Computer applications; Computer simulation; Conservation of mass; Crack propagation; Exact solutions; Finite element method; finite element method (FEM); Fracture mechanics; generalized finite element method (GFEM); high‐performance computing; Hydraulic fracturing; Matrix methods; Stiffness matrix
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2977

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.