Abstract
This article presents a comprehensive overview of several recent theoretical results at Northwestern University and demonstrates them by new numerical simulations of branching of hydraulic fractures. To model the inelastic behavior and fracturing of shale as an inherently anisotropic material, the recently developed spherocylindrical microplane model is described. Regarding the spread and branching of hydraulic cracks during the fracking process, it is emphasized that two kinds of water flow must be simulated: (1) the Poiseuille flow through the hydraulic fractures and natural cracks and (2) the Darcy diffusion flow of leak-off water through the pores of intact shale. The body forces due to gradient of Darcy flow pressure must be taken into account. The crack opening width is computed by means of the crack band model, in which each finite element is imagined to contain at the outset a potential cohesive crack, one in each of three spatial orientations, with the fracking water flowing through if the crack gets opened. The use of this model to suppress problems of mesh sensitivity due to localization of distributed fracturing is explained. Computer simulations of the growth of branched hydraulic system are preformed in two dimensions (2D) only. The results illustrate the effects of anisotropy and natural cracks on the evolution of 2D fracture patterns during the fracking process. These effects are not large, but much stronger effects are expected in future three-dimensional simulations.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 975-992 |
| Number of pages | 18 |
| Journal | Acta Mechanica |
| Volume | 229 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2018 |
Funding
Acknowledgements Partial financial support from the US Department of Energy through Subcontract No. 37008 of Northwestern University with Los Alamos National Laboratory is gratefully acknowledged. The simulation of fracturing damage also received some support from ARO Grant W911NF-15-101240 to Northwestern University. The first author wishes to thank the Department of Science and Technology of Sichuan Province (Nos. 2015JY0280, 2012FZ0124) and CSC for supporting him as a Research Fellow at Northwestern University. Collaboration with Sichuan University which led to important understanding of Longmaxi shale is deeply appreciated.
ASJC Scopus subject areas
- Computational Mechanics
- Mechanical Engineering