Recent advances in mechanics of fracking and new results on 2D simulation of crack branching in anisotropic gas or oil shale

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.