Crack band approach to model 3D hydraulic fracturing of gas shale stratum

The recent advances in hydraulic fracturing of oil and gas bearing rocks, aka "fracking", have been nothing less than astonishing. However, several aspects of shale tracking such as the topology, geometry, and evolution of the crack system remain not yet understood. In this contribution, based on the known shale permeability, on the known percentage of gas extraction from shale stratum, and on two key features of the measured gas outflow which are (1) the time to peak flux and (2) the halftime of flux decay, it is shown that the fracturing process is characterized by a very dense crack system, with crack spacing of only about 0.1 m. Then, a multi-physics approach to 3D modeling of fluid-driven propagation of a vast network of cracks and open joints in shale is presented. The complex nonlinear and anisotropic mechanical behavior of shale is captured by means of a microplane model. Because the crack spacing must be only about 10 cm, the fracture of shale is analyzed as a softening damage, in a smeared way, by the crack band model. 3D nonlinear equations governing the flow of compressible cracking fluid through the cracks whose opening and length is controlled by fracture mechanics are formulated.