This contribution presents a multi-physics modeling of fluid-driven propagation of a vast network of fractures and open joints in shale, with a fracture spacing of about 10 cm, as deduced from the observed gas extraction history at wellhead. Because of the vast number of fractures and quasibrittle nature of shale, the fracture of shale is analyzed in a smeared way by the crack band model. One key idea is that, to model lateral fractures branching from a primary fracture wall, fracture pressurization, by viscous Poiseuille type flow, of compressible (proppant-laden) fracturing water must be complemented with the pressurization of a sufficient volume of micropores and microfractures by Darcy-type water diffusion into the shale, which generates tension along the existing fracture walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in fractures, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, transitional between Biot's two-phase medium and Terzaghi's effective stress. Finiteelement/finite-volume simulations demonstrate the growth of a large hydraulic fracture system. Study of the effects of various parameters could increase the efficacy of fracturing and reduce water injection.


The recent advances in hydraulic fracturing of oil and gas bearing shale, which have made the US selfsufficient in energy for the first time in a half century, have been nothing less than astonishing. In 2010 shale gas production accounted for 23% of the total US gas production and it is projected to reach 50% by 2035 even at the current extraction efficiency. Although many aspects of hydraulic fracturing are well understood by now [1, 16, 30, 33, 44, 53, 54, 56], the details of topology, geometry, and evolution of the fracture system are not. Progress in this aspect of fracturing promises increasing the rate of gas extraction, currently standing at only 5% to 15%.

Based on the equations relating the measured gas flux histories at the wellhead (in Fayetteville basin) to the typical permeability of shale [34, 35, 59], a recent study [13] concluded that the spacing of fractures and opened rock joints in gas shale must be on the order of 0.1 m. Because the typical depth of a gas or oil bearing stratum of shale is about 2.5-3 km [24, 49] (Fig. 1), the overburden pressure is assumed to exceed the fluid pressure. Consequently, all the fractures and joints are modeled as essentially vertical, and no horizontal fractures allowed.

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