Although spectacular advances in hydraulic fracturing, also known as fracking, have taken place and many aspects are well understood by now, the topology, geometry, and evolution of the crack system remain an enigma and mechanicians wonder: Why fracking works? Fracture mechanics of individual fluid-pressurized cracks has been clarified but the vital problem of stability of interacting hydraulic cracks escaped attention. First, 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 crack spacing must be only about 0.1 m. Attainment of such a small crack spacing requires preventing localization in parallel crack systems. Therefore, attention is subsequently focused on the classical solutions of the critical states of localization instability in a system of cooling or shrinkage cracks. Formulated is a hydrothermal analogy which makes it possible to transfer these solutions to a system of hydraulic cracks. It is concluded that if the hydraulic pressure profile along the cracks can be made almost uniform, with a steep enough pressure drop at the front, the localization instability can be avoided. To achieve this kind of profile, which is essential for obtaining crack systems dense enough to allow gas escape from a significant portion of kerogen-filled nanopores, the pumping rate (corrected for the leak rate) must not be too high and must not be increased too fast. Furthermore, numerical solutions are presented to show that an idealized system of circular equidistant vertical cracks propagating from a horizontal borehole behaves similarly. It is pointed out that one useful role of the proppants, as well as the acids that promote creation of debris in the new cracks, is to partially help to limit crack closings and thus localization. To attain the crack spacing of only 0.1 m, one must imagine formation of hierarchical progressively refined crack systems. Compared to new cracks, the system of pre-existing uncemented natural cracks or joints is shown to be slightly more prone to localization and thus of little help in producing the fine crack spacing required. So, from fracture mechanics viewpoint, what makes fracking work?–the mitigation of fracture localization instabilities. This can also improve efficiency by fracturing more shale. Besides, it is environmentally beneficial, by reducing flowback per m3 of gas. So is the reduction of seismicity caused by dynamic fracture instabilities (which are more severe in underground CO2 sequestration).

We propose a machine learning approach to address a key challenge in materials science: predicting how fractures propagate in brittle materials under stress, and how these materials ultimately fail. Our methods use deep learning and train on simulation data from high-fidelity models, emulating the results of these models while avoiding the overwhelming computational demands associated with running a statistically significant sample of simulations. We employ a graph convolutional network that recognizes features of the fracturing material and a recurrent neural network that models the evolution of these features, along with a novel form of data augmentation that compensates for the modest size of our training data. We simultaneously generate predictions for qualitatively distinct material properties. Results on fracture damage and length are within 3% of their simulated values, and results on time to material failure, which is notoriously difficult to predict even with highfidelity models, are within approximately 15% of simulated values. Once trained, our neural networks generate predictions within seconds, rather than the hours needed

The spectral approach is used to examine the wave dispersion in linearized bond-based and state-based peridynamics in one and two dimensions, and comparisons with the classical nonlocal models for damage are made. Similar to the classical nonlocal models, the peridynamic dispersion of elastic waves occurs for high frequencies. It is shown to be stronger in the state-based than in the bond-based version, with multiple wavelengths giving a vanishing phase velocity, one of them longer than the horizon. In the bond-based and state-based, the nonlocality of elastic and inelastic behaviors is coupled, i.e., the dispersion of elastic and inelastic waves cannot be independently controlled. In consequence, the difference between: (1) the nonlocality due to material characteristic length for softening damage, which ensures stability of softening damage and serves as the localization limiter, and (2) the nonlocality due to material heterogeneity cannot be distinguished. This coupling of both kinds of dispersion is unrealistic and similar to the original 1984 nonlocal model for damage which was in 1987 abandoned and improved to be nondispersive or mildly dispersive for elasticity but strongly dispersive for damage. With the same regular grid of nodes, the convergence rates for both the bond-based and state-based versions are found to be slower than for the finite difference methods. It is shown that there exists a limit case of peridynamics, with a micromodulus in the form of a Delta function spiking at the horizon. This limit case is equivalent to the unstabilized imbricate continuum and exhibits zero-energy periodic modes of instability. Finally, it is emphasized that the node-skipping force interactions, a salient feature of peridynamics, are physically unjustified (except on the atomic scale) because in reality the forces get transmitted to the second and farther neighboring particles (or nodes) through the displacements and rotations of the intermediate particles, rather than by some potential permeating particles as on the atomic scale.

One contribution of 12 to a theme issue 'Energy and the subsurface' .

While the hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as the current commercial softwares, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000×. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. But their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nano-or micro-cracking damage. It is numerically demonstrated that a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings.Fracking | Poromechanics | Biot Coefficient | Seepage forces | Damage