Summary Hydraulic-fracturing treatments have become an indispensable part of well completion in shale gasfield development. Shale formations often contain natural fractures, and complex hydraulic-fracture networks may form during a treatment. The complex fracture network is strongly influenced by the interaction between the hydraulic fracture and the pre-existing natural fractures. A criterion has been developed to determine whether a fracture crosses a frictional interface (pre-existing fracture) at nonorthogonal angles. This criterion is an extension of the one for orthogonal crossing originally developed by Renshaw and Pollard (1995). The dependence of crossing on the intersection angle is shown quantitatively using the extended criterion. The fracture is more likely to turn and propagate along the interface than to cross it when the angle is less than 90°. The validation of the criterion using laboratory experiments for various angles is described and discussed. When applied to laboratory experiments, good agreement between the criterion and experiments is observed for a wide range of angles. The criterion can be used to determine whether hydraulic fractures cross natural fractures under particular field conditions, and it has been incorporated in a hydraulic-fracture model that simulates hydraulic-fracture propagation in a naturally fractured formation.

32 33 Fine-grained sedimentary rocksnamely mudrocks, including their laminated fissile variety -34 shales -make up about two thirds of all sedimentary rocks in the Earth's crust and a quarter of 35 the continental land mass. Organic-rich shales and mudstones are the source rocks and reservoirs 36 for conventional and unconventional hydrocarbon resources. Mudrocks are relied upon as natural 37 barriers for geological carbon storage and nuclear waste disposal. Consideration of mudrock 38 multi-scale physics and multi-scale spatial and temporal behavior is vital to address emergent 39 phenomena in shale formations perturbed by engineering activities. Unique physical 40 characteristics of shales arise as a result of their layered and highly heterogeneous and 41 anisotropic nature, low permeability fabric, compositional complexity, and nano-scale confined 42 chemical environments. Barriers of lexicon among geoscientists and engineers impede the 43 development and use of conceptual models for the coupled thermal-hydraulic-mechanical-44chemical-biological (THMCB) processes in mudrock formations. This manuscript reviews the 45 THMCB process couplings, resulting emergent behavior, and key modeling approaches. We 46 identify future research priorities, in particular fundamental knowledge gaps in understanding the 47 phase behavior under nano-scale confinement, coupled chemo-mechanical effects on fractures, 48 the interplay between physical and chemical processes and their rates, and issues of non-linearity 49 and heterogeneity. We develop recommendations for future research and integrating multi-50 disciplinary conceptual models for the coupled multi-scale multi-physics behavior of mudrocks. 51 Consistent conceptual models across disciplines are essential for predicting emergent processes 52 in the subsurface, such as self-focusing of flow, time-dependent deformation (creep), fracture 53 network development, and wellbore stability. 54 55 56 temporal scale, THCMB 57 58 59 60 61 62 65 66Sedimentary rock containing more than 50 percent (by weight or volume) of particles less than 67 62.5 microns in size are known variously as shale, siltstone, claystone, mudstone, and are 68 cumulatively referred to as mudrocks [1][2][3] . Some workers apply "shale" narrowly to refer to the 69 visibly laminated, fissile variety of this sedimentary rock, but in this paper we apply this term as 70 the overall name for the broad class of fine-grained layered sedimentary rocks, and, where 71 appropriate, use it interchangeably with the term "mudrock" [4] . Shale constitutes around two-72 thirds of the sedimentary record of planet Earth [5, 6] , and a quarter of the continental land mass 73 [7] . In some portions of sedimentary basins, distant from the principal axes of sediment transport, 74 the abundance of mudrocks may approach 90 percent of the local sediment volume [8] . Shales are 75 volumetrically dominant in both marine and terrigenous successions, and host significant 76 portions of the fluid-rock interactions controlling ...

This paper investigates the details of reflection, transmission, and conversion of plane waves incident upon a fracture at arbitrary angles. The elastic compliance of fractures that is produced by the presence of a planar collection of void spaces and asperities of contact is modeled as a displacement‐discontinuity boundary condition between two elastic half‐spaces. Closed‐form expressions for the transmission and reflection coefficients on a fracture are derived by replacing the boundary conditions for a welded interface by those for a fracture into the standard procedure for plane wave analysis. The closed‐form expressions reveal that a single fracture can produce a variety of potentially diagnostic waves such as transmitted waves, reflected waves, converted waves, head waves, and P interface waves and introduce a finite group time delay to all these waves with respect to the incident wave. The amplitude and group time delay of the fracture‐induced waves are controlled by the fracture stiffness, wave frequency, and the Poisson's ratio of the medium. The head wave and inhomogeneous P interface waves are generated when an SV wave is incident upon a fracture, at and beyond a critical angle, respectively, which is determined by Snell's law. For some combinations of the fracture stiffness and the Poisson's ratio of the half‐spaces, no reflection or transmission of a P wave or an SV wave occurs.

Hydraulic fracturing treatments have become an indispensable part of well completion in shale gas field development. Shale formations often contain natural fractures and complex hydraulic fracture networks may form during a treatment. The complex fracture network is strongly influenced by the interaction between the hydraulic fracture and the pre-existing natural fractures. A criterion has been developed to determine whether a fracture crosses a frictional interface (pre-existing fracture) at non-orthogonal angles. This criterion is an extension of the one for orthogonal crossing originally developed by Renshaw and Pollard (1995). The dependence of crossing on the intersection angle is shown quantitatively using the extended criterion. The fracture is more likely to turn and propagate along the interface than to cross it when the angle is less than 90°. The validation of the criterion using laboratory experiments for various angles is described and discussed. When applied to laboratory experiments, good agreement between the criterion and experiments is observed for a wide range of angles. The criterion can be used to determine whether hydraulic fractures cross natural fractures under particular field conditions, and it has been incorporated in a hydraulic fracture model that simulates hydraulic fracture propagation in a natural fractured formation.

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