The tensile strength characteristics and related strain-softening/hardening laws were derived from laboratory tests on nano-cantilever beams of kerogen rich shales (KRS) at nominal low, medium and high values of kerogen content and implemented as a user-defined spring model in e (a lattice code developed by Itasca based on the discrete element method). The brittleness of the shale samples in the nano-scale experiments were more pronounced in samples with lower values of kerogen content. The macroscopic toughness, and tensile strength properties (assuming the material has no structural defect) were obtained by performing direct, self-similar notched tension tests on microscopic samples with low, medium and high kerogen contents in the lattice code. The notched tests were characterized by two dimensionless parameters, i.e., the ratio of initial crack size over sample width, and the crack resolution in the lattice (the ratio of initial crack size over the lattice resolution). With the first ratio and lattice resolution fixed, extensive parametric studies were performed to generate log-log plots of the critical tensile stress versus the crack resolution in the lattice. The macroscopic tensile strength of the simulated KRS material was estimated from the horizontal plateau obtained at low crack resolution values in the plots. The toughness corresponding to the condition of LEFM (linear elastic fracture mechanics) was measured from the segment observed at high values of crack resolution in the logarithm plots where the slope was -½ Some interesting phenomena were observed in the simulations, e.g., the extent of the process zone near crack tips appeared to remain constant in the tests at nominal low kerogen content; the value of crack resolution beyond which LEFM applies increases as the kerogen content increases (which is consistent with the lower brittleness, or higher plasticity level, at high kerogen content). Using the calibrated macroscopic toughness, fluid injection tests were simulated in meter-scale numerical models at uniform nominal kerogen content. The numerical injection results indicated that, as kerogen content increases, the cluster injection pressure and hydraulic fracture radius increase but the maximum aperture decreases. The behavior is consistent with that expected from the evolution of a penny-shaped crack in the viscosity-dominated regime.

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