We have investigated the use of an energy-based numerical algorithm and its ability to simulate growth of a single planar hydraulic fracture by matching modeled dimensions to those inferred from a microseismic map. The energy-based microseismic fracture model accounts for the various physical processes expressed as a balance between the work expended (input/injected energy) and work done (output/lost energy) during growth of a vertical, 3D, laterally symmetric, planar, ellipsoidal, and tensile (mode I) fracture. These canonical fracture models provide a simple but useful proxy for more complex fracture networks that occur in reality. The tensile fracture is positioned in a three-layer geologic medium defined by elastic, material, and stress properties. Fracture half-length, half-width, half-height, and effective crack-opening pressure were computed using a time-stepping algorithm that solved energy balance equations using a Lagrangian formulation. Two parameters are adjusted to calibrate the fracture model to microseismic data; observed upward growth is fit by adjusting stress-barrier contrasts, and fracture length is fit by altering an empirical parameter, fracture toughness. In the case of a symmetric model with equivalent stress and material properties above and below the fracture, an increase in fracture toughness results in a corresponding increase in modeled net pressure and fracture width profile. In the case of a model with different stress states in the layers above and below the injection level, fracture height growth is enhanced in the layer with lower in situ stress. In both cases, net work is minimized in response to trade-offs between creation of new fracture surface area and fracture volume. Our primary objective was to incorporate microseismic observations into a geomechanical simulation of hydraulic fracture growth. Our approach is novel; it explains hydraulic-fracture behavior from an energy-balance perspective using the spatial-temporal evolution of microseismicity to constrain and validate the model.

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