Enhanced geothermal systems (EGS) rely on the artificial creation of fractures (i.e., hydraulic fractures) to enhance the permeability of the formation which would, otherwise, be too low to allow for fluid circulation. Hydraulic fracturing involves complex nucleation and propagation processes, which are key to the analysis and prediction of well productivity. Numerical simulations are commonly employed to understand the specific mechanisms behind nucleation and propagation of hydraulic fractures. However, most numerical approaches face tremendous challenges in tracking and accommodating the evolving fracture geometry, especially when curved and branched fractures occur. The phase-field method can overcome this obstacle, as it can model fracture propagation without the need for tracking the fracture tip nor for remeshing. However, the most common phase-field formulation is unable to accurately capture fracture nucleation. In this work, we develop a new phase-field approach for hydraulic fracturing that accounts for fracture nucleation due to the strengths of geologic material and the existence of small defects. Verification examples show that the proposed formulation can accurately predict near-wellbore nucleation and propagation of hydraulic fractures and the wellbore breakdown pressure. Simulation of a three-dimensional wellbore problem further demonstrates the efficiency of the proposed phase-field method in handling fracture nucleation and propagation.

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