Many geo-engineering applications, e.g., enhanced geothermal systems, rely on
hydraulic fracturing to enhance the permeability of natural formations and
allow for sufficient fluid circulation. Over the past few decades, the
phase-field method has grown in popularity as a valid approach to modeling
hydraulic fracturing because of the ease of handling complex fracture
propagation geometries. However, existing phase-field methods cannot
appropriately capture nucleation of hydraulic fractures because their
formulations are solely energy-based and do not explicitly take into account
the strength of the material. Thus, in this work, we propose a novel
phase-field formulation for hydraulic fracturing with the main goal of modeling
fracture nucleation in porous media, e.g., rocks. Built on the variational
formulation of previous phase-field methods, the proposed model incorporates
the material strength envelope for hydraulic fracture nucleation through two
important steps: (i) an external driving force term, included in the damage
evolution equation, that accounts for the material strength; (ii) a properly
designed damage function that defines the fluid pressure contribution on the
crack driving force. The comparison of numerical results for two-dimensional
(2D) test cases with existing analytical solutions demonstrates that the
proposed phase-field model can accurately model both nucleation and propagation
of hydraulic fractures. Additionally, we present the simulation of hydraulic
fracturing in a three-dimensional (3D) domain with various stress conditions to
demonstrate the applicability of the method to realistic scenarios