A Fully Coupled Hydro-Mechanical Phase-Field Model for Hydraulic Fracture Initiation and Complex Propagation in Porous Rock Media

Hydraulic fracturing in low-permeability porous rocks involves strong interactions between rock deformation, pore fluid transport, and progressive fracture damage. In this study, a hydro-mechanical phase-field model was developed to investigate hydraulic fracture evolution in saturated porous media. Biot poroelasticity, tensile–compressive strain energy decomposition, irreversible phase-field fracture evolution, and damage-dependent permeability were incorporated within a common finite element framework. The model was implemented in COMSOL Multiphysics 6.4 and used to examine the effects of the horizontal principal stress difference, injection rate, and fracturing fluid viscosity on the fracture morphology and pressure response. Within the investigated parameter ranges, increasing the horizontal principal stress difference from 2 to 14 MPa reduced the stimulated fracture area from 42,640 to 21,300 m2 (50.0%) and the number of secondary branches from 12 to 5. Increasing the injection rate from 3 to 6 m3/min increased the stimulated fracture area from 35,771 to 44,138 m2 (23.4%), the branch count from 6 to 11, and the breakdown pressure from 135.19 to 162.11 MPa (19.9%). Increasing the fluid viscosity from 1 to 100 mPa·s increased the stimulated fracture area from 35,771 to 48,722 m2 (36.2%) and the breakdown pressure from 135.19 to 183.21 MPa (35.5%). The injection rate sensitivity was also compared with published granite hydraulic fracturing experiments, which demonstrated a positive increase in breakdown pressure with injection rate. This comparison was interpreted as trend-level physical consistency rather than direct material-specific validation because the experimental and numerical systems differed in their rock type, scale, stress state, temperature, and injection rate range. The results demonstrated systematic sensitivities of the hydraulic fracture geometry and pressure response within the investigated two-dimensional model configuration.