A hybrid XFEM–SWCC technique for modeling hydraulic fracture and fluid dispersion in a variably saturated porous media for storage purposes

Injection of fluid, such as liquid CO₂, into fractured porous matrix containing pre-existing cracks can lead to the propagation of hydraulic fractures (HF) in the solid phase, causing leakage-induced dispersion of fluid into surrounding pore spaces from the crack edges. These coupled hydro-mechanical processes play a central role in many subsurface energy and environmental applications. Hydraulic fracture propagation creates a high-conductivity pathway for the injected fluid to reach the surface and can result in irreversible displacements, while simultaneous fluid dispersion within the porous medium poses geomechanical challenges and environmental risks for the stability of underground caverns and subsurface resource exploitation. Understanding crack propagation and fluid dispersion is crucial for predicting the behavior of porous media after injection. Additionally, joints along the crack path make predicting the final behavior of the porous medium more challenging. Furthermore, an earthquake during fluid injection complicates the analysis. In this paper, a computational modeling approach is developed to ensure safe storage without leakage and crack propagation. To achive this objective, the solid phase motion equation is coupled with the fluid phase continuity equation, and the resulting governing system is discretized and solved using the extended finite element method (XFEM). Fluid dispersion is computed using the soil water characteristic curve (SWCC), accounting for variations in saturation. Several benchmark examples are used to validate the developed finite element model, with results compared to those in the literature. The influence of each term in the fluid phase continuity equation on saturation levels is also examined. Numerical factors affecting the solution—such as joints or defects in the crack path, the simultaneous occurrence of an earthquake during injection, the frequency content of ground motions, and the temporal evolution of fluid dispersion— are investigated. Finally, the effect of temperature variations during injection is assessed through supplementary non-isothermal analyses.