On the role of poroelasticity in the near-tip region of a hydraulic fracture

Hydraulic fracturing, originally developed to enhance hydrocarbon production, is increasingly applied to geothermal systems, subsurface thermal energy storage, and carbon sequestration. In these applications, reservoir containment is critical: controlling fracture growth through careful management of injection pressure and flow rate is essential to prevent unintended fluid migration and ensure long-term caprock integrity. Hydraulic fracture growth is strongly influenced by near-tip processes, including rock breakage, viscous fluid flow within the fracture, and fluid exchange with the surrounding reservoir. In permeable, fluid-saturated formations, the mechanical response of the rock is coupled to pore pressure diffusion, giving rise to poroelastic phenomena such as additional normal stress acting on the fracture walls (backstress), which increases the fluid pressure required for propagation. This work investigates the near-tip region of a hydraulic fracture propagating in a homogeneous poroelastic medium to identify when poroelastic coupling significantly affects fracture opening and fluid pressure fields.

The near-tip region is modeled as a semi-infinite plane strain crack propagating at constant velocity in a linear isotropic poroelastic medium. Formulated in the moving tip reference frame, the problem is steady. Fracture propagation is governed by linear elastic fracture mechanics. We consider the two-dimensional nature of fluid exchange between the fracture and the surrounding reservoir, assuming the fracturing and pore fluids are identical Newtonian liquids. A fully coupled hydro-mechanical boundary integral formulation is developed. The model accounts for reciprocal poroelastic interactions: backstress generated by pore pressure diffusion in the surrounding rock and pore pressure perturbations induced by deformation of the solid skeleton. The resulting nonlinear system comprises boundary integral equations governing the normal stress along the fracture surfaces and the fluid pressure within the fracture, both dependent on the fracture opening and fluid exchange rate. The system is closed by the fracture propagation criterion and the lubrication equation for flow inside the fracture.

Analytical solutions are obtained for the near- and far-field regions. In the near-field, the fracture opening follows the square-root asymptote with drained elastic moduli, while the fluid pressure within the fracture is uniform. In contrast, the far-field is governed by the storage-viscosity asymptote with undrained elastic moduli. The solution bridging these regions is obtained numerically. Dimensional analysis shows that the problem is governed by four dimensionless coefficients: a dimensionless permeability, a dimensionless effective confining stress, a poroelastic stress coefficient, and a normalized difference between undrained and drained Poisson's ratios. Using parameter ranges representative of sandstone reservoirs, the fully coupled model is compared with reduced formulations that neglect reciprocal poroelastic interactions or retain only the backstress effect. We find that poroelastic effects intensify with increasing permeability and poroelastic stress coefficient, and as reservoir pressure approaches normal conditions, resulting in significant modifications of fracture opening and fluid pressure profiles. While backstress generally dominates deformation-induced pore pressure perturbations, the latter become pronounced in overpressured reservoirs during rapid fracture propagation. The results clarify the conditions under which fully coupled poroelastic interactions must be considered to accurately predict near-tip behavior, providing guidance for reliable modeling of hydraulic fracture propagation in poroelastic media.