Stress intensity factors in poroelastic half-space under steady-state flow

This study investigates the evolution of the stress intensity factor (SIF) at a fracture tip in a porous medium subjected to fluid injection. A comprehensive model is developed that considers both fluid flow within the fracture and the surrounding matrix with their mechanical effects on the SIF. It accounts also for the fracture-matrix mass exchange without assuming an a priori leak-off model. Numerical simulations reveal that the SIF changes during the transient flow phase and stabilizes at a limit value in the steady state. It is shown that for simple fracture geometries and constant injection conditions, the SIF reaches its maximum in the steady-state regime. Additionally, the steady-state flow analysis provides upper and lower bounds for fracture propagation length under constant pressure and constant flow rate injection conditions, respectively. This finding simplifies hydraulic fracture propagation analysis by allowing the simulation to focus solely on the steady-state flow. High-accuracy closed-form approximate solutions for the SIF are derived from theoretical and numerical analyses. It is shown that these solutions are particularly useful for studying fracture propagation in typical geometric configurations encountered in CO₂ sequestration projects and hydraulic fracturing around wellbores.