Hydraulic fracture propagation under steady state fluid flow

The stress intensity factor at a fracture tip in a porous medium subjected to a fluid injection is studied. This factor evolves during the transient flow phase and tends to a limit value for the steady state. For simple fracture geometries, the finite element simulations show that for constant injection pressures this factor reaches its maximum value in the steady state regime. This result allows simplifying significantly the study and modeling of hydraulic fracture propagation because the determination of the steady flow solution is much easier and faster than the transient flow. In addition, some couplings between hydraulic and mechanical problems disappear under steady state flow and make it possible to establish some closed-form approximate expressions. These can be useful especially in the context of CO₂ sequestration projects where the fluid injection is pressure-controlled.