Growth Rate of Natural Hydraulic Fracture

Natural hydraulic fractures (NHFs) are tensile fractures that form in fluid-saturated rocks when in-situ pore pressure exceeds the minimum compressive stress. Their propagation is controlled by the inflow of pore fluid, which depends on both pore pressure diffusion in the surrounding rock and the evolving fracture size. However, the long-term growth behavior of NHFs remains an open question. This study demonstrates that, after an initial transient phase triggered by a perturbation that caused the fracture to grow, an NHF attains a steady-state propagation rate. An explicit expression for this rate is derived, linking it to the rock poromechanical properties and to the difference between in-situ pore pressure and minimum compressive stress. This result is achieved by recognizing that, over time, fracture growth outpaces diffusion, effectively confining pore pressure evolution to a one-dimensional diffusion process within thin layers adjacent to the fracture plane.