This paper is concerned with an analysis of the near-tip region of a fluid-driven fracture propagating in a permeable saturated rock. The problem is characterized by the existence of a tip cavity resulting from a lag between the fracturing fluid and the fracture tip. This cavity is filled by pore fluid, which is drawn by suction at the tip of the advancing fracture from the porous medium, and is reinjected to the porous medium behind the tip, near the interface between the two fluids. An analytical solution for he pore pressure distribution in the cavity is derived within the framework of fracture mechanics theory for the aperture of the cavity, diffusion theory for the exchange of the pore fluid between the cavity and the porous medium and the fluid flow within the porous medium, and lubrication theory for the viscous flow along the crack. Such a solution provides the appropriate tip conditions when considering the large-scale problem of fluid-driven fracture in a permeable rock.
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