Exact quasi-steady solution of the problem of hydraulic fracturing of a permeable formation Journal of Applied Mechanics and Technical Physics Volume 54, Issue 6, 2013, Pages 937-944

An exact solution of the problem of hydraulic fracturing in a permeable medium with continuous fluid injection in a partially penetrated formation is constructed using the Perkins-Kern fracture model. The amount of fluid leakage from the fracture is determined using the pressure field of the fluid filtrate defined by the Shchelkachev equation (of the piezoconductivity type). Universal profiles of the fluid pressure in the fracture and the rate of fluid flow from it are obtained. It is shown that at the Perkins-Kern fracture tip, there is a dramatic increase in the leakage from the fracture.
Indexed keywords
Exact solution; Fluid injections; Fluid pressures; Fracture model; Permeable formations; Pressure field; Quasi-steady solutions; Universal profile