Similarity Solutions for Wedge-Shaped Hydraulic Fractures Driven into a Permeable Medium by a Constant Inlet Pressure

摘要

Similarity solutions are derived for wedge-shaped hydraulic fractures driven by a constant inlet pressure, P sub 0 , into a permeable medium under uniform confining stress, sigma. These results describe the seepage-dominated regime in which most of the injected fluid is lost into the permeable walls of the fracture; they complement previous results for the capacitance-dominated regime in which seepage is negligible. Fracture propagation velocity is obtained as an analytical function of fracture length, driving pressure, confining stress, material properties, and a single separation-constant or eigenvalue which is determined numerically. Self-similar profiles of pressure, opening displacement, and fluid velocity along the fracture are presented together with the self-similar isobars of the two-dimensional pressure field within the permeable surroundings. Comprehensive results are reported for laminar or turbulent flow of a constant-compressibility liquid or an ideal gas driven by overpressures, (P sub 0 - sigma)/sigma, ranging from 10 exp -2 to 10 exp 2 . (ERA citation 11:017039)