Hydraulic fracturing of a saturated porous medium-II: Special cases

Abstract

This analysis investigates the steady-state propagation of a hydraulic fracture in an infinite isotropic fluid-saturated elastic porous medium in the limiting cases of slow and rapid crack growth. In the limiting case of slow crack propagation, it is found that the governing field equations become decoupled, and that a closed-form solution for the stress and pore pressure components can be obtained by solving these equations subject to the appropriate boundary conditions. In the limiting case of rapid crack propagation, it is found that the field equations reduce to a degenerate form, and that the stress and pore pressure components given by the solution of the equations do not satisfy the boundary conditions imposed at the crack faces and at the crack tip. This suggests the presence of stress and pore pressure boundary layers along the surfaces and at the tip of the propagating crack. Closed-form solutions for stress and pore pressure components in the boundary layer are then obtained by formulating a singular perturbation problem which is subsequently investigated by the method of matched asymptotic expansions.