Transient Gas or Liquid Flow Along a Preexisting or Hydraulically-Induced Fracture in a Permeable Medium

Abstract

Similarity solutions are derived for the transient two-dimensional flow of a gas or liquid along an isolated fracture in a permeable medium. The driving pressure at the fracture inlet is constant, and the confining stress is uniform. Two different cases are considered, preexisting fractures with uniform aperture as well as hydraulic fractures with a variable aperture proportional to the local overpressure (fluid pressure less confining stress). The evolution of the pressure distribution is described by a set of four asymptotic solutions, each having a self-similar form. At early times the flow in the fracture is turbulent, and Darcian seepage losses into the porous surroundings are negligible. At late times the flow in the fracture is laminar, and seepage losses become a dominant consideration. At intermediate times there are two alternative asymptotes, depending upon the physical parameters. The mathematical model also describes the flow along a fracture which is filled with high-permeability porous material as well as the flow in an assemblage of porous blocks.