Self-Similar Solution in Problems of Hydraulic Fracturing

Abstract

The problem of hydraulic fracturing in geological materials is investigated based on a model of the growth of a finite crack in an infinite and linearly elastic medium induced by fluid pressure. The fluid is injected into the crack through an injection well at the center of the crack. The surface of the crack is considered to be impermeable. Flow is present in the crack as the crack propagates. In this study, the fluid is considered to be inviscid and incompressible. Assumptions of a one-dimensional flow in the fracture and a plane-strain deformation of the medium are imposed. At the crack tip, the value of stress intensity factor is considered to be constant during crack propagation. Self-similarity is found in the solution. Crack length, crack profile, fluid pressure, and other related physical characteristics are evaluated as functions of time.