- Pressurization of a PKN Fracture in a Permeable Rock During Injection of a Low Viscocity Fluid
- E. Sarvaramini ; D.I. Garagash
- Book Title / Journal: Effective and Sustainable Hydraulic Fracturing
- Year: 2013 , Series: Chapter 30
- Rock Mechanics ; Groundwater & Seepage
- Keywords: rock mass ; low viscocity fluid ; PKN fracture
- The aim of the present work is to investigate injection of a low-viscosity ﬂuid into a pre-existing fracture within a linear elastic, permeable rock, as may occur in waterﬂooding and supercritical CO2 injection. In conventional hydraulic fracturing, high viscosity and cake building properties of injected ﬂuid limit diffusion to a 1-D boundary layer incasing the crack. In the case of injection of low viscosity ﬂuid into a fracture, diffusion will take place over wider range of scales, from 1-D to 2-D, thus, necessitating a new approach. In addition, the dissipation of energy associated with fracturing of the rock dominates the energy expended to ﬂow a low viscosity ﬂuid into the crack channel. As a result, the rock fracture toughness is an important parameter in evaluating the propagation driven by a low-viscosity ﬂuid. We consider a pre-existing, un-propped, stationary Perkins, Kern and Nordgren’s (PKN) fracture into which a low viscosity ﬂuid is injected under a constant ﬂow
rate. The fundamental solution to the auxiliary problem of a step pressure increase in a fracture  is used to formulate and solve the convolution integral equation governing the
transient crack pressurization under the assumption of negligible viscous dissipation. The
propagation criterion for a PKN crack  is then used to evaluate the onset of propagation.
The obtained solution for transient pressurization of a stationary crack provides initial conditions to the fracture propagation problem.