Section Days abstract book 2010.indd - RUB Research School ...

NSE_25
TOWARDS A MULTI-SCALE MODEL
OF HYDRAULIC FRACTURING
Carlo Vinci, Jörg Renner and Holger Steeb
Mechanics – Continuum Mechanics
Ruhr-Universität Bochum, 44780 Bochum, Germany
email: vinci@lkm.rub.de
The aim of the present project is to investigate a deformable
fluid-filled fracture embedded in a porous rock matrix and
the coupled hydro-mechanical interaction between fluidfilled
joint and matrix. Injection of fluid into a porous
fractured rock mass alters the opening aperture of preexisting
joints and faults or alternatively initiates formation
of new fractures. The associated dilatation affects the
hydraulic properties of the joint and leads to an increase of
the effective permeability of the rock. Therefore, the flow of
Fig. 1 Borehole intersected by
vertical fractures
fluids and the propagation of hydraulic fractures from boreholes intersecting jointed rock are
controlled by the mechanical response of deformable fractures to transient pressure gradients
imposed by pumping operations. A good understanding of the response of a single fluid-filled
joint to transient pressure changes forms the basis for more advanced physically-based multiscale
continuum models.
The model of the single fracture is based on a simple
deformable ellipsoidal joint [1]. The deformation of the
joint is complemented by the time-dependent diffusion
process of the pore fluid in the joint itself, resulting in a
coupled problem consisting of a) an elastic deformation
problem and b) a non-linear diffusion problem. Here, we
Fig. 2 Half length ellipsoidal joint
investigate the coupled problem with a staggered solution
scheme, in which the one-dimensional non-linear diffusion
problem of the fluid in the joint is solved numerically by the Galerkin Finite Element Method
(FEM). Based on the numerical results, we will discuss the time-dependent non-equilibrium
configurations of the joint and the corresponding pressure profiles.
References:
[1] Murdoch L.C. and L.N. Germanovich, Analysis of a deformable fracture in permeable material, International
Journal for numerical and Analytical Methods in Geomechanics 30, 529-561 (2006).
[2] Murphy H., C. Huang, Z. Dash, G. Zyvoloski and A. White: Semianalytical solutions for fluid flow in rock
joints with pressure-dependent openings, Water Resources Research 40 (2004).