Crisman Annual Report 2009 - Harold Vance Department of ...

Numerical Modeling of Fracture Permeability Change in Naturally Fractured
Reservoirs using a Fully Coupled Displacement Discontinuity Method
Introduction
Pressure depletion in a naturally fractured reservoir
can result in effective stress change that, in turn,
can affect fracture aperture and the reservoir
permeability. The dependence of fracture aperture and
reservoir permeability on stress must be considered
in modeling a naturally fractured reservoir. The
dependence involves coupled interactions among
fluid, porous matrix, and fracture. The previous
methods on the dependence of fracture permeability
on the pressure depletion did not consider the fully
coupled interactions of fluid, porous matrix, and
fracture or the real deformation mechanism of
fracture.
Approach
We developed a new approach to solve the fluid
pressure, stress change, and fracture aperture
change in fractures simultaneously. We did this
by combining a finite difference method (FDM) to
solve the fluid diffusion in fractures a fully coupled
displacement discontinuity method (DDM) to
build the global relation of fracture deformation,
and a nonlinear Barton-Bandis model of fracture
deformation to build the local relation of fracture
deformation. The fully coupled DDM is based on
Biot’s theory of poroelasticity which is a linear
elastic theory to account for the coupled interactions
between porous matrix and fluid in a porous medium
saturated with a compressible fluid. The analytical
solution of induced stress and pore pressure by the
deformation of a finite thin fracture in an infinite
elastic porous medium is provided. The influences
of deformation of complicated fracture network are
obtained by the superposition of the fundamental
analytical solution. The stress acting on the fracture
surface and the deformation of the fracture also must
comply with the fracture deformation model (e.g.
Barton-Bandis model). The fluid flow in the fracture
network is solved by an FDM. The interface flow
rate between the fracture and matrix is implicitly
included in the fully coupled DDM. As a result, the
approach is able to model the fracture deformation
due to reservior pressure change in naturally
fractured reservoirs by considering the fully coupled
interactions of fluid, porous matrix, and fractures.
Application
This method has been applied to model the fracture
permeability change for a two-dimensional regular
Fig. 1. Pore pressure (psi) distribution after 360 days production.
fractured network (Fig. 1) in a compressible
single-phase fluid-saturated porous medium. Under
isotropic in-situ stress conditions, the fracture
permeability decreases with the pressure reduction
during production (Fig. 2). But at high anisotropic
stress conditions, the fracture permeability could
be enhanced by production due to shear dilation
(Fig. 3).
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Project Information
3.2.10 Well Test Models for Caves in a Karstic Carbonate
Reservoir
Contacts
Christine Ehlig-Economides
979.458.0797
c.economides@pe.tamu.edu
Qingfeng Tao
CRISMAN INSTITUTE
Crisman Annual Report 2009
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