Page 159 - Reservoir Geomechanics

142 Reservoir geomechanics

S Hmax −S v plane. If such fractures were to form in the current stress field and have an
appreciable effect on fluid flow in otherwise low permeability reservoirs, it would result
in a simple relationship between fracture orientation, stress orientation and permeability
anisotropy. Moreover, the simplistic cartoon shown in Figure 5.1a has straightforward
implications for using geophysical techniques such as seismic velocity anisotropy,
shear-wave splitting, and amplitude versus offset (AVO) to identify in situ directions
of permeability anisotropy (e.g. Crampin 1985;Winterstein and Meadows 1995). The
subject of the relationships among freacture orientation, stress orientation and shear
velocity will be revisited at the end of Chapter 8.

Faults, fractures and fluid flow

While Mode I features are ubiquitous in some outcrops (e.g. Engelder 1987; Lorenz,
Teufel et al. 1991) and can be seen as micro-cracks in core (e.g. Laubach 1997), it
is unlikely that they contribute appreciably to fluid flow at depth where appreciable
stresses exist. To consider flow through a fracture, we begin by considering a parallel
plate approximation for fluid flow through a planar fracture. For a given fluid viscosity,
η, the volumetric flow rate, Q, resulting from a pressure gradient,∇ P,is dependent on
the cube of the separation between the plates, b,

b 3
Q = ∇ P (5.1)
12η
To make this more relevant to flow through a Mode I fracture, consider flow through a
long crack of length L, with elliptical cross-section (such as that shown in the inset of
Figure 4.21). The maximum separation aperture of the fracture at its midpoint is given
by
2
2(P f − S 3 )L(1 − ν )
b max = (5.2)
E
where P f is the fluid pressure in the fracture, ν is Poisson’s ratio and E is Young’s
modulus. This results in a flow rate given by

π
b max 3
Q = ∇ P (5.3)
8η 2
which yields
3
2
π L(1 − ν )(P f − S 3 )
Q = ∇ P (5.4)
8η E
Hence, the flow rate through a fracture in response to a pressure gradient will be
proportional to the cube of the product of the length times the difference between the
fluid pressure inside the fracture (acting to open it) and the least principal stress normal