Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

CHAPTER 3.
INVERTING SHEAR-WAVE SPLITTING MEASUREMENTS FOR FRACTURE PROPERTIES
B T v will only differ when significant VTI anisotropy is present.
Furthermore, I believe that they
will only differ when the mechanism causing VTI anisotropy acts at a smaller length-scale than the
vertical fractures (e.g., horizontally aligned anisotropic minerals). If the VTI anisotropy is induced
by horizontally aligned fractures or by larger scale sedimentary layers (e.g., Backus, 1962) then it is
not clear that B T h and B T v should be allowed to differ.
It is possible to calculate the fracture normal and tangential compliance as a function of fracture
density, aspect ratio and fill by assuming an idealised fracture geometry (e.g., penny-shaped or elliptical).
Several such methods are available in the literature (e.g., Hudson, 1981; Hudson et al., 1996),
and well summarised by Hall and Kendall (2000).
Fractures and fluids
A key difference between fracture models in the literature is how they treat the fluids that fill the
fractures. Reservoirs will be saturated with gas, brine or oil (or a multiphase mixture), and these
fluids will also saturate the fractures. The presence of fluid in a fracture will have a significant effect
on the fracture compliance, and hence the overall rock stiffness tensor.
The compliance of a flat, low aspect ratio crack will be far greater than a spherical pore. As a
result, the incidence of a pressure wave will compress a fracture far more than a pore, leading to
non-uniform compression of the saturating fluid and the development of pressure gradients between
fluids in the pores and fractures. The fluid will attempt to flow to equalise these gradients, however
it will be restricted by the permeability of the rock matrix and its own viscosity. The extent to which
this pressure gradient equalisation can occur is crucial for determining the fracture compliance. This
phenomenon is known as squirt-flow, and can be best demonstrated by considering an idealised system
of aligned penny-shaped fractures that can either be fully connected to a system of spherical pores,
partially connected to them, or totally isolated from the porosity (Figure 3.1).
Isolated fractures
Early effective medium models models such as Hudson (1981) and Tandon and Weng (1984) consider
there to be no fluid connection between fractures. An incident P-wave travelling normal to the fracture
faces must compress both the fracture faces and the fluid within it. Because the fluid has some stiffness
the overall compliance of the fracture is decreased. The normal and tangential compliance, B N and
B T , of a set of isolated, fluid-filled fractures is given by Hudson (1981) as
B N = 4 ( ) ( ξ λ r + 2µ r ) 1
3 µ r λ r + µ r 1 + K ,
B T = 16 ( ) ( ξ λ r + 2µ r ) 1
3 µ r 3λ r + 4µ r 1 + M , (3.7)
where
K = K fl
πaµ r (λ r + 2µ r )
(λ r + µ r ) ,
M = 4µ fl
πaµ r (λ r + 2µ r )
(3λ r + 4µ r ) . (3.8)
30