Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

3.2. INVERSION METHOD
1. P-wave incident
normal to the
fracture
3. Stiff, spherical pore is
not compressed by the
wave
2. Flat, compliant fracture
is compressed by the wave,
causing a volume decrease
4. Fluid tries to flow
from the fracture into
the pore to equalise the
pressure gradient
Figure 3.1: Schematic cartoon showing how squirt-flow occurs in fractured rocks. As a compressive
wave travels through this system, the volume change of the compliant fracture is larger than that
of the stiff pore. As a result, fluid will try to flow from the fracture into the pore-space. The extent
to which this can occur will control the effective compliance of the fracture, and is determined by
the permeability of the rock and the viscosity of the fluid.
λ r and µ r are the Lamé parameters of the rock matrix along the axis of deformation in question (i.e.,
when computing B N and B T h , µ r = C r 66 and λ r + 2µ r = C r 11, but when computing B T v , µ r = C r 44
and λ r + 2µ r = C r 33). K fl and µ fl are the bulk and shear moduli of the fluid (usually, µ fl = 0),
and ξ and a are the scalar density and average aspect ratio of the fracture set. The fracture density
is a non-dimensional term given by the number of fractures in a volume and their average radius,
ξ = Nr 3 /V .
For the assumption of isolated fractures made by Hudson (1981) to be valid, either the pore space
and fractures must be hydraulically isolated (this is unrealistic for reservoir rocks), or the frequency
of the propagating wave must be high enough that there is no time for the pressure gradient to be
equalised. Thus, theories which consider fractures to be hydraulically isolated must be considered as
applicable only at high (generally ultrasonic) frequencies (though without violating the condition that
wavelength is much larger than inclusion size) or where the fluid bulk modulus is ∼ 0. If fluid flow
between fractures can occur, this theory becomes inaccurate. This inaccuracy has been demonstrated
in experimental tests by Rathore et al. (1994).
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