Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

CHAPTER 6.
GENERATING ANISOTROPIC SEISMIC MODELS BASED ON GEOMECHANICAL SIMULATION
essence means that, although a rock might be initially anisotropic, the change in velocity caused by
a particular stress change will be the same regardless of the axis along which this stress is applied.
The ability to deal with intrinsic and stress induced anisotropy represents a significant advantage
for the Prioul et al. (2004) model. However, as with all of the models discussed above, the observed
nonlinear stress-velocity relationship is fitted with a linear trend. Prioul et al. (2004) get around
this issue by fitting low and high stress regions separately, an approach that significantly limits the
general applicability of the model. Furthermore, the model can only be parameterised with triaxial
stress velocity measurements. Such experiments are much less common in the literature, so the kind
of extensive calibration that I was able to perform for the micro-structural approach is not as easily
performed. Given that the Prioul et al. (2004) model is already less intuitive to grasp, the difficulties
in parameterisation mean that this approach does not provide such an intuitive framework within
which understand how seismic velocities respond to changes in applied stress.
The model I have outlined in this chapter attempts to describe the micro-structural response to
stress changes, using this as a route to describe seismic properties via an effective medium model.
Real rocks do not contain the idealised, penny-shaped discontinuities that I use as the framework for
my modelling. However, it has long been recognised (e.g., Hudson, 1981; Sayers and Kachanov, 1995;
Schoenberg and Sayers, 1995; Thomsen, 1995; Hall et al., 2008) that the response of compliant grain
boundary discontinuities to the infinitesimal strain, high strain rate deformation induced by a seismic
wave can be approximated very closely using such an approach. The additional step that I have made
is to assume that the compliant grain boundary discontinuities respond in the same manner to the
finite strain, low strain rate deformation induced by geomechanical stress changes as they do to the
deformation during the passage of a seismic wave. This is a reasonable assumption to make so long
as geomechanical deformation remains elastic. The second assumption that I make is that the size
distribution of the grain boundary discontinuities can be modelled with an exponential distribution.
This assumption is somewhat more arbitrary in its nature, as there is no physical reason why a power
law distribution could not be used instead. However, the exponential distribution provides a good
match to velocity observations, and is easily parameterised.
The advantage gained by describing stress sensitive velocities using a micro-structural model is that
we can move closer to understanding the physics behind the phenomenon. By doing so, it is possible
to develop a more intuitive understanding of the processes involved. The model I have developed is
far more intuitive in its use than the third-order elasticity approach. For instance it is not intuitive to
say how increased core damage will affect the three independent terms of Prioul’s isotropic third order
tensor. Furthermore, given the need to limit the third-order tensor to isotropy, this model cannot
account for anisotropic rock fabrics as seen in many clay and/or mica rich rocks.
In contrast, for the micro-structural model it is intuitive to conceive that damage will increase
the initial microcrack density terms, while alignment of platy minerals will increase the crack density
along one axis of symmetry alone. Additionally, the improved understanding of the physical processes
that a micro-structural analysis provides leads to a model that can account for observed phenomena
such as intrinsic and stress-induced anisotropy, and the nonlinear response of velocities to stress
(the micro-structural model has no need to fit separate linear portions of the stress-velocity curve).
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