Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

6.2. STRESS-SENSITIVE ROCK PHYSICS MODELS
Figure 6.1: Using 3rd order elasticity to model the nonlinear elasticity of a North Sea shale. Two
linear fits are given, for the low stress region (30MPa). From
Prioul et al. (2004).
Pressure (MPa) C 111 ± ∆C 111 (GPa) C 112 ± ∆C 112 (GPa) C 123 ± ∆C 123 (GPa)
5-30 -11300 ± 2900 -4800 ± 2500 5800 ± 4000
30-100 -3100 ± 600 -800 ± 500 40 ± 800
Table 6.1: Third-order terms used by Prioul et al. (2004) to empirically approximate the nonlinear
elastic behaviour of a North Sea shale.
defined by the three independent non-linear coefficients C 111 , C 112 and C 123 that describe the isotropic
3rd-order tensor.
The 3rd-order terms are determined empirically from lab ultrasonic measurements on core samples
by minimising a least-squares misfit function between observed measurements and model predictions
(see Prioul et al., 2004, for details). Equation (6.2) still requires a linear fit to the non-linear
stress/stiffness curve, so linear fits are determined for high stress and low stress regions (see Figure
6.1). The values of the third-order terms for the North Sea shale shown in Figure 6.1 are given in
Table 6.1.
The need to fit high and low pressure regions separately stems from trying to fit the nonlinear
relationship between stress and velocity with a linear regression. The choice of where to assign the
high and low pressure zones is somewhat arbitrary. Indeed, there is no conceptual reason why multiple
regions could not be defined (i.e., high, medium and low stress regions). It has been suggested that
the low pressure region, where velocities are more sensitive to stress, corresponds to stresses below
the in situ stress from which the core was taken (e.g., Holt et al., 2000). As the core is extracted, the
removal of these stresses damages the core, creating microcracks and increasing the stress sensitivity.
When the core is re-stressed to in situ conditions in lab experiments, the microcracks are closed, and
so the stress sensitivity is lowered. However, it is very difficult to test this assertion empirically.
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