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A21 The Effects of Geomechanical Deformation on Seismic Monitoring


The Effects of Geomechanical Deformation on
Seismic Monitoring of CO2 Sequestration
J. Verdon* (University of Bristol), D.A. Angus (University of Bristol), J.M.
Kendall (University of Bristol), J. Segura (University of Leeds), S. Skachkov
(University of Leeds) & Q.J. Fisher (University of Leeds)

When CO2 is injected into the subsurface, changes in pore pressure may lead to deformation of both the
reservoir and the subsurface. Of concern is that this deformation may create or reactivate fracture
networks, providing pathways for CO2 to migrate away from the targeted zone. By coupling a commercial
reservoir fluid flow simulator with a finite element geomechanical solver, we model the geomechanical
effects of CO2 injection into a simple reservoir. In order to link deformation with changes in seismic
observables, a stress dependent rock physics model is outlined and calibrated. We utilize this model to
show how injection induced stress changes might be imaged using shear wave splitting.

             First EAGE CO2 Geological Storage Workshop — Budapest, Hungary,
                                 29 & 30 September 2008
Sequestration of CO2 in deep subsurface aquifers and disused hydrocarbon reservoirs presents
an opportunity for reducing carbon emissions whilst exploiting the knowledge and
infrastructure invested in the hydrocarbon industry. If this technology is to become
economically and politically viable, we must be able to monitor movement of injected CO2 in
the subsurface, and we must be able to construct models that will assess the risk of CO2
leakage back into the atmosphere.

Injection of CO2 into the subsurface will lead to changes in the pore pressure of the reservoir
formation. These changes in pore pressure have the potential to cause geomechanical
deformation of both the reservoir and surrounding rock. Of concern with respect to long term
CO2 storage is that stress changes caused by injection could lead to the formation or
reactivation of fracture networks, providing pathways for CO2 migration through previously
impermeable rocks. In the first part of this paper we present a linked fluid-
flow/geomechanical simulation, allowing us to assess the geomechanical deformation caused
by CO2 injection.

Empirical observation (e.g., Nur and Simmons, 1969) indicates that changes in the stress and
strain acting on a rock will lead to changes in seismic properties. This will lead to changes in
seismic observables such as time-shifts and anisotropy that can be monitored to infer the
reservoir stress state. For example, Herwanger and Horne (2005) observed P-wave time shifts
and S-wave splitting attributable to the stress changes caused by depletion of a reservoir.
Developing an understanding of how seismic properties are affected by deformation allows us
to make inferences about the stress state in the subsurface. In order to do this a rock physics
model must be used that is capable of modeling the effects of stress on seismic properties.
This model should be capable of modeling empirically observed physical effects such as
nonlinearity and stress induced anisotropy, but should also be easy to parameterize and use. In
the second part of this paper we outline a model that meets these requirements, and
demonstrate its application by predicting the changes in seismic observables for the
geomechanical model that we have developed.

Though well developed and routinely applied in tunneling and mining industries, the use of
geomechanics in the hydrocarbon industry is relatively recent. An important development is
the coupling of fluid flow effects within the reservoir with geomechanical deformation of the
reservoir and surrounding non-pay units, allowing pore pressure changes to be mapped into
geomechanical deformation, and allowing changes in porosity and permeability caused by
deformation to affect fluid flow simulations.

Although fully coupled fluid-flow/geomechanical simulation is available, the computational
expense of such an approach makes the iterative or loosely coupled approaches more
attractive (see Minkoff et al. 2003). The fluid flow component of our model, including
supercritical CO2 properties, was modeled using a commercial fluid flow simulator
(TEMPEST, developed by Roxar). This is coupled to a finite element geomechanical solver
(ELFEN, developed by Rockfield Ltd). The elastic and plastic behavior of the geomaterials
used by ELFEN is defined by a constitutive formulation using laboratory core stress/strain
data. Thus, the mechanism incorporates linear elastic, plastic, and lithology specific behavior
(Crook et al. 2006).

The model we have chosen to build is simple in its geometry, consisting of a rectangular,
brine-filled, stiff sandstone reservoir of dimensions 4000x4000x75m, surrounded by a softer
shale over- and side-burden. The grid is densest in the reservoir region, with block size in the
x and y directions of 700x700m, and 15m in the z direction, becoming coarser away from the

            First EAGE CO2 Geological Storage Workshop — Budapest, Hungary,
                                29 & 30 September 2008
reservoir. This is a quarter symmetry model, using symmetry arguments to model a larger
reservoir without increasing computational time. To simulate a CO2 injection scenario, a
vertical well injecting CO2 at a rate of 0.2x106 tonnes/yr is placed at the corner of the
reservoir (representing the centre of the quarter symmetry reservoir that we are simulating).
At each time-step our simulation outputs information about stresses and strains in the
overburden and reservoir, porosity, and changes in fluid saturation. This information is used
to compute seismic properties using the rock physics model outlined in the following section.

In this section we develop a microstructural rock physics model in order to model the effects
of stress on seismic velocities. This model is based on the effective medium model described
by Sayers & Kachanov (1995), and is capable of considering both nonlinear effects and the
effects of non-hydrostatic stress. This model uses an effective medium model to describe the
compliance tensor, (Sijkl) of a rock in terms of a homogenous matrix material and a
distribution of low volume, low aspect ratio discontinuities. The overall compliance is
calculated as the sum of the compliance of the matrix (Sbijkl) and the additional compliance
caused by the discontinuities (ΔSijkl). Hence Hooke’s law is rewritten
                                   E ij = (Sijkl + ΔSijkl )σ kl .
The compliance of the matrix mineral can be estimated using petrographic analysis or from
behavior at high pressures. If we consider the discontinuities as rotationally invariant disc
shaped objects, ΔSijkl is given by
                         ΔSijkl =     (δikα jl + δilα jk + δ jkα il + δ jlα ik ) + β ijkl ,   (2)
where δij is the Kronecker delta. A number of authors have shown that it is reasonable to
ignore the 4th rank tensor βijkl (e.g., Grechka and Kachanov 2006; Verdon et al. 2008,
Geophysics, in press.). Hence, the stress dependence of the rock compliance can be calculated
by considering how the 2nd rank tensor αij, which is representative of the discontinuity number
density and orientation, responds to stress. We do this be considering how stress effects the
number density of 3 mutually orthogonal aligned sets of microcracks that represent the non-
zero diagonal components of αij.

Following the approach of Tod (2002), we derive an equation for the number density of
aligned cracks deforming elastically under an applied stress,
                                ε(σ ) = ε 0 exp(−c rσ c(n ) ) ,                (3)
                                           2(1− ν )
                                    cr =            ,                                         (4)
                                            πμa 0
σc(n) is the effective stress resolved normal to crack face, μ and ν are respectively the shear
modulus and Poisson’s ratio of the background matrix, and a0 and ε0 are the average aspect
ratio and number density of the crack set at a defined initial pressure (usually 0MPa). Hence
we can model the nonlinear stress dependent behavior for a fully triaxial stress field solely by
considering the initial free parameters a0 and ε0.

In order that our model be of use when linking with geomechanical models, we seek
calibration and rules of thumb that can be used to aid the population of seismic models. With
this in mind, we have computed ε0 and a0 from stress dependent seismic velocity
measurements for over 200 samples taken from the literature. The results are shown in Figure
1. We observe that, with the exception of shales, initial aspect ratios are remarkably consistent
both within and between lithologies. We find that variation of ε0 often correlates with
independent observations of damage, indicating that it may serve as an gauge for how well
consolidated and/or damaged the sample may be. The consistency of a0 and the correlation of

            First EAGE CO2 Geological Storage Workshop — Budapest, Hungary,
                                29 & 30 September 2008
ε0 with damage greatly increase our confidence in the microstructural approach to the

      Figure 1. Initial aspect ratio and crack density parameters as calculated for a range of published
      samples. Initial aspect ratio is seen to be consistent between and within lithologies. Initial crack
      density can be considered as a damage parameter.

Figure 2a shows the displacement in the horizontal plane after 7 years of injection. The pore
pressure increases during injection from an initial value of 30MPa to 43MPa. The decrease in
effective stress caused by the pore pressure increase forces the reservoir to expand in all
directions. At the edges of the reservoir, where the stiff reservoir is able to expand easily into
the softer side-burden, the magnitude of displacement is greatest (~10cm).

      Figure 2. (a) Displacement in the x-y plane at the top of the reservoir after 7 years of injection. The
      reservoir (shaded red) extends from 0 to 4000 in both x and y, with injection in the lower left corner.
      The largest arrows indicate a displacement of 10cm. (b) Percentage shear wave splitting for a
      vertically propagating shear wave through the reservoir level. The ticks indicate the orientation of the
      fast shear wave, and the size of the ticks and contours show the magnitude of splitting.

Geomechanical deformation has the potential to manifest itself in a number of seismic
observables, including 4-D time-shifts, anisotropy, reflectivity, and shear wave splitting. We
consider here the effects of deformation described above on shear wave splitting.

Shear wave splitting occurs when a shear wave is split into orthogonally polarized fast and
slow waves upon entering an anisotropic region. It may be caused by alignment of mineral
fabrics, the presence of fractures, or, as in this case, non-hydrostatic stresses. In Figure 2b we
use our rock physics model to compute the shear wave splitting caused by the displacement
shown in Figure 2a. The polarization of the fast shear wave is parallel to the maximum stress
direction, in this case parallel to the edge of the reservoir, and largest where the difference in

            First EAGE CO2 Geological Storage Workshop — Budapest, Hungary,
                                29 & 30 September 2008
principle stresses is largest, at the edges of the reservoir. At the center of the reservoir, where
stress changes are hydrostatic, no splitting develops.

Despite its simple nature, this model demonstrates how we can build forward models to
predict changes in seismic observables caused by geomechanical deformation. The
knowledge imparted by such modeling will be invaluable when considering the inverse
problem: inferring the reservoir stress state based on seismic observables. If we wish to assess
the risk of geomechanical deformation creating pathways for CO2 migration beyond the target
reservoir, then such modeling, combined with seismic observations, will be critical.
A coupled fluid-flow/geomechanical simulation has been used to predict the deformation
caused by injection of CO2 into a brine-filled reservoir. We outline a rock physics model that
enables us to link our geomechanical model with seismic modeling applications. The rock
physics model is simple in nature, and yet, through calibration with over 200 literature
samples, is shown to be easy to use and to parameterize. However, this simplicity does not
compromise our capability to model such empirically observed effects as nonlinearity and
stress-dependent anisotropy.

The geomechanical model used here is simple in nature, and as such there are limits to its
realism. However, the most important aspect of this work is the outline and demonstration of
a workflow that can be followed in order to model the geomechanical deformation caused by
CO2 injection, and how we can predict the typical seismic signature of such deformation,
allowing us to assess which seismic techniques will be the most useful in distinguishing stress
effects from fluid substitution effects. One such observation – shear wave splitting – is
demonstrated here. Where there is a risk that geomechanical deformation could allow leakage
of CO2 intended for sequestration, modeling of this type must be considered requisite for the
technology to develop into a viable emission reduction possibility.

This work was completed as part of the IPEGG project. The authors would like to thank the
IPEGG sponsors (BG Group, BP, ENI, Statoilhydro) and partners. We thank Roxar and
Rockfield for the use of their software. James Verdon was sponsored by a UKERC
interdisciplinary studentship.

Crook, A., Willson, S., Yu, J., Owen, D. [2006] Predictive modelling of structure evolution in
    sandbox experiments. Journal of Structural Geology, 28, 729-744.
Grechka, V. and Kachanov, M. [2006] Effective elasticity of fractured rocks: A snapshot of
    the work in progress. Geophysics, 71, W45–W58.
Herwanger, J. and Horne, S. [2005] Predicting time-lapse stress effects in seismic data. The
    Leading Edge, 12, 1234-1242.
Minkoff, S., Stone, C., Bryant, S., Peszynska, M. and Wheeler, M. [2003] Coupled fluid flow
    and geomechanical deformation modeling. Journal of Petroleum Science and
    Engineering, 38, 37-56.
Nur, A. and Simmons, G. [1969] The effect of saturation on velocity in low porosity rocks.
    Earth and Planetary Science Letters, 7, 183-193.
Sayers, C.M. and Kachanov, M. [1995] Microcrack induced elastic wave anisotropy of brittle
    rocks. Journal of Geophysical Research, 100, 4149-4156.
Tod, S.R. [2002] The effects of stress and fluid pressure on the anisotropy of interconnected
    cracks. Geophysical Journal International, 149, 149-156.

            First EAGE CO2 Geological Storage Workshop — Budapest, Hungary,
                                29 & 30 September 2008

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