S i jkl = 1 4 (δ ikα jl + δ il α jk + δ jk α il + δ jl α ik )+β i jkl, (2)

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1 The effects of geomechanical deformation on seimsic monitoring of CO 2 sequestration James P. Verdon, Doug A. Angus, J-Michael Kendall, Dept of Earth Sciences, University of Bristol Jose Segura Serra, Sergey Skachkov, Quentin J. Fisher, RDR, Leeds University SUMMARY Recent work in hydrocarbon reservoir monitoring has focussed on developing coupled geomechanical/fluid flow simulations to allow production related geomechanical effects such as compaction and subsidence to be included in reservoir models. In order to predict realistic time-lapse seismic observables from geomechanical modeling, the generation of appropriate elastic models from geomechanical output is required. We develop and calibrate a micro-structural rock physics model in order to map the effects of stress changes on seismic velocities. This approach is then used to predict seismic observables based on a simple geomechanical model for injection of CO 2 into a reservoir for storage purposes. INTRODUCTION Sequestration of CO 2 in deep subsurface aquifers and disused hydrocarbon reservoirs presents an opportunity for reducing carbon emissions without compromising our economic dependence on hydrocarbon energy. However, if this technology is to become economically and politically viable, we must be able to monitor movement of injected CO 2 in the subsurface, and we must be able to construct models that will assess the risk of CO 2 leakage back into the anthroposhere. Of concern is that stress changes caused by injection could lead to fracturing and loss of integrity of previously impermeable caprock. In order to assess this risk we must develop geomechanical models for CO 2 injection scenarios, and we must consider how we can use changes in seismic observables to monitor stress changes in the subsurface. 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 in the hydrocarbon industry is the coupling of fluid flow effects within the reservoir with geomechanical deformation of the reservoir and surrounding non-pay units (e.g., Dean et al., 2003). To relate coupled fluidflow and geomechanical simulation to seismic observables it is necessary to construct elastic models based on information given not only from fluid flow and geomechanical output, but also constraints given by geologic, engineering and seismic observations. This can be done by combining a rock physics model that includes the effects of various intrinsic rock properties as well as the influence of the stress (and strain) field. Such a model should be capable of modeling empirically observed physical effects such as nonlinearity and stress induced anisotropy, but should also be easy to parameterise and use. In this paper we outline a model that meets these requirements, and demonstrate its application by predicting the seismic properties for a simple gas injection model. ROCK PHYSICS MODEL 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 and Kachanov (1995), and is capable of considering both nonlinear effects and the effects of nonhydrostatic stress. Theory Sayers and Kachanov (1995) describe an effective medium model to describe the comliance, S i jkl of a rock in terms of a homogenous matri material and a random distribution of low volume, poorly bonded discontinuities, commonly referred to as microcracks or grain boundaries. The overall compliance can be considered as the sum of the compliances of the background material (Si b jkl ) and the additional compliance caused by the discontinuities ( S i jkl ), such that the the relationship between stress, σ, and strain, E, is written E i j = (S b i jkl + S i jkl)σ kl. (1) S b can be estimated from the mineral makeup of a rock (e.g., Kendall et al., 2007), or, if this information is not available, from the behaviour at high pressures (e.g., Sayers, 2002). For a set of discontinuities,, in a volume V, that are considered as planar, rotationally invariant (disc-shaped) features with normals n and surface area S, S i jkl is given by S i jkl = 1 4 (δ ikα jl + δ il α jk + δ jk α il + δ jl α ik )+β i jkl, (2) where δ i j is the Kronecker delta, and the second and fourth rank tensors α i j and β i jkl are given by α i j = 1 B T V n i n j S β i jkl = 1 (B N V B T )n i n j n k n l S, (3) where B N and B T characterise the normal and tangential compliances across an individual discontinuity surface. A number of authors (e.g., Grechka and Kachanov, 2006; Hall et al., 2007; Verdon et al., 2008) show that for most rocks β i jkl can be ignored. In this limit, any discontinuity distribution is assessed only by the contribution to the 3 diagonal components of α, and hence can be represented by 3 mutually orthogonal sets of aligned microcracks. Hence, from equations (1), (2) and (3), we can derive the overall stiffness of a rock from the compliance of the background material and the number density of sets of microcracks. Assuming that the changes in stress are not of sufficient magnitude to cause phase changes or cataclastic collapse, which might affect the background matri, the response of seismic velocities to stress can be considered soley by assessing the response to stress of sets of aligned microcracks.

2 Effects of stress on crack density Following the approach of Tod (2002), van der Neut et al. (2007) derive an equation for the number density of aligned cracks deforming elastically under an applied stress, where ε(σ) = ε 0 ep( c r σ c(n) ), (4) c r = and σ c(n) is the crack normal stress, given by 2(1 ν) πµa 0, (5) σ c(n) = σ i j n i n j P f l. (6) Geomechanics and seismics Sample Crack set a 0 ε 0 α α α α α α Table 1: Best fit initial average aspect ratios (a 0 ) and number densities (ε 0 ) used to calculate the velocities as a function of stress shown in Figure 1. P f l is the pore fluid pressure, µ and ν are the shear modulus and Poisson s ratio of the background matri material, and ε 0 and a 0 are respectively the number density and aspect ratio at a defined initial pressure (usually 0 MPa). As discussed in the previous section, we treat the overall microcrack distribution as three mutually orthogonal aligned sets, each contributing to one of the diagonal components of α. For each set, an initial number density and aspect ratio is defined. Hence, for any stress field, α is calculated using equations (4) to (6) to give α i j = 1 h ε 1(σ c(n 1) ) ε 2 (σ c(n 2) ) ε 3 (σ c(n 3) ), (7) where h is the normalisation parameter given by Gueguen and Schubnel (2003). We have developed an procedure to invert these parameters from anisotropic ultrasonic velocity measurements. An eample is shown in Figure 1 for two sanstone samples taken from a UKCS reservoir. (Kendall et al., 2007). The best fit parameters we find are shown in Table a , which is a reasonable value to be epected for a distribution of flat, pennny shaped cracks (Kuster and Toksoz, 1974). Sample 1909 is a clean sandstone with little anisotropy, and so we find little difference between the discontinuity number densities. However, sample 1784 contains a significant amount of aligned, platy mica grains. The aligned grains lead to the development of anisotropy, and as a result we predict that the number density of features aligned horizontally (normal to the 3 ais) greater than those orientated vertically. The results from Figure 1 and Table 1 indicate that the nonlinear elastic behaviour of a rock can be modelled based on the assumption that it is made up of stiff, nondeforming mineral grains and displacement discontinuities in the form of flat, disc-shaped cracks with physically reasonable initial aspect ratio distributions. Calibration In order that our model be of use when linking with geomechanical model, we seek rules of thumb that can be applied to aid the population of seismic models. With this in mind, we have performed this inversion for approimately 200 samples from the literature. The results of our inversion - initial aspect ratio and density - are shown in Figure 2. We observe that, with the eception of shales, the initial aspect ratios are remarkably consistent both within and between lithologies. This greatly increases our confidence in this model Velocity (m/s) Velocity (m/s) Average aspect ratio Pressure (MPa) (a) Pressure (MPa) Figure 1: Observed velocity measurements (symbols) and velocities calculated using the rock physics model (red=v P, blue=v Py, green=v Pz, cyan=v Sy, magenta=v Sz, yellow=v Syz ). (b) Crack density Carbonate Anhydrite Conglomerate Sandstone Tight gas sandstone Shale Figure 2: Initial aspect ratio and number density for a range of literature rock samples. The fit between observed and modelled velocities is reasonable. Furthermore, the initial aspect ratios are found to be There is some variation in initial number density. We find that the initial discontinuity number density can be considered as

3 Geomechanics and seismics an indication of how well consolidated and/or damaged a sample is. For instance, we find that, where damage has been intentionally caused to a sample by either thermal effects (e.g., MacBeth and Schuett, 2007), or deviatoric stresses (e.g., King, 2002), initial aspect ratios remain unchanged whilst initial discontinuity number density is found to increase. The treatment of anisotropy and core damage serve as an indication of how we might interpret the physical meaning of crack density and aspect ratio. We note at this point that these terms have been developed as theoretical parameters to model stress dependent elasticity. However, they do appear to have a correlation, if only in a qualitative sense, with physical observations such as alignment of elongate or platy grains, or the degree of damage done to a sample. This correlation strengthens our confidence in the conceptual validity of the microstructural approach for modeling nonlinear stress dependent velocities. We now show a how this model can be applied to predict seismic observables from a simple geomechanical model. GEOMECHANICAL MODELING In this section we outline how this approach can be used to model seismic observables based on geomechanical models. The model we have chosen to build is simple in its geometry, consisting of a rectangular sandstone reservoir of dimensions 75m, surrounded by a shale over- and sideburden. The grid is densest in the reservoir region, with block size in the and y directions of m, and 15m in the z direction, becoming coarser away from the reservoir. Ths is a quarter symmetry model, using symmetry arguments to model a larger reservoir without increasing computational time. In order to simulate a CO 2 injection scenario, a vertical well injecting at a constant rate of sm 3 /day is placed at the corner of the reservoir (representing the centre of the quarter symmetry reservoir that we are modelling). We note at this stage that this model has been developed principally to demonstrate proof of concept and is probably too simplified to accurately represent a realistic scenario. The fluid flow component of our model was simulated with a commercial reservoir simulator (MORE). This is coupled to a finite element geomechanical solver (ELFEN, developed by Rockfield Ltd). The geomechanical and fluid-flow elements are coupled using the loose coupling procedure described by Minkoff et al. (2004), where at each time step the changes in pore pressure caused by fluid flow are passed via an MPI to the geomechanical solver. The geomechanical solver computes the deformation caused by a pore pressure change, and any changes in porosity and permeability are passed back to update the fluid flow simulation. At each timestep our simulation outputs information about stress and strain in the overburden and reservoir, porosity, and changes in fluid saturation. We use this information to compute seismic properties using the method outlined above. Results Figure 3 shows the changes in travel time for a vertically propagating P-wave reflecting off the top of the reservoir at the end of the injection period (7 years). At the edges of our model there has been no significant change, hence these regions are representative of initial conditions. Note that these waves travel only in the overburden, so will not be affected by processes occuring within the reservoir, where there are larger effective stress changes, and also fluid substitution effects. However, we still predict a significant ( 3-4ms) change in travel time above the centre of the reservoir, decreasing towards the sides, caused by stress transfer into the overburden. Y y Travel time (s) X Figure 3: Travel time for a P-wave reflected from the top of the reservoir after 7 years of injection. The reservoir etends from 0 to in both the and y directions, with injection at = y = 0. Shear wave splitting Figure 4: Shear wave splitting for an S-wave propagating vertically through the reservoir at the end of the injection period. The ticks indicate the orientation of the fast shear wave, the length of ticks and the contours indicate the magnitude of splitting Shear wave splitting is caused by seismic anisotropy, causing S-waves to be split into orthogonally polarized fast and slow waves. It may be caused by alignment of mineral fabrics, the presence of fractures, or, as in this case, non-hydrostatic stresses. Figure 4 shows the splitting patterns caused by stress

4 changes during injection. Initially, stresses in the and y directions are equal, and no splitting occurs. As injection continues, non-hydrostatic stresses are focused at the edges of the reservoir, leading to the development of anisotropy and shear wave splitting. In the centre of the reservoir, stress changes are approimately hydrostatic, so no splitting develops. Despite the simplicity of this model, it neatly demonstrates how geomechanical deformation can lead to changes in seismic observables. In order to assess the risk that stress changes caused by CO 2 injection will lead to deformation and loss of integrity of the caprock, modeling of this nature combined with seismic observations will be crucial. Geomechanics and seismics CONCLUSIONS A simple geomechanical model has been developed to model CO 2 injection into the subsurface. By coupling fluid-flow simulation with a finite element geomechanical solver we can predict how injection will affect the stress and strain field both within and without the reservoir. In order to relate deformation with changes in seismic observables, we develop a microstructural rock physics model. This model is relatively simple to use, and, having calibrated with 200 literature samples, is shown to be easy to parameterise and physically intuitive. However, this simplicity does not cost us the ability to consider the effects of nonlinearity and non-hydrostatic stresses. The geomechanical model shown here is simple in nature and as such is limited in its applicability to real-world situations. 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 CO 2 injection, and how we can predict the typical seismic signature of such deformation, allowing us to assess which seismic techniques will be te most useful in distinguishing stress effects from fluid substitution effects. Two such observations - overburden travel time and shear wave splitting - are demonstrated here. Where there is a risk that geomechanical deformation could lead to CO 2 leakage, modeling of this type must be considered requisite for CO 2 sequestration to develop into a viable emissions reduction technology. Acknowledgments This work was completed as part of the IPEGG project. The authors would like to thank the IPEGG sponsors and partners. James Verdon was sponsored by a UKERC interdisciplinary studentship.

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