Correspondence author: Viktoriya M. Yarushina, Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT, 06520-8109, USA. (email@example.com)
 The seismic safety of current technologies for CO2 sequestration has been questioned in several recent publications and whitepapers. While there is a definite risk from unbalanced subsurface fluid injection because of hydraulic fracturing, we propose a simple model to demonstrate that mineral carbonation in mafic rocks can mitigate seismic risk. In particular, mineral precipitation will increase the solid grain-grain contact area, which reduces the effective fluid pressure, distributes the deviatoric stress load, and increases frictional contact. Thus, mineral sequestration can potentially reduce seismic risk provided fluid pumping rates do not exceed a critical value.
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 The recent analyses of Zoback and Gorelick  and the US National Research Council [NRC, 2012] raised concerns about the safety of current subsurface CO2 sequestration technologies, in particular over the risk of earthquake triggering due to fluid injection. Induced seismicity is a well-known effect of hydraulic fracturing—technology widely used for waste-water storage and enhanced hydrocarbon recovery [NRC, 2012]. However, as stated in the report [NRC, 2012], injection of wastewater poses a higher seismic risk than hydraulic fracturing itself. In particular, hydraulic fracturing operations are designed to balance fluid injection and withdrawal. However, during CO2 injection, no such balance is maintained, and this can lead to significant increases in fluid pressure even to the point of fracturing [Rutqvist and Tsang, 2002; Rutqvist et al., 2008]. These findings therefore raise concerns for the future of carbon capture that involves long-term subsurface storage of large volumes of aqueous solution of CO2 and supercritical CO2 under high pressure.
 However, CO2 (both supercritical and in solution) also can react with silicate minerals, dissolving the original minerals and precipitating carbonate reaction products along the flow path. Mineral trapping of CO2 in mafic and ultramafic rocks due to carbonation reactions was proposed as an option for permanent CO2 capture, with reduced risk of CO2 leakage back into the atmosphere [e.g., Kelemen et al., 2011]. Carbonation reactions significantly increase solid volume while consuming fluids, and this process can alter the pore pressure and stress state at the injection site [e.g., see Kelemen and Hirth, 2012]. This effect therefore introduces significant uncertainties in assessing the seismic risk of fluid injection. In this communication, we propose a simple conceptual model with which to study the effect of carbonation reactions on the mechanical failure of host rock and earthquake triggering during CO2 injection.
2 Mathematical Model
 A simple model of the change in local stress state during CO2 injection can be constructed by assuming that the host rock is composed of identical spherical grains as shown in Figure 1. All grains are composed of a reactive mafic rock such as basalt or peridotite. The pore space is filled with fluid such as supercritical CO2 or a carbonic acid aqueous solution. The overburden presses grains together resulting in local stresses at the grain contacts. Pore pressure is assumed to rapidly equilibrate at the initial pumping stages so that there is no gradient in pore pressure. The system is well confined between an overlying, low-permeability caprock and underlying basement rock so that the total volume of the target rock formation does not change. We employ this simplifying assumption since the precise pore geometry during carbonation reactions is still a topic of ongoing research [Emmanuel et al., 2010; Olsson et al., 2012].
 The confining and shear stresses in the host rock induce local normal and shear stresses and at grain-grain contacts. The magnitude of these local stresses depends on the imposed global stresses as well as on the precipitation and growth of mineral grains during the carbonation reaction. The reaction progress can be modeled by considering the evolution of a mineral grain of size R (or equivalently minerals with a mean grain size R) with growth-rate (in cm/s),
where b is the reference grain size, k is the reaction rate parameter (in cm/s), which is related to the product of the measured specific reaction rate (in mol/(cm2 s)), and the mineral molar volume (in cm3/mol). The factor in equation (1) slows down the reaction kinetics with time for n > 0, as commonly observed in experiments [Kelemen et al., 2011] even though k has the same value for all n.
 In a simple cubic packing of spheres (Figure 1), the total stress applied to an external boundary is compensated by both local stresses at grain contacts and fluid pressures. Considering a small representative volume with a single grain (Figure 1b), the total normal stress σn applied over the area 4a2 must be balanced by the sum of the local stress at the grain-grain contact of area π(R2 − a2) and the fluid pressure pf distributed over the area 4a2 − π(R2 − a2). The force balance between the applied and contact stresses requires that
for normal and shear stresses, respectively. Here, a is the original unreacted grain size, τ is the global shear stress, and is the local shear stress. Normal stresses are assumed to be positive in compression, shear-stresses positive if inducing counterclockwise torques. In this case, the carbonation reaction affects grain radius R, which alters the local contact stresses and . The contact area between two grains cannot exceed the contact between unit cells, i.e., π(R2 − a2) ≤ 4a2 which is considered as the limiting condition on growth of R. Brittle failure and seismic slip occur when local stresses at the grain contacts satisfy the Mohr-Coulomb friction law:
where c is cohesion and μ is the friction coefficient, which lies in the range μ = 0.6 − 0.9 for most rocks [Byerlee, 1978].
3 Discussion and Results
 Several scenarios are investigated using equations (1)-(3) with various reaction rates and stress states to assess the possibility of induced seismicity during fluid injection. Results are presented via Mohr diagrams of normal versus shear stress. The local stress state in equation (2) is represented as a Mohr circle in which the minimum and maximum shear stress are assumed to be ± in this case, the center of each circle is the point and its radius is The failure envelope (equation (3)) is as usual depicted as a straight line with a slope μ, and the initial stress state of the injection site is assumed to be below the failure line. During fluid injection, the pore pressure increases monotonically, so that
where Q is assumed positive. The rate of fluid mass injection dm/dt into a fixed volume V0 is related to the rate of pressure increase according to (for constant Q) where K and ρ are the bulk modulus and density of injected fluid. Using water (ρ = 1 g/cm3, and K = 2.2 GPa), the conversion from Q to dm/dt is approximately 0.45 kg/MPa per unit volume.
 The rate of carbonation reaction is important for assessing seismic risk during CO2 injection. In our calculations, we use experimental data on magnesite precipitation that suggest k = 10–13–10–10 cm/s at neutral to alkaline conditions and 100–200 °C, and saturation with respect to magnesite 3.4–67.2 [Saldi et al., 2012]. We consider cases with both fast carbonation reactions that progress on the time scale of fluid injection, and with slow reactions that continue for several years after fluid pumping ceases. We also examine various initial shear-stress states that place the sample at different proximities to the failure envelope. In all calculations, we assume that the initial fluid pressure is 16 MPa and lithostatic stress σn = 35 MPa. For these sample cases, we assume Q is constant. This corresponds to an injection at 1.2 km depth into rock with an average density of 2.95 g/cm3 saturated with slightly over-pressured fluid with density of 1.02 g/cm3. We assume average initial and reference grain sizes of a = b = 1 mm, cohesion c = 0, and friction coefficient μ = 0.6. The reaction rates for our first tests are assumed constant with time so that n = 0, although other values of n are tested below.
 Subsurface fluid injection changes the local stress state by increasing pf, decreasing the normal stress , and shifting the Mohr circles towards the failure line (Figure 2). If injection proceeds without carbonation reactions, the Mohr circle reaches the failure line and seismic triggering is expected. The exact timing of a seismic event depends on the magnitude of the initial shear stress (Figures 2a, 2d, and 2g). For a shear stress of τ = 6 MPa, failure occurs in about 12.4 years (Figure 2d). However, mineral carbonation increases the contact area between the neighboring grains, reducing both the local normal and shear stresses simultaneously. As a result, the Mohr circles shrink as they move leftward, and thus take longer to reach the failure envelope.
 For the slowest reaction rate and the same initial stress as for the 12.4-year event, seismic triggering is induced in 13.5 years (Figure 2e). However, for lower initial shear stress, the seismic risk might be completely avoided during the entire injection sequence, even for slow reaction rates (Figure 2b). Analysis of the grain radius, fluid pressure, and contact stresses corresponding to this low stress case (Figure 3) shows that the most active reduction in stresses occurs during injection (first 35.9 years). However, after the injection ceases, carbonation continues to reduce the contact stresses and increases the grain radius, thus migrating the Mohr circles away from the failure line. Therefore, if the seismic event is not triggered during active stages of pumping, it will not occur afterwards.
 For the fastest reactions that proceed on the injection time scale, seismic risk is completely eliminated for low to moderate initial shear stresses (Figures 2c and 2f) and extensively delayed for high shear stresses (Figure 2i). However, sites with high initial shear stresses (e.g., in tectonically active environments) are poor candidates for CO2 injection. In all considered cases, seismic triggering is expected at the early stages of injection if reactions do not have sufficient time to reduce contact stresses. At the higher reaction rates, mineral precipitates fill all available pore space within 35.9 years, after which both reactions and pumping stop. Unless reactive cracking can occur [Kelemen and Hirth, 2012], further injection is only possible with active hydraulic fracturing to open new pore space and reacting surfaces.
 In the examples presented above, the reaction rate is assumed constant with time, i.e., n = 0 in equation (1). Deceleration of the reaction (with n > 0) slightly alters the evolution of the stress state and leads to different time scales for pore clogging (Figure 4). The timing for a seismic event depends modestly on n, decreasing only fractionally for every unit increase in n (Figure 5).
 In order to assess the possibility of seismic triggering, we determine a critical pumping rate below which seismic risk can be avoided. Since the pumping rate can be controlled to avoid failure, here we allow Q to be a function of time. Failure leading to a seismic event first occurs when the failure line is tangent to the Mohr circle, which is given by the condition
 Substituting equations (2) and (4) into equation (5), we obtain an equation for the critical pumping rate Q at which one can just avoid seismic triggering (Figure 6)
 The solution for the critical pumping rate Qc is an analytical function of t (since the solution to equation (1) is Rn + 1 = an + 1 + bn(n + 1)k t). The critical pumping rate must first decrease with time to avoid failure before mineral growth is significant (i.e., while R ≈ a), but then can increase once the reaction expands the grain-grain contact area (Figure 6a). The critical pumping rate depends on the exponent n, which governs how the reaction decelerates as grains grow; in particular, the larger the value of n, the lower the pumping rate must be to avoid seismic risk. For constant pumping (as in Figure 2), seismic risk would be avoided if Q is below the minimum critical pumping rate min(Qc) (Figure 6a), which is necessarily also a function of n (Figure 6b).
 Many factors outside the scope of our model potentially influence the actual stress state in the reservoir. In particular, we have neglected fluid diffusion into the host rock (which reduces fluid pressure) and large-scale stress inhomogeneity (which corresponds to larger shear stresses). Changes in rock and fluid densities also alter the stress state in rocks. Rheological changes (such as in rock strength and creep processes) associated with carbonation or even hydration will also influence the response to stress. Reaction rates likely depend on pressure, temperature, and lithology, although we have tried to cover a wide range of rates. While these effects might be important for assessing the precise risk of induced seismicity, they are second-order complexities relative to the dominant effects considered in the present communication. In the end, mineral carbon sequestration might not only provide the best options for permanent carbon storage, but also one that likely mitigates the risk of earthquake triggering.
 The authors thank two anonymous reviewers for their helpful comments and are grateful to Edward Bolton, Jay Ague, and Zhengrong Wang for advice on reaction kinetics. This work was supported in part by a grant (DE-FE0004375) from the National Energy Technology Laboratory of US Department of Energy.