The basic principle of induced seismicity is that the pressure buildup caused by fluid injection reduces the effective stresses, which brings the stress state closer to failure (Fig. 1). If failure conditions are reached, the elastic energy stored in the rock mass is released and a (micro)seismic event is induced. Failure in geomaterials can occur either in tensile or shear mode (Jaeger et al., 2009). While tensile failure induces microseismic events of such low magnitude that they cannot be felt on the ground surface, shear failure may lead to perceivable earthquakes if a sufficiently large area of a pre-existing discontinuity, i.e., a fracture or fault, is reactivated. Nevertheless, in the cases in which tensile failure is sought, i.e., to create hydraulic fractures to enhance rock permeability, shear failure of pre-existing faults may also occur if they become pressurized during the hydraulic fracturing operations. In such a situation, perceivable earthquakes associated with hydraulic fracturing operations may occur (Rubinstein and Mahani, 2015). For example, a perceivable earthquake occurred at the Preese Hall 1 exploration well for shale gas near Blackpool, UK, during hydraulic fracturing because a pre-existing nearby fault was reactivated (Clarke et al., 2014).

Figure 1(a) Initial stress state of a fracture or fault of arbitrary orientation with respect to the far-field effective stress and (b)  Mohr circles showing how the reduction in effective stresses as a result of pressure buildup, ΔP, may induce shear failure in pre-existing discontinuities, i.e., fractures or faults. ${\mathit{\sigma }}_{\mathrm{1}}^{\prime }$ and ${\mathit{\sigma }}_{\mathrm{3}}^{\prime }$ are the maximum and minimum principal effective stresses, respectively, τ is tangential stress, ${\mathit{\sigma }}_{\mathrm{n}}^{\prime }$ is normal effective stress to the fracture or fault, and μ is the friction coefficient. The failure surface has been plotted by considering the nonlinear failure criterion (Barton, 1976).

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In principle, fluid pressure buildup may seem the only mechanism that induces seismicity. Thus, intuition suggests that stability should improve in the vicinity of the injection well after injection is stopped because fluid pressure drops rapidly. Far away from the injection well, fluid pressure continues to rise and thus pressure diffusion could explain continued post-injection induced seismicity (Hsieh and Bredehoeft, 1981), which is often observed after stimulation of EGS (Parotidis et al., 2004). However, pressure diffusion cannot explain why the magnitude of post-injection seismicity is often higher than that induced during injection, e.g., at Basel, Switzerland (Deichmann and Giardini, 2009), at Soultz-sous-Forêts, France (Evans et al., 2005), and at Castor, Spain (Gaite et al., 2016). Even though this high-magnitude post-injection seismicity has not been observed in geologic carbon storage projects, its causes should be understood to prevent it. The counterintuitive occurrence of high-magnitude post-injection-induced seismicity may be explained by the fact that fluid injection in the subsurface involves coupled processes that are more complex than just the hydraulic effect:

• The stress state changes in response to pore pressure variations (Streit and Hillis, 2004; Rutqvist, 2012). Specifically, the total stress increases in the direction of flow due to the lateral confinement that opposes the expansion of the rock in this direction (Zareidarmiyan et al., 2018). This poro-mechanical effect modifies the initial stress state and thus the analysis of fault stability cannot be performed as a simple subtraction of the pressure buildup from the initial effective stress state;

• The injected CO₂ usually reaches the injection depth at a colder temperature than that of the rock because CO₂ does not reach thermal equilibrium with the geothermal gradient along its way down the well (Paterson et al., 2008). As a result, the storage formation cools down around the injection well, inducing a thermal stress reduction that brings the stress state closer to failure conditions (Vilarrasa and Rutqvist, 2017). The magnitude of induced thermal stresses is proportional to the rock stiffness. Thus, induced thermal stresses depend on the rock type in which fluid is injected, becoming larger in reservoir rocks than in clay-rich caprocks because reservoirs are usually stiffer (Vilarrasa and Makhnenko, 2017);

• The stress changes that arise in the storage formation and the caprock as a result of pressure buildup and cooling vary depending on the rock properties and the contrast between geological layers (Verdon et al., 2011);

• Each (micro)seismic event provokes a stress redistribution around the portion of the fracture or fault that undergoes shear slip (Okada, 1992). This stress transfer controls the distribution of aftershocks in natural seismicity (King et al., 1994) and may be the reason for observed rotations in the direction of the sheared faults in sequences of induced seismicity during stimulation of EGS (De Simone et al., 2017b);

• Not all the shear slip occurring in fractures or faults induces seismic events. Actually, shear slip may occur aseismically (Cornet et al., 1997). This aseismic slip may induce (micro)seismic events away from the slipped surface (Guglielmi et al., 2015);

• Geochemical reactions may alter the frictional strength of faults, which could lead to failure conditions if a fault is weakened;

• Heterogeneity in the rock type, strength of faults and the stress field, which may present local variations around faults (Faulkner et al., 2006), affect fault stability.

All these potential triggering mechanisms are usually neglected because pressure diffusion is considered sufficient to explain induced seismicity. Though pore pressure diffusion alone may explain certain sequences of induced events (Shapiro et al., 2002), seismic sequences are usually more complex and imply a combination of several coupled processes. For example, cooling-induced stresses resulting from CO₂ entering the storage formation 45 ^∘C colder than the rock may explain part of the microseismicity detected at In Salah, Algeria (Vilarrasa et al., 2015). Another example is Weyburn, Canada, where the scarce microseismic events (around 200) that were induced in the caprock at the beginning of injection were interpreted to be caused by stress changes resulting from the contrast in stiffness between the reservoir and caprock (Verdon et al., 2011). Thus, when assessing the potential for induced (micro)seismicity of CO₂ storage projects, all these coupled processes should be considered (Fig. 2).

Figure 2Schematic representation of several coupled effects on fracture and/or fault stability. Pressure buildup, ΔP, decreases the effective stresses and may cause poro-mechanical stresses that change the size of the Mohr circle; cooling, −ΔT, induces thermal stress reduction; seismic and aseismic shear slip and interactions between geological layers with different rock properties produce total stress changes; and geochemical reactions may alter the strength of fractures and/or faults.

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A careful examination of the subsurface stress state reveals that crystalline rocks accumulate more stress than sedimentary rocks as a result of tectonics (Vilarrasa and Carrera, 2015). The dependence of the stress state on the rock type reflects the contrast in the rock stiffness. Since crystalline rocks are much stiffer than sedimentary rocks, stresses induced by tectonics mainly accumulate in the crystalline basement. In contrast, the relatively soft sedimentary rocks deform without accumulating large stresses and as a result they do not usually become critically stressed. This is demonstrated in Table 1, which displays the estimated stress state at several CO₂ storage sites with the corresponding mobilized friction coefficient, ${\mathit{\mu }}_{\mathrm{mob}}=\tan {\mathit{\varphi }}_{\mathrm{mob}}^{\prime }$, where ${\mathit{\varphi }}_{\mathrm{mob}}^{\prime }$ is the mobilized friction angle. ${\mathit{\varphi }}_{\mathrm{mob}}^{\prime }$ is the angle that forms the tangent to the Mohr circle assuming no cohesion. Thus, if the mobilized friction coefficient is lower than the actual friction coefficient, which is generally equal to 0.6 (Barton, 1976), the rock is not critically stressed. Interestingly, the mobilized friction coefficient is lower than 0.6 for all the CO₂ storage sites included in Table 1. Since CO₂ will be stored in sedimentary basins, the less likely criticality of stress implies that a certain pressure buildup and cooling can be applied without reaching failure conditions. Yet, there may be cases of critically stressed sedimentary rocks, which may lead to unexpected seismicity if no stress measurements are performed. Therefore, mechanical characterization must be required at potential storage sites.

Table 1Stress state (maximum principal stress, σ₁; intermediate principal stress, σ₂; minimum principal stress, σ₃; and pore pressure, P) and mobilized friction coefficient (μ_mob) at several CO₂ injection sites.

References: ^a Morris et al. (2011). ^b White and Johnson (2009). ^c Nelson et al. (2006), Vidal-Gilbert et al. (2010). ^d Chiaramonte et al. (2013). ^e Kano et al. (2013). ^f Konstantinovskaya et al. (2012). ^g Bauer et al. (2016). ^h Lee et al. (2017)

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The stress state at each site should be measured in order to determine the maximum sustainable injection pressure and maximum cooling that would lead to a safe CO₂ storage (Rutqvist et al., 2007; Kim and Hosseini, 2014). Thus, stress measurements should be routinely performed during wellbore perforation, determining both the magnitude and orientation of the principal stresses (Cornet and Jianmin, 1995). The range of strikes and dips of potentially reactivated faults can be determined once the stress state is known (Morris et al., 1996). This exercise is crucial to identify faults that may induce large seismic events, to foresee an optimal design of the injection strategy and to define mitigation measures (e.g., Birkholzer et al., 2012; Buscheck et al., 2012; Dempsey et al., 2014) if induced seismicity is predicted to possibly occur above a predefined threshold.

The pressure evolution of CO₂ injection is favorable to achieve a long-term geomechanically stable situation. In contrast to water injection, which yields a linear increase in pressure with the logarithm of time when a continuous flow rate is injected (Theis, 1935), CO₂ leads to a peak at the beginning of injection followed by a relatively constant overpressure (Fig. 3). Thus, pressure evolution is relatively easy to control in CO₂ injection operations, which should help to minimize induced (micro)seismicity (Vilarrasa and Carrera, 2015). Such a pressure evolution has been observed in the field, at Ketzin, Germany (Henninges et al., 2011), numerically (e.g., Vilarrasa et al., 2010; Okwen et al., 2011) and analytically (Vilarrasa et al., 2013a).

Figure 3(a) CO₂ pressure evolution when injecting 1 Mt yr⁻¹ of CO₂ through a vertical well in a 100 m thick aquifer with an intrinsic permeability of 10⁻¹³ m² and a radius of 100 km; (b) the CO₂ plume shape at the beginning of injection, coinciding with the peak in injection pressure (see number 1 in panel a); and (c) the CO₂ plume once gravity override dominates and the capillary fringe has been developed, leading to a slight pressure drop (see number 2 in panel a). The color bar displaying the liquid saturation degree in (b) applies for both (b) and (c).

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The initial sharp increase in pore pressure is due not only to viscous forces opposing fluid displacement, but also to capillary forces caused by the desaturation around the injection well, which decreases the relative permeability to both CO₂ and water (Fig. 3b). However, once CO₂ fills the pores around the injection well (Fig. 3c), the CO₂ relative permeability rises. Additionally, since CO₂ viscosity is 1 order of magnitude lower than that of brine, CO₂ can flow easily inside the storage formation, which leads to a constant or even a slight drop in overpressure (Fig. 3a). This constant evolution of fluid pressure is maintained as long as the pressure perturbation does not reach a boundary. Once a boundary is reached, pressure will decrease in the presence of a constant pressure boundary and will increase in the presence of a low-permeability boundary. The pressure evolution shown in Fig. 3 is not affected by boundary effects because the pressure perturbation does not reach the outer boundary during the displayed injection time. This fluid pressure evolution induces the largest effective stress changes in the caprock at the beginning of injection, coinciding with the peak in pressure increase.

Maintaining the caprock integrity in the long term is favored by two effects that tend to decrease overpressure inside the storage formation: (1) CO₂ dissolution into the resident brine and (2) brine flow across the low-permeability formations that confine the storage formation, i.e., caprock and base rock (Vilarrasa and Carrera, 2015). On the one hand, when CO₂ dissolves into brine, fluid pressure decreases because the total fluid volume is reduced (Mathias et al., 2011a; Steele-MacInnis et al., 2012). As observed in natural analogues, the percentage of CO₂ that may eventually become trapped by dissolution can be as high as 90 % in carbonate storage formations (Gilfillan et al., 2009). In the short term, CO₂ dissolution can also be high in storage formations with high vertical permeability ($k>{\mathrm{10}}^{-\mathrm{13}}$ m²) because of the formation of gravity fingers induced by the unstable situation of having a fluid of a higher density, i.e., CO₂-rich brine, above a fluid of lower density, i.e., the resident brine (Riaz et al., 2006; Hidalgo and Carrera, 2009; Pau et al., 2010). On the other hand, caprock permeability at the field scale is 2 to 3 orders of magnitude larger than that at the core scale as a result of the presence of fractures and faults (Neuzil, 1994). Thus, resident brine of the storage formation can flow across the caprock and base rock, lowering the pressure buildup inside the storage formation. Though brine can flow through the caprock because single-phase flow is not hindered by capillarity, CO₂ cannot because of the high CO₂ entry pressure of clay-rich formations (Benson and Cole, 2008).

To quantify the flow across the caprock in the long term, let us assume a 100 m thick caprock with permeability of 10⁻¹⁸ m², water viscosity of $\mathrm{4}\times {\mathrm{10}}^{-\mathrm{4}}$ Pa s (assuming a temperature of 60 ^∘C) and a mean overpressure of 1 MPa distributed in a radial distance of 20 km. This scenario yields a flux across the caprock of $\mathrm{2.5}\times {\mathrm{10}}^{-\mathrm{11}}$ m s⁻¹ in an area of 1.26×10⁹ m². Thus, the flow rate across the caprock is 0.031 m³ s⁻¹, which is on the order of magnitude of industrial-scale injection rates (on the order of 0.05 m³ s⁻¹ for annual megatonne injection), effectively lowering the pressure increase inside the storage formation.

Figure 4(a) Model setup, (b) liquid saturation degree, (c) temperature distribution and (d) volumetric plastic strain after 2 years of injecting 0.2 Mt yr⁻¹ of CO₂ at 20 ^∘C through a vertical well. While panels (c) and (d) are plotted at the same scale, panel (b) is plotted at a smaller scale.

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In addition to pressure increase, thermal effects are also relevant in geologic carbon storage because temperature changes induce thermal stresses that affect fracture stability (Vilarrasa and Rutqvist, 2017). CO₂ reaches the bottom of the injection well at a temperature lower than that of the storage formation because CO₂ flow within the well is isenthalpic (Pruess, 2006) and thus it heats up at a lower rate than the geothermal gradient (Lu and Connell, 2008). As a result, the rock around injection wells cools down.

To illustrate the effect on fracture stability, we present the simulation results of cold CO₂ injection into a deep saline aquifer. Figure 4a displays the model setup with the initial and boundary conditions. The material properties are included in Table A1 in the Appendix. The advance of the cooling front with respect to the CO₂ plume is retarded because the rock has to be cooled down (compare Fig. 4b and c) (Bao et al., 2016; LaForce et al., 2015; De Simone et al., 2017a). Cooling mainly advances by advection in the reservoir, but it also extends into the lower portion of the caprock by conduction (Fig. 4c). The extent of the cooling region can become a few hundreds of meters after some decades of CO₂ injection at industrial-scale rates, i.e., megatonne injection (Vilarrasa et al., 2014). Thus, unless faults are present in the vicinity of the injection well, they will not be directly affected by cooling. Nevertheless, faults located far from the cooling region may undergo stability changes as a result of the contraction of the cooled rock, which causes changes in far-field stresses (Jeanne et al., 2014).

Figure 5Total stresses in the (a) vertical and (b) horizontal direction after 2 years of injecting 0.2 Mt yr⁻¹ of CO₂ at 20 ^∘C through a vertical well, indicating the sign of the induced stresses. Thermal stresses, Δσ_T, are proportional to the bulk modulus, K; the thermal expansion coefficient, α_T; and the temperature difference, ΔT. The changes in the Mohr circles at a point placed 25 m away from the injection well in (c) the reservoir (2 m below the reservoir–caprock interface) and (d) the caprock (2 m above the reservoir–caprock interface) are also represented.

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The cooling-induced rock contraction and thermal stress reduction shift the stress state towards shear failure conditions and, theoretically, tensile fractures could be formed if the tensile strength were reached (Luo and Bryant, 2010; Goodarzi et al., 2010, 2012; Gor et al., 2013). The temperature-induced stresses are not isotropic (Fig. 5); and thus the effect on fracture stability depends on the stress regime, i.e., normal faulting, strike–slip or reverse faulting (Vilarrasa, 2016). In general, fracture stability becomes more compromised in the reservoir than in the caprock, which may lead to injectivity enhancement while maintaining the caprock sealing capacity (Goodarzi et al., 2015; Vilarrasa et al., 2017c).

This favorable situation occurs especially in normal-faulting stress regimes (Vilarrasa et al., 2013c; Kim and Hosseini, 2015). Figure 5 displays how stress variations induced in the reservoir and caprock as a result of cooling affect fracture stability in a normal-faulting stress regime (i.e., vertical stress larger than horizontal stresses). Both the vertical and horizontal stresses decrease inside the reservoir within the cooled region. The stress reduction is proportional to the rock stiffness, the rock thermal expansion coefficient and the temperature change. The vertical stress reduction within the reservoir causes a disequilibrium in this direction because the overburden on top of the reservoir remains constant so that vertical stresses become smaller than the weight of the material above (Fig. 5a). Thus, to satisfy stress equilibrium and displacement compatibility, an arch effect develops to support the weight of the material above, leading to a reduction of horizontal stresses within the reservoir and an increase in the lower portion of the caprock (Fig. 5b). The net result of these stress changes is to (1) bring the reservoir towards shear failure conditions (the Mohr circles shifts to the left and increases in size, Fig. 5c) and (2) improve stability of the caprock by tightening it (the Mohr circle becomes smaller, Fig. 5d). This contrast in stability between the reservoir and the caprock is highlighted in Fig. 4d, which shows that plastic strain, i.e., strain that occurs because failure conditions have been reached, only takes place in the reservoir and not in the caprock (for details on the failure surface see Vilarrasa and Laloui, 2015).

The situation is slightly different in a reverse-faulting stress regime, where the vertical stress is the minimum principal stress (Vilarrasa, 2016). The cooling-induced increase in horizontal stress in the lower portion of the caprock causes the Mohr circle to increases in size (i.e., the deviatoric stress increases). Nevertheless, this increase is slight because of the high confinement in reverse-faulting stress regimes. Still, shear failure may occur as a result of cooling. Similarly, the deviatoric stress is maintained in a strike–slip stress regime (Vilarrasa, 2016), which may induce shear failure of pre-existing fractures, and thus induced microseismicity, in the cooled region of the caprock, as was likely the case at In Salah, Algeria (Vilarrasa et al., 2015). These results highlight again the importance of characterizing the stress state.

The simulation results shown in Figs. 4 and 5 consider that the thermal expansion coefficient of the storage formation and the caprock are equal. Despite the limited range of the values that the thermal expansion coefficient can take in geomaterials, its magnitude will generally vary between the two formations. Different thermal expansion coefficients between the storage formation and the caprock lead to differential expansion of the rock, building up shear stress in the interface between the two layers. When the thermal expansion coefficient of the caprock is greater than that of the storage formation, deviatoric plastic strain may occur in the lower portion of the caprock as a result of cooling (Vilarrasa and Laloui, 2016). Nonetheless, regardless of the stress regime and the relative values of the thermal expansion coefficient between the storage formation and the caprock, the overall sealing capacity of the caprock is not compromised because only the lower portion of the caprock is affected by cooling and the subsequent stress changes.

Shear slip of faults induces static stress transfer, decreasing stability in some regions – where seismicity rate increases – and increasing stability in others – the so-called stress shadows – where seismicity rate decreases or is even suppressed (Harris and Simpson, 1998). Static stress transfer resulting from induced earthquakes has been found to be relevant for explaining post-injection events in EGS stimulations (Schoenball et al., 2012; De Simone et al., 2017b). The stress transfer causes rotation of the stress tensor, changing the orientation of the faults that are critically oriented to undergo shear failure. Such a change in the orientation of the faults that rupture during water injection and after shut-in was observed at the EGS Basel Deep Heat Mining Project (Deichmann et al., 2014).

Shear slip does not need to be seismic in order to induce stress transfer. Actually, aseismic slip has been reported to indirectly induce seismicity in non-pressurized fault patches (Cappa et al., 2019). The capacity of injection-induced aseismic slip for bringing to failure zones of faults that are not pressurized has been measured in decameter-scale rock laboratories (Guglielmi et al., 2015; Duboeuf et al., 2017). The magnitude of the induced microseismicity in these field experiments is small, on the order of −3.5 (Duboeuf et al., 2017). However, magnitudes may become large in industrial operations if aseismic slip stresses faults below the injection formation. For example, induced earthquakes with a magnitude of up to 5 were triggered close to a geothermal plant at Brawley, California, USA (Wei et al., 2015). The accumulated aseismic slip inducing these earthquakes was estimated to be some 60 cm, nucleating the earthquakes 5 km below the injection formation.

Both seismic and aseismic slip induce stress transfer that affects fracture and fault stability and may induce (micro)seismicity. This effect has been widely studied in natural seismicity, but has received relatively little attention in induced seismicity. Nonetheless, recent studies show that it is a non-negligible effect, which is relevant in post-injection seismicity and for explaining induced events in non-pressurized regions (De Simone et al., 2017b; Cappa et al., 2019). Thus, even though microseismicity induced by shear slip stress transfer has not been observed to date at geologic carbon storage sites, it should be considered a potential triggering mechanism.

The dissolution of CO₂ into the resident brine forms an acidic solution that has the potential of dissolving minerals, which in turn may lead to subsequent precipitation of other minerals (Zhang et al., 2009). The fastest geochemical reactions occur in carbonate rocks and in rocks with carbonate-rich cement (Vilarrasa et al., 2019). Carbonate minerals dissolve when they interact with the acidic CO₂-rich brine, leading to porosity and permeability increase (Alam et al., 2014). The porosity increase leads to a reduction in rock stiffness and strength, which has been measured in the laboratory to be on the order of 20 %–30 % (Bemer and Lombard, 2010; Vialle and Vanorio, 2011; Vanorio et al., 2011; Kim et al., 2018). The measured changes become smaller for increasing confining pressure (Vanorio et al., 2011) because the higher the confinement, the lower the porosity and the available reactive surface and, thus, the reaction rate. The reduction in rock stiffness affects the strain and stress induced by CO₂ injection and the reduction in strength may cause failure of initially stable fractures and faults (recall Fig. 2), leading to induced microseismicity. Thus, the changes in geomechanical properties of rocks (especially carbonate-rich rocks) as a result of CO₂–brine–rock geochemical interactions should be evaluated in the laboratory in order to properly assess the induced microseismicity potential.

Caprocks are also affected to some extent by geochemical reactions. Carbonate and feldspar minerals dissolve in shale, leading to precipitation of other carbonate minerals (Yu et al., 2012). But the overall response of caprocks depends on the rock type. While certain caprocks undergo permeability increase due to interaction with CO₂ (Olabode and Radonjic, 2014), others present a self-sealing response to CO₂ flow due to porosity decrease (Espinoza and Santamarina, 2012) or fracture clogging (Noiriel et al., 2007). Nevertheless, CO₂ is only expected to penetrate a short distance, if any, into the caprock because of its high entry pressure, which prevents upwards CO₂ flow (Busch et al., 2008).

For other types of host rock, laboratory studies have shown that geochemically induced changes in the geomechanical properties are in general minor (Rohmer et al., 2016). This minor effect has also been observed in fault gouges that have been exposed to acidic conditions for a long period in natural CO₂ reservoirs (Bakker et al., 2016). In summary, there is no evidence to expect significant alteration of geomechanical properties induced by geochemical reactions in general, but (1) the issue should not be abandoned and (2) it should receive special attention and site-specific studies in carbonate-rich rocks.

Faults are present at all scales and have been observed to play a role in CO₂ storage projects (e.g., Vidal-Gilbert et al., 2010; Rutqvist, 2012; Castelletto et al., 2013b). To name a few, (i) a fault or fractured rock zone opened as a result of pressure increase at In Salah, Algeria, leading to a double-lobe pattern of uplift on the ground (Vasco et al., 2010; Rinaldi and Rutqvist, 2013); (ii) the storage formation at Snøhvit, Norway, was surrounded by low-permeability faults, which limited its storage capacity (Hansen et al., 2013; Chiaramonte et al., 2015); (iii) the Spanish pilot test site at Hontomín contained several minor faults within a few hundred meters from the injection well (Alcalde et al., 2013, 2014); and (iv) the pilot test site at Heletz, Israel, is placed in an anticline crossed by two faults, confining the storage formation to be a few hundred meters wide (Figueiredo et al., 2015). The nature of these faults, i.e., flow barriers or conduits (Caine et al., 1996), controls the stress changes occurring around the fault and thus fault stability (Vilarrasa et al., 2016). Low-permeability faults may lead to the premature closure of storage sites because of pressure limitations on the storage capacity of the formation (Szulczewski et al., 2012). Actually, if multiple low-permeability faults are present and intersecting each other, they will lead to a compartmentalized reservoir (Castelletto et al., 2013a). In such cases, pressure would increase linearly with time (Zhou et al., 2008; Mathias et al., 2011b), increasing injection costs and eventually leading to fault reactivation, and thus induced seismicity, if injection were maintained (Cappa and Rutqvist, 2011a; Pereira et al., 2014; Rutqvist et al., 2016).

Changes in fault permeability due to its reactivation depend on the type of material. Fault reactivation may enhance fault permeability in hard rocks due to dilatancy by 1 to 2 orders of magnitude (Cappa and Rutqvist, 2011b; Guglielmi et al., 2015). This permeability increase raises the question of whether fault reactivation may lead to CO₂ leakage. Such an assessment must be made site specific, taking into account the hydro-mechanical properties of the rock and faults. Nonetheless, in general, faults crossing sequences of reservoirs and caprocks maintain a low permeability, at least, in the sections that cross caprocks as a result of the high clay content of the fault (Takahashi, 2003; Egholm et al., 2008). But more importantly, the CO₂ entry pressure of the fault remains high in the caprock sections (Vilarrasa and Makhnenko, 2017), hindering upwards CO₂ leakage, as observed in numerical simulations that incorporate fault heterogeneity (Rinaldi et al., 2014). Additionally, the stress state of the upper crust, which is characterized by a critically stressed crystalline basement overlaid by generally noncritically stressed sedimentary rock (recall Sect. 3), favors nucleation of the largest seismic events in the crystalline basement rather than in the sedimentary rock where CO₂ is stored. This hypocenter distribution has been observed in the central USA as a result of wastewater injection in the basal aquifer, which is consistent with permeability enhancement below the storage formation but not in the caprock and above, which limits the risk of CO₂ leakage (Verdon, 2014).

Figure 6(a) Geological setting in a normal-faulting stress regime (plane strain model), including a low-permeability fault that leads to (b) reservoir pressurization, ΔP, and (c)  horizontal total stress changes in the in-plane direction, Δσ_x, when CO₂ is injected in the hanging wall at a rate of $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{3}}$ $\mathrm{kg}{\mathrm{s}}^{-\mathrm{1}}{\mathrm{m}}^{-\mathrm{1}}$ for 1 year.

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Apart from CO₂ leakage, the magnitude of potential induced earthquakes is a concern because of the damage and fear that they could generate. The magnitude of earthquakes, M, is proportional to the rock shear modulus, the rupture area and the mean shear slip (Stekettee, 1958). Thus, the magnitude is controlled by the pressurized area of the fault. In this way, the orientation of the injection well affects the magnitude of potential induced seismicity because wells that are parallel to strata pressurize a larger area than vertical wells, but take a longer time to exceed the critical pressure at the fault (Rinaldi et al., 2015). The magnitude of induced seismic events is also controlled by the brittleness of the fault. While brittle faults with a slip-weakening behavior can induce large earthquakes (M>4) (Rutqvist et al., 2016), ductile faults give rise to progressive ruptures in which shear slip progressively accumulates, giving rise to aseismic slip or a swarm-like seismic activity (Vilarrasa et al., 2017b).

Another aspect that controls fault stability as a result of fluid injection is fault offset. Figure 6a represents a typical scenario that can be encountered in a normal-faulting stress regime setting, i.e., a steep fault in which the hanging wall has slid downwards with respect to the footwall. The fault is considered to have an offset equal to half of the storage formation thickness and consists of a low-permeability core (10⁻¹⁹ m²) and damage zones on the core sides. Properties of the damage zone depend on the material it is in contact with, becoming more permeable and less stiff than the intact rock as a result of fracturing (Table A2). Thus, the damage zone is of high permeability next to the storage formation, but of relatively low permeability and high entry pressure next to the caprock and base rock. The caprock and base rock are more deformable than the storage formation (Table A3). The model is plane strain, with a constant vertical stress equal to 29.3 MPa acting on the top boundary and no displacement perpendicular to the other boundaries. The top of the storage formation in the hanging wall is placed at 1.5 km depth. CO₂ is injected at a constant mass flow rate of $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{3}}$ $\mathrm{kg}{\mathrm{s}}^{-\mathrm{1}}{\mathrm{m}}^{-\mathrm{1}}$ in the hanging wall, 1 km away from the fault, which leads to the pressurization of the storage formation.

Pressure in the hanging wall of the storage formation, where CO₂ is being injected, increases by up to 10 MPa after 1 year of injection (Fig. 6b). The low-permeability fault core acts as a flow barrier, causing a rapid reservoir pressurization. This pressure increase expands the storage formation, pushing the fault towards the right-hand side. While pressurization is quite uniform across the storage formation, the resistance to displacement on the other side of the fault depends on the stiffness of the rock. Since the storage formation is stiffer than the base rock, it absorbs larger stresses. As a result, the induced horizontal stresses in the in-plane direction are high where the storage formation is present on both sides of the fault, but it is low where the base rock is on the other side of the fault (Fig. 6c).

Figure 7Distribution of stability changes induced by the pressure and stress changes shown in Fig. 6, measured in terms of the mobilized friction angle changes, Δϕ_mob. The inset shows the Mohr circles before and after reservoir pressurization.

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These stress changes have a direct implication on fault stability. Figure 7 displays the changes in the mobilized friction angle around the fault as a result of CO₂ injection. The most destabilized region is the lower half of the pressurized storage formation. Thus, an induced microseismic event would be initiated in that region of the fault, but slip would be arrested below the caprock because fault stability improves within the damage zone of the storage formation on the side that is not pressurized. Thus, induced large-magnitude events are unlikely in geological settings comparable to this simulated scenario. This difference in fault stability can be easily appreciated by representing Mohr circles in these zones (see inset in Fig. 7). Mohr circles shift to the left, getting close to failure, both at the top and bottom of the storage formation due to overpressure. But, while the deviatoric stress is maintained in the lower portion of the pressurized storage formation because the horizontal stress in the in-plane direction does not increase (see red circle in Fig. 7), the size of the Mohr circle decreases in the upper portion of the pressurized storage formation because of the increase in the horizontal stress in the in-plane direction where the storage formation is placed on both sides of the fault (see green circle in Fig. 7). This fault stability analysis highlights the fact that the accurate assessment of fault stability changes in geologic carbon storage sites completely depend on proper site characterization.

Site characterization has been traditionally considered an activity that should be performed for project design and, therefore, prior to operation. These kinds of characterization tests are limited in time and can only characterize a small volume of rock around the injection well (Niemi et al., 2017). The size of the region affected by injection grows with the square root of time and since geologic carbon storage projects are planned to last several decades, full characterization can only be achieved by considering operation as a continuous characterization, which we deem necessary to reduce uncertainty in predictive models of perceivable seismicity.

To assess whether CO₂ injection may induce perceivable seismicity, it is necessary to characterize the geological media in order to build a model of the site. The conceptual model should include the geological layers (at least the caprock, potential secondary caprocks, the storage formation and subjacent layers down to the crystalline basement) and faults. Apart from the geometry, the hydraulic (permeability and porosity), thermal (thermal expansion coefficient, thermal conductivity and heat capacity) and geomechanical (stiffness and strength) properties are required. Additionally, the initial conditions should be determined, i.e., the fluid pressure profile (if pressure is hydrostatic or if there are pressure anomalies), the geothermal gradient, Gutenberg–Richter law and, especially for induced seismicity purposes, the stress state. Determining the magnitude and orientation (and their variability) of the stress tensor is critical because fault stability depends on the orientation of a given fault with respect to the stress tensor (Morris et al., 1996). Hydraulic, thermal and geomechanical properties of each model layer can be measured in the laboratory from core samples or in the field. While laboratory measurements allow a tight control of test conditions, they usually test only the rock matrix and fail to acknowledge scale effects associated with spatial variability of the above properties and the impact of discontinuities (e.g., Sanchez-Vila et al., 1996; Ledesma et al., 1996; Zhang et al., 2006; Cai et al., 2007). Thus, interpretation of field tests leads to parameters that are more representative of operation conditions than laboratory experiments.

Figure 8Hydro-mechanical characterization test proposed by Vilarrasa et al. (2013b) to quantify the rock properties at the field scale and obtain an initial estimate of the maximum sustainable injection pressure. P refers to pressure, T to temperature and u_z to vertical displacement.

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To obtain estimates representative at the field scale of the hydraulic and geomechanical properties, Vilarrasa et al. (2013b) proposed a hydro-mechanical characterization test for CO₂ storage sites (Fig. 8). The test consists in injecting water at a high flow rate until microseismic events are induced. Ideally, the same brine from the storage formation should be injected to avoid geochemical reactions around the injection well that may alter rock properties. However, injecting brine would imply having a large facility on the surface to store the brine from the storage formation that would have been pumped previously. The test has to be closely monitored with pressure, temperature, deformation and microseismicity monitoring. The hydraulic properties of the storage formation and caprock can be determined from the interpretation of injection as a hydraulic test (Cooper and Jacob, 1946; Hantush, 1956). If heterogeneities are present in the storage formation, their effect is only detectable for a limited period of time (Wheatcraft and Winterberg, 1985; Butler and Liu, 1993). For this reason, it is extremely important to continuously measure pore pressure changes during injection. As for the geomechanical properties of the storage formation and caprock, they can be derived from the interpretation of the vertical displacement at the top of the storage formation and the caprock. Additionally, measuring the pressure evolution in the caprock, which undergoes a pressure drop in response of the pressure buildup in the storage formation (Hsieh, 1996), also gives information on the geomechanical properties. The magnitude of this reverse-water-level fluctuation is inversely proportional to the storage formation stiffness (Vilarrasa et al., 2013b). Injection should be maintained until microseismic events are induced in the caprock, which gives an initial estimate of the maximum sustainable injection pressure that should not be exceeded during CO₂ injection to avoid compromising the caprock sealing capacity. This test is valuable to characterize storage sites at a pre-operation stage; but it should be complemented by a continuous site characterization during operation to characterize geological features present in the far field and reduce subsurface uncertainty.

Figure 9(a) Concept of the continuous characterization technique proposed by Vilarrasa et al. (2017a) to detect and locate low-permeability faults using diagnostic plots; (b) asymmetric CO₂ plume as a result of the additional pressurization caused by a low-permeability fault, which displaces CO₂ towards the opposite direction of the fault; (c) detection of multiple faults by updating the conceptual model of the site and comparing field measurements with predictive simulations; and (d) estimation of the fault location from the measured divergence time in the derivative of the pressure evolution using type curves.

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An example of a continuous characterization technique that permits detecting and locating low-permeability faults is that proposed by Vilarrasa et al. (2017a). The idea is to use diagnostic plots, i.e., plots that include the fluid pressure evolution together with the derivative of the fluid pressure with respect to the logarithm of time (Bourdet et al., 1983; Renard et al., 2009), to detect faults significantly before (on the order of days) than if only fluid pressure evolution interpretation would be used (Fig. 9a). This early identification of faults should permit decision makers to perform pressure management if necessary to mitigate future induced seismicity. This methodology only detects faults that are at least 3 orders of magnitude less permeable than the storage formation. However, this should not be a problem in terms of induced seismicity because faults that do not act as a flow barrier induce relatively small changes in fault stability (Vilarrasa et al., 2016). Low-permeability faults generate an additional pressure increase that differs from the expected pressure evolution in an aquifer that would not contain that fault. Thus, by comparing the measured pressure evolution, and its derivative with respect to the logarithm of time, with the predicted one, low-permeability faults can be detected. This additional pressurization also affects the CO₂ dynamics because CO₂ is pushed away from the direction of the fault, leading to an asymmetric CO₂ plume (Fig. 9b). Such asymmetry could be detected at monitoring wells, suggesting the presence of a low-permeability fault, but it could also be due to reservoir heterogeneity (Chen et al., 2014). Once a fault is detected and located from the interpretation of pressure evolution (Fig. 9c and d), it should be incorporated into the conceptual model of the site. Additional characterization techniques may be necessary to obtain precise information on the detected faults. Then, field measurements should be compared with the updated conceptual model, which will permit identifying and locating new faults (Fig. 9c) from the determination of the divergence time and the use of type curves (Fig. 9d).

These characterization techniques entail a number of challenges. To begin with, the drilling of a network of monitoring wells is not yet common practice. Additionally, monitoring techniques also present challenges. Pressure is usually measured at the well head, but calculating the bottom-hole pressure from the well-head pressure is not straightforward given the nonlinearities of the injected fluid, especially for CO₂ injection (e.g., Lu and Connell, 2014). Unfortunately, pressure measurements in wells different than the injection well are almost inexistent. Temperature measurements receive even less attention because thermal effects are usually neglected. As for deformation measurements, the ground surface can be measured with InSAR (interferometric synthetic aperture radar) data; but for characterization tests that last a few days, the deformation of the ground may not be detectable given the great depths of suitable storage formations. Thus, deformation should be measured at depth within the boreholes. These measurements pose the question of whether the measured deformation refers to that of the rock or to that of the well. Since the casing of wells is stiffer than rock, the rock may deform more than the well and sliding could even occur between the rock and the cement surrounding the well casing, making accurate measurements difficult. Fiber optics may solve part of these monitoring challenges, but the way this monitoring should be performed is still not crystal clear for the moment. As far as microseismicity monitoring is concerned, arrays of geophones should be placed at depth. Otherwise, the signal-to-noise ratio is too high, which complicates detecting microseismic events. Additionally, multi-sensor arrays with a wide aperture coverage are necessary to accurately locate the events. Despite the existing challenges, such continuous characterization techniques are needed in order to minimize the risk of inducing seismicity in geologic carbon storage projects.

The issues discussed in the previous sections make it apparent that it is possible to effectively minimize the risk of inducing earthquakes that are sufficiently large to be felt on the ground surface and may damage structures. We propose here a workflow consisting of the following steps:

1. performing a detailed initial site characterization, with special emphasis on the geological formations relevant to the site (at least of the storage formation, the caprock, base rock and faults), including the determination of

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     geomechanical properties (Young's modulus, Poisson ratio, cohesion and friction angle);

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     hydraulic properties (permeability and porosity);

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     thermal properties (thermal expansion coefficient, thermal conductivity and heat capacity);

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     the seismic velocities v_p and v_s from the surface to the crystalline basement. An accurate determination of these velocities is important not only for proper interpretation of geophysics, but also to locate the hypocenters of the induced seismicity with precision;

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     the baseline of natural seismicity to establish the initial a and b values of the Gutenberg–Richter law in order to distinguish induced from natural seismicity;

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     the initial pressure, temperature and stress profiles with depth from the surface to the crystalline basement. The determination of the stress state is particularly important to perform a fault stability analysis of the identified faults and determine the strike and dip of critically oriented faults;

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     characteristics of geological formations and faults and their location and orientation through 3-D seismic data;

2. putting in place proper monitoring for performing continuous characterization, including

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     an array of geophones at depth to measure and locate induced microseismicity;

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     a network of geophones on the surface or in shallow wells with adequate spatial distribution, covering the whole footprint of the storage site to accurately locate induced seismicity. Induced events should be located in quasi-real-time, together with their focal mechanisms, to detect potentially unidentified faults that may induce large earthquakes. Inversion of the stress tensor is also important to detect possible local rotations of the stress tensor (Martínez-Garzón et al., 2013, 2014), which could be induced by pressure increase, cooling and/or shear slip stress transfer (De Simone et al., 2017b). This continuous seismic characterization is particularly important when CO₂ is injected in the basal aquifer (Verdon, 2014; Will et al., 2016);

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     monitoring wells measuring pressure, temperature and CO₂ saturation in the storage formation, caprock and secondary aquifer above the storage formation. Monitoring in secondary aquifers is useful for detecting brine and CO₂ leakage (e.g., Chabora and Benson, 2009; Zeidouni et al., 2014). Pressure measurements are necessary for continuous characterization techniques as the one described in Sect. 9;

3. carrying out pressure management

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     storage alternatives to the conventional concept of storing CO₂ in deep saline aquifers may be used to have a better control on pressure increase. For example, injection of CO₂ dissolved in brine is achieved by creating dipoles of wells in which brine is extracted from the storage formation and reinjected together with CO₂ in the same formation (Burton and Bryant, 2009; Jain and Bryant, 2011; Pool et al., 2013). The dipoles of wells limit pressure increase and allow operators to have a better control on it. Similarly, geothermal energy production using CO₂ as a working fluid permits lowering pressure increase and additionally extracts geothermal energy (Randolph and Saar, 2011). Despite the promising potential of this technology, the only pilot site that has tried using CO₂ as a working fluid yielded a low performance because the thermosyphon that should permit circulating CO₂ with a negligible energy consumption did not develop properly (Freifeld et al., 2016). Nevertheless, future research should enable a successful deployment of this technology;

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     in any case, predictive models of induced seismicity that consider coupled thermo–hydro–mechanical (THM) processes should be applied to identify the injection scenario that minimizes future induced seismicity. These predictive models should be based on THM monitoring and continuous characterization. Continuous characterization will permit updating of the fault stability analysis by incorporating newly detected faults (recall Fig. 9). The range (taking into account the uncertainty in fault properties) of pressure increase that makes faults become critically stressed for shear failure can be determined from the initial stress state, the strike and dip of faults, and the stress changes induced by CO₂ injection. Pressure management should be applied to avoid exceeding hazardous levels of pressure increase around faults. To limit pressure, the injection rate may need to be lowered or pressure may need to be released in the vicinity of critically oriented faults (Birkholzer et al., 2012).

The numerical code that was used to solve the simulations presented in this paper can be downloaded from https://deca.upc.edu/en/projects/code_bright/downloads (last access: 14 June 2019). The required data to reproduce the numerical simulations are provided in the paper and references.

VV designed the review, wrote the paper and performed the numerical simulations. All authors contributed to the interpretation of the results and edited the paper.

The authors declare that they have no conflict of interest.

This research has been supported by the European Research Council (grant no. 801809) and the U.S. Department of Energy, Lawrence Berkeley National Laboratory (grant no. DEAC02-05CH11231).

This paper was edited by Florian Fusseis and reviewed by two anonymous referees.