GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 814–818, doi:10.1002/grl.50196, 2013
Mineral carbon sequestration and induced seismicity
Viktoriya M. Yarushina1 and David Bercovici1
Received 28 November 2012; revised 21 January 2013; accepted 24 January 2013; published 14 March 2013.
[1] 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. Citation: Yarushina, V. M., and D. Bercovici (2013),
Mineral carbon sequestration and induced seismicity, Geophys.
Res. Lett., 40, 814–818, doi:10.1002/grl.50196.
1. Introduction
[2] The recent analyses of Zoback and Gorelick [2012]
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 wellknown 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.
[3] 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
1
Department of Geology and Geophysics, Yale University, New Haven,
Connecticut, USA.
Correspondence author: Viktoriya M. Yarushina, Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT,
06520-8109, USA. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
0094-8276/13/10.1002/grl.50196
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
[4] 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].
[5] The confining and shear stresses in the host rock induce local normal and shear stresses e
sn and et 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),
n
dR
b
¼k
dt
R
(1)
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/(cm2s)),
n and the mineral
molar volume (in cm3/mol). The factor Rb 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.
[6] 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 sn applied over the area
4a2 must be balanced by the sum of the local stress e
sn at
the grain-grain contact of area p(R2 a2) and the fluid pressure pf distributed over the area 4a2 p(R2 a2). The force
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YARUSHINA AND BERCOVICI: CO2 SEQUESTRATION AND INDUCED SEISMICITY
a)
b)
n
n
rock
grain
2a
n
2a
R
CO2
a
R
n
n
Figure 1. Simple model of a porous rock reservoir, represented by cubic-packed spheres, undergoing stress loading and
carbonation reactions with the pore fluid. The target reservoir is under lithostatic stress sn, which causes the contact between
“spherical” grains to press together with a normal contact stress e
sn . The presence of the shear stress t in the reservoir rock
induces local shear stress et at the grain-grain contact. Before the reaction, rock is composed of identical spherical grains of
radius a. As carbonation proceeds, grains grow due to precipitation of the reaction product at the free surface. We assume
that growth occurs uniformly along overlapping spherical surfaces of radius R > a. Panel (a): two-dimensional view of a representative volume element. Panel (b): three-dimensional view of a single grain in cross-section.
balance between the applied and contact stresses requires
that
4a2 sn pf ¼ p R2 a2 e
sn pf and 4a2 t ¼ p R2 a2 t (2)
for normal and shear stresses, respectively. Here, a is the
original unreacted grain size, t is the global shear stress,
and et 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 e
sn and et . The contact area between two
grains cannot exceed the contact between unit cells, i.e.,
p(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 MohrCoulomb friction law:
et ¼ c þ me
sn
(3)
where c is cohesion and m is the friction coefficient, which
lies in the range m = 0.6 0.9 for most rocks [Byerlee, 1978].
3. Discussion and Results
[7] 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 et; in this case, the
center of each circle is the point ðe
sn ; 0Þ and its radius is et:
The failure envelope (equation (3)) is as usual depicted as
a straight line with a slope m, 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
pf ¼ p0f þ Qt
(4)
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
dr
V0 rQ
increase according to dm
(for constant Q)
dt ¼ V0 dt ¼ K
where K and r are the bulk modulus and density of injected
fluid. Using water (r = 1 g/cm3, and K = 2.2 GPa), the conversion from Q to dm/dt is approximately 0.45 kg/MPa per
unit volume.
[8] 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
sn = 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 overpressured 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 m = 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.
[9] Subsurface fluid injection changes the local stress state
by increasing pf, decreasing the normal stress e
sn , and shifting
the Mohr circles towards the failure line (Figure 2). If injection
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YARUSHINA AND BERCOVICI: CO2 SEQUESTRATION AND INDUCED SEISMICITY
High shear stress
Moderate shear stress
Low shear stress
a)
No reaction
800
b)
c)
Slow reaction
800
dt=9y
Fast reaction
800
dt=3.6y
600
dt=0.7y
600
t=26.8y
600
t=358.7y
t=35.9y
400
400
400
200
200
200
0
0
500
0
0
1000
500
0
0
1000
d)
e)
f)
800
800
800
dt=12.4y
dt=6.8y
600
t=13.5y
400
200
200
200
0
0
1000
500
0
0
1000
g)
h)
i)
800
800
800
dt=0.6y
dt=0.6y
600
t=1.8y
400
400
200
200
200
500
1000
1000
600
t=0.6y
400
0
0
500
dt=0.6y
600
t=0.6y
1000
t=35.9y
400
500
500
600
400
0
0
1000
dt=0.7y
600
t=12.4y
500
0
0
500
0
0
1000
Figure 2. Mohr diagram including Mohr-Coulomb failure envelope (equation (3)). Horizontal rows correspond to three different values of global shear stress: low (t = 1.5 MPa), moderate (t = 6 MPa), and high (t = 9.7 MPa) when the initial stress state
brings the rock close to the failure. Vertical columns represent different carbonation reactions, i.e., a baseline cases without
carbonation (k = 0), cases with slow reaction (k = 4410–13 cm/s) and those with fast reaction (k = 44 10 12cm/s). These particular values of k correspond to olivine molar volume over a wide range of specific molar reaction rates (in mol/(cm2 s)). Circles
on the right in each figure correspond to the initial stress state at t = 0. With time, the circles move leftward until the seismic
event occurs (indicated with a red star), or complete pore clogging is reached. The timing of seismic events (a, d, e, g, h, and i)
or pore clogging (b, c, and f) t is indicated in each plot. Circles at equal time intervals dt are also indicated. The pumping rate is
taken to be Q = 0.62MPa/y to insure that the final fluid pressure after 35.9 years of pumping does not exceed the lithostatic stress.
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
3
R/a
1.6
2
1.4
1
1.2
1
0
pf, MPa
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 t = 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.
[10] 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.
[11] For the fastest reactions that proceed on the injection
time scale, seismic risk is completely eliminated for low to
100
200
300
400
0
0
35
4
30
3
25
2
20
1
15
0
100
200
300
time, years
400
0
0
100
200
300
400
100
200
300
400
time, years
Figure 3. Dynamics of dimensionless grain size R/a, fluid
pressure pf and contact stresses normalized by global stresses for Figure 2b with the slow reaction rate and low
shear stress.
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YARUSHINA AND BERCOVICI: CO2 SEQUESTRATION AND INDUCED SEISMICITY
et 2 þ m2 et2 e
s2n ¼ 0
11
time to seismic event, years
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.
[12] 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).
[13] 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
n=2
n=4
9
n=5
8
7
6
5
0
0.5
1
1.5
2
2.5
3
reaction rate, k
3.5
4
4.5
x10
-11
Figure 5. Dependence of time to a seismic event on the reaction rate for different n at a fixed pumping rate of
Q = 1.5MPa/y and moderate shear stress (t = 6 MPa). A high
value of the pumping rate is chosen to insure that failure
occurs for all reaction rates before the fluid pressure exceeds
the lithostatic stress.
(5)
[14] 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)
2
4a2
4a2 sn
Qt þ p0f
1 þ
þ cm 2
2
2
2
pðR a Þ
8 pðR a Þ
3 2 9
2
>
>
2
<
=
2
4a2 Qt þ p0f sn
4ta
4Qt þ p0 5
ð1 þ m2 Þ c2 þ
¼0
f
2
2
2
2
>
>
pðR a Þ
pðR a Þ
:
;
(6)
[15] 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
120
120
100
100
n=0, t=36.3y
80
80
60
60
40
40
20
20
0
0
50
100
150
200
120
0
0
n=2, t=58.3y
50
100
150
200
100
150
200
120
100
100
n=4, t=97.2y
80
80
60
60
40
40
20
20
0
n=0
10
0
50
100
150
200
0
0
n=5, t=127.1y
50
Figure 4. Same as Figure 2i, but demonstrating the effect of time dependent reaction rate for four cases with n ≥ 0 in equation (1). The precipitate fills the pore space within different times for each case, as indicated. The circles are at equal time
intervals of 5.2 years. Circles correspond to high shear stress t = 9.7 MPa and fast reaction rate k = 44 10 12cm/s. A moderate pumping rate of Q = 0.14MPa/y is maintained in all four cases so that the final fluid pressure by the end of pumping
does not exceed lithostatic stress in all cases. In each case, pumping stops when precipitate clogs the pores.
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YARUSHINA AND BERCOVICI: CO2 SEQUESTRATION AND INDUCED SEISMICITY
n =0
n =2
n =4
n =5
2
1.5
1
0.5
0
critical constant pumping rate, MPa/y
critical pumping rate, MPa/y
2.5
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.
0.44
0.42
0.4
[17] Acknowledgments. 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.
0.38
0.36
References
0
20
40
60
t, years
80
0
2
4
6
n
Figure 6. Critical pumping rate, Qc, below which seismic
triggering can be avoided. (a) Evolution of critical pumping
rate with time for different reaction grain growth exponents
n. (b) Dependence of the minimum critical pumping rate
on the exponent n. Calculations are performed for the same
set of parameters as in Figure 2i (k = 4410–12 cm/s and very
high shear stress value t = 9.7 MPa).
critical pumping rate min(Qc) (Figure 6a), which is necessarily
also a function of n (Figure 6b).
[16] 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
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