CO[subscript 2] migration in saline aquifers: Regimes in
migration with dissolution
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Citation
MacMinn, C.W., M.L. Szulczewski, and R. Juanes. “CO[subscript
2] Migration in Saline Aquifers: Regimes in Migration with
Dissolution.” Energy Procedia 4 (2011): 3904–3910.
As Published
http://dx.doi.org/10.1016/j.egypro.2011.02.328
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Elsevier
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Energy
Procedia
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Energy Procedia 4 (2011) 3904–3910
Energy Procedia 00 (2010) 000–000
www.elsevier.com/locate/XXX
GHGT-10
CO2 migration in saline aquifers: regimes in
migration with dissolution
C. W. MacMinn, M. L. Szulczewski, and R. Juanes*
Massachusetts Institute of Technology, 77 Massachusetts Ave, Bldg. 48-319, Cambridge, MA 02139, USA
Elsevier use only: Received date here; revised date here; accepted date here
Abstract
We incorporate CO2 dissolution due to convective mixing into a sharp-interface mathematical model for the post-injection
migration of a plume of CO2 in a saline aquifer. The model captures CO2 migration due to groundwater flow and aquifer slope,
as well as residual trapping and dissolution. We also account for the tongued shape of the plume at the end of the injection
period. We solve the model numerically and identify three regimes in CO2 migration with dissolution, based on how quickly the
brine beneath the plume saturates with dissolved CO2. When the brine saturates slowly relative to plume migration, dissolution is
controlled by the dimensionless dissolution rate. When the brine saturates “instantaneously” relative to plume migration,
dissolution is instead controlled by the solubility of CO2 in brine. We show that dissolution can lead to a several-fold increase in
storage efficiency. In a companion paper, we study migration and pressure limitations on storage capacity [Szulczewski et al., GHGT10, Paper 917 (2010)].
c 2010
⃝
2011Elsevier
Published
Elsevier
Ltd.
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Ltd.byAll
rights reserved
Keywords: Geologic storage; saline aquifers; capillary trapping; post-injection; sharp-interface; migration distance; capacity estimates
Carbon capture and storage in geological formations is widely regarded as a promising tool for reducing
atmospheric CO2 emissions, and deep saline aquifers are an attractive target for long-term CO2 storage [1]. Deep
saline aquifers are permeable layers of, for example, limestone or cemented sand that are saturated with brine and
bounded above and below by layers of much less permeable rock such as clay or anhydrite. They are located
roughly 1 to 3 km underground, are horizontal or weakly sloped, and many have a slow natural groundwater
through-flow. While the properties of CO2 at aquifer conditions vary with temperature and pressure, the CO2 will
always be less dense and less viscous than the groundwater, making it buoyant and mobile in the aquifer. After
injection, the CO2 plume will spread upward against the top boundary of the aquifer while migrating due to a
combination of groundwater flow and aquifer slope. Several trapping mechanisms act to prevent the migration of
buoyant CO2 back to the surface—these include (1) structural or stratigraphic trapping: the mobile CO2 is kept
underground by a relatively impermeable caprock [2]; (2) capillary trapping: disconnection of the bulk CO2 plume
into immobile (trapped) blobs [3;4]; (3) solubility trapping: dissolution of the CO2 into the ambient brine [5;6]; and
(4) mineral trapping: geochemical binding of CO2 to the aquifer rock due to mineral precipitation [2].
* Corresponding author. Tel.: +1-617-253-7191; fax: +1-617-258-8850.
E-mail address: juanes@mit.edu
doi:10.1016/j.egypro.2011.02.328
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C.W. MacMinn et al. / Energy Procedia 4 (2011) 3904–3910
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In a previous study [7], we developed a complete solution to a hyperbolic gravity-current model for CO2
migration in a deep saline aquifer due to groundwater flow and aquifer slope, subject to residual trapping, and
including the tongued end-of-injection plume shape. We showed that the migration behavior depends strongly on
three parameters: the importance of aquifer slope relative to groundwater flow, the mobility ratio, and the capillary
trapping number. We also explored the impact of these parameters on the overall storage efficiency, a measure of
the fraction of the aquifer pore space that can be used to store CO2, and we showed that the competition between
groundwater flow and aquifer slope leads to nontrivial results in terms of the storage efficiency. Here, we
incorporate CO2 dissolution into this model and study the interaction of dissolution with migration and residual
trapping. We do not include mineral trapping because it occurs over very long timescales, and is unlikely to
influence plume migration.
It is well-known that CO2 is weakly soluble in groundwater, and therefore that both residual CO2 and CO2 from
the mobile plume will dissolve slowly into the nearby groundwater as the plume migrates. Because the density of
groundwater increases with dissolved CO2 content, the boundary layer of CO2-saturated groundwater near the
mobile plume is unstable. This unstable density stratification eventually results in a Rayleigh–Bénard-type flow
referred to as convective mixing, where fingers of “heavy”, CO2-saturated brine sink away from the plume as
fingers of “fresh” groundwater rise upward. This process has been studied in various contexts [8–10]. The
implications of convective mixing for the geological storage of CO2 were first pointed out by [11] and discussed by
[12]. Several studies have since been made of the onset of the instability for a stationary layer of CO2 overlying a
layer of water [5,6;13;14]. In all cases, the onset time for convective mixing has been shown to be relatively short
compared to timescales of interest in geological CO2 storage. It has also been shown that convective mixing
dramatically increases the rate of CO2 dissolution compared to diffusive transport alone [5;15;16], and that the timeaveraged rate of CO2 dissolution due to convective mixing is approximately constant. We take advantage of these
results here.
We are interested in large CO2 storage projects, and therefore in the evolution of the CO2 plume at the geologicbasin scale as proposed by [17]—a schematic of the basin scale geologic setting is shown in Figure 1.
injection wells
1–3 km
y
100 m
x
z
100 km
x
100 km
(a)
(b)
Figure 1. Geological storage of CO2 in a saline aquifer at the basin scale: (a) From a bird’s eye view, the plumes
from individual wells merge together as CO2 (dark gray) is injected via a “line-drive” array of wells (black dots)
[17], and we model the single resulting plume as symmetric in the y direction; (b) in cross-section, the buoyant
plume of CO2 (dark gray) migrates after the end of injection due to a combination of aquifer slope and groundwater
flow (arrows), dissolving due to convective mixing and leaving behind residual CO2 (light gray). Typical horizontal
and vertical scales are indicated—note that the vertical scale of the aquifer is greatly exaggerated.
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We take the aquifer to be homogeneous, with an arbitrary tilt relative to the horizontal and a net groundwater
through-flow to the right. We take the fluids to be incompressible and Newtonian, with constant and uniform
properties within the aquifer. We employ a sharp-interface approximation, neglecting saturation gradients as well as
the capillary pressure. We further assume vertical equilibrium, neglecting the vertical component of the fluid
velocity relative to the horizontal one. We divide the domain into three regions of uniform fluid saturation with
sharp interfaces corresponding to saturation discontinuities, as illustrated in Figure 2. Region 1 is the plume of
mobile CO2, containing free-phase CO2 and a saturation Swc of connate brine; Region 2 is the region from which the
plume has receded, containing mobile brine and a saturation Sgr of trapped, free-phase CO2; and Region 3 contains
mobile brine with some dissolved CO2, and no free-phase CO2.
k, φ
x
h1(x, t)
Un
h2(x, t)
g
H
ϑ
h3(x, t)
Figure 2. A schematic of the plume during post-injection migration, as the mobile CO2 (dark gray) is pushed to the
right by a combination of groundwater flow and aquifer slope, leaving trapped CO2 (light gray) in its wake. CO2
dissolves from the plume due to convective mixing, as indicated by the fingers of “heavy” brine (blue) falling away
from the plume. We divide the domain into three regions of uniform CO2 and groundwater saturation, separated by
sharp interfaces corresponding to saturation discontinuities. Region 1 (dark gray) contains mobile CO2 and a
saturation Swc of connate brine; Region~2 (light gray) contains mobile brine and a saturation Sgr of residual CO2;
Region~3 (white, blue) contains mobile brine with some dissolved CO2. The aquifer has a total thickness H , and
the thickness of Region i , i = 1, 2, 3, is denoted hi (x, t) . Groundwater flows naturally through the aquifer from
left to right with velocity U n ; the aquifer has permeability k and porosity φ , as well as an arbitrary angle of tilt ϑ
measured counterclockwise from the direction of gravity.
The complete derivation of the model and the details of the underlying assumptions are given elsewhere [18–
21]—the resulting equations in dimensionless form are
∂η
∂f
∂
∂ ⎡
∂η ⎤
R˜ + N f
+ N s [(1 − f ) η ] − N g ⎢(1 − f )η ⎥ = −R˜ N d ,
∂ξ
∂τ
∂ξ
∂ξ ⎣
∂ξ ⎦
(1)
∂η ⎤
∂η
∂f
∂
∂ ⎡
R˜ d + N f d − N s
1 − f d )η + N g ⎢(1 − f d )η ⎥ = R˜ N d Γd ,
(
∂ξ ⎦
∂ξ
∂ξ ⎣
∂τ
∂ξ
(2)
and
[
]
where η = h1 H is the scaled thickness of the CO2 plume, ηd = hd H is the scaled thickness of the “curtain” of
brine with dissolved CO2, τ = t Tc , and ξ = x Lc . We choose the characteristic length Lc to be the length of a
rectangle of aquifer containing a volume QiTi 2 of CO2, Lc = QiTi 2 (1 − Swc )φH , where Qi is the volume rate of
CO2 injection during the injection period, per unit length of the well array, and Ti is the duration of the injection
period such that QiTi is the total volume of CO2 injected. The characteristic time Tc is arbitrary. The discontinuous
coefficient R˜ captures capillary trapping by changing value depending on whether the CO2-brine interface is locally
in drainage or imbibition,
C.W. MacMinn et al. / Energy Procedia 4 (2011) 3904–3910
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⎧ 1
if ∂η ∂τ > −N d ,
R˜ = ⎨
otherwise,
⎩1 − Γ
(3)
where Γ = Sgr (1 − Swc ) is the capillary trapping number, which measures the fraction of mobile CO2 that is left
behind due to capillary trapping as the plume migrates. The fractional flow functions f and f d are given by
f (η) =
Mη
,
(M −1)η +1
f d (ηd ,η) =
ηd
(M −1)η +1
(4)
where M = λ1 λ 3 is the mobility ratio and λ i is the mobility of the fluid in Region i . The constants N f , N s , and
N g measure the relative importance of groundwater flow, up-slope migration, and buoyant spreading, respectively,
and are given by
Nf =
H
Tc Q
T
T
, N s = c κ sin ϑ , N g = c κ sinϑ ,
Ti Qi 2
Lc
Lc
Lc
(3)
where κ = Δρgkλ1 (1 − Swc )φ is the characteristic buoyancy velocity of CO2 in this system, Δρ is the density
difference between mobile CO2 and brine, and Q is the total volume rate of fluid flow through the formation from
left to right, per unit length of the well array. The parameter N d measures the rate of dissolution, and is given by
⎧⎪
T
CΓ κ c
Nd = ⎨ d d H
⎪⎩
0
(
if η > 0 and ηd < 1 − η,
(3)
otherwise,
)
where Γd = c s 1 − Swc , c s is the volume fraction of CO2 dissolved in brine at saturation, and C ≈ 0.017 is a
dimensionless constant [16]. κ d = Δρ d gkλ 3 φ is the characteristic buoyancy velocity of brine saturated with
dissolved CO2 in this system and Δρ d is the density difference between brine and brine saturated with dissolved
CO2. Note that we assume that CO2 dissolves at a constant rate until the “curtain” of brine with dissolved CO2
reaches the bottom of the aquifer (i.e., until the brine underneath the plume saturates with dissolved CO2), at which
point we assume that dissolution stops abruptly.
Equations 1 and 2 are coupled, nonlinear conservation laws for migration of the mobile CO2 and migration of the
“curtain” of brine containing dissolved CO2, respectively. They are coupled by the fluid flow, and also by
dissolution. We need not solve Equation 2 when there is no dissolution, or when the brine underneath the plume
saturates with dissolved CO2 slowly compared to the migration of the plume. Otherwise, we must solve both
equations simultaneously. Here we do so numerically for several values of the dissolution rate N d for fixed values
of M , Γ , N f , N s , N g , Γd —the results are illustrated in Figure 3.
We identify three regimes in CO2 migration with dissolution, as illustrated qualitatively in Figure 3: (1) slow
saturation: the brine beneath the plume saturates with dissolved CO2 slowly relative to plume migration; (2) fast
saturation: at least some of the brine beneath the plume becomes saturated with dissolved CO2 as the plume
migrates; and (3) instantaneous saturation: all of the brine beneath the plume saturates very quickly
(“instantaneously”) relative to plume migration. To illustrate quantitatively the transition from the slow saturation
regime to the instantaneous saturation regime, we fix M , Γ , N f , N s , N g , and Γd , and solve Equations (1) and
−5
(2) numerically for N d ranging from 10 to 100 . The results are presented in Figure 4. We are also able to solve
Equations (1) and (2) semi-analytically in some cases in the slow- and instantaneous-saturation regimes. We
include a semi-analytical solution to Equation (1) in the slow-saturation regime in Figure 4—these rest of these
semi-analytical results are presented elsewhere [20].
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Nd = 0
(a)
Nd = 0.02
(b)
Nd = 0.08
(c)
Nd = 2
(d)
Figure 3. Numerical solutions to Equations 1 and 2 for the shape of the plume during post-injection migration at
τ = 2.25 for M = 5, Γ = 0.3 ,, N f = 1 , N s = 0.5, N g = 0 , Γd = 0.1, and N d = 0 , 0.02, 0.08, and 2. As in
Figure 2, mobile CO2 is shown in dark gray, residual CO2 is shown in light gray, and the “curtain” of brine with
dissolved CO2 is shown in blue. Qualitatively, we identify three regimes: (b) slow saturation, where the dissolution
front does not interact with the bottom of the formation and the entire plume dissolves as it migrates; (c) fast
saturation, where the brine below the plume becomes saturated at some point in space so that the leading portion of
the plume dissolves but the trailing portion does not; and (d) “instantaneous” saturation, where all of the brine below
the plume is saturated with dissolved CO2 and the plume subsequently dissolves only at the leading edge.
ε
slow saturation
inst. saturation
fast saturation
Nd
Figure 4. The storage efficiency as a function of the dimensionless rate of dissolution, N d for M = 5, Γ = 0.3 ,
N f = 1 , N s = 0.5, N g = 0 , and Γd = 0.1 from numerical solutions to Equations (1) and (2) (black dots) and a
semi-analytical solution to Equation (1) in the slow-saturation limit (solid black line). The numerical solutions
depart from the semi-analytical curve when N d is large enough that some of the brine beneath the plume saturates
with dissolved CO2 as the plume migrates. The three saturation regimes are indicated, separated by dotted gray
lines. The storage efficiency increases monotonically from the no-dissolution value as the rate of dissolution
increases, reaching a plateau when N d is sufficiently large that the brine underneath the plume saturates
“instantaneously”. In this limit, dissolution leads to a six-fold increase in storage efficiency for this particular case.
C.W. MacMinn et al. / Energy Procedia 4 (2011) 3904–3910
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We have presented a model for CO2 migration due to groundwater flow and aquifer slope, and subject to
capillary trapping and dissolution due to convective mixing. We have identified three regimes in migration with
dissolution, depending on how quickly the brine beneath the plume saturates with dissolved CO2 relative to plume
migration. Note that while the model characterizes dissolution with two parameters, dissolution in the slow- and
instantaneous-saturation regimes depends only on one of the two parameters. In the slow-saturation regime,
dissolution behavior depends only on N d — Γd is unimportant because the brine beneath the plume does not
saturate. In the instantaneous-saturation limit, dissolution depends only on Γd — N d is unimportant because the
brine beneath the plume is completely saturated. Finally, we have shown that dissolution can lead to a several-fold
increase in storage efficiency over the value for capillary trapping alone. In a companion paper, we study migration
and pressure limitations on storage capacity [Szulczewski et al., GHGT-10, Paper 917 (2010)].
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