How pressure buildup and CO[subscript 2] migration can
both constrain storage capacity in deep saline aquifers
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Citation
Szulczewski, M.L., C.W. MacMinn, and R. Juanes. “How
Pressure Buildup and CO[subscript 2] Migration Can Both
Constrain Storage Capacity in Deep Saline Aquifers.” Energy
Procedia 4 (2011): 4889–4896.
As Published
http://dx.doi.org/10.1016/j.egypro.2011.02.457
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Elsevier
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Final published version
Accessed
Thu May 26 21:19:40 EDT 2016
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http://hdl.handle.net/1721.1/92030
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Energy
Procedia
Energy Procedia 4 (2011) 4889–4896
Energy Procedia 00 (2010) 000–000
www.elsevier.com/locate/procedia
www.elsevier.com/locate/XXX
GHGT-10
How pressure buildup and CO2 migration can both constrain storage
capacity in deep saline aquifers
M. L. Szulczewski, C. W. MacMinn, and R. Juanes1
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139
Elsevier use only: Received date here; revised date here; accepted date here
Abstract
A promising way to mitigate global warming is to sequester CO2 in deep saline aquifers. In order to determine which aquifers
are the best for sequestration, it is helpful to estimate how much CO2 they can store. Currently, this is difficult because both the
pressure buildup from injection and the volume of available pore space have been identified as constraints, but have not been
compared to determine which is more important. In this study, we evaluate their relative importance using simple, but dynamic
models of how pressure rises during injection and how CO2 becomes trapped in the pore space. Our results show that the more
important constraint depends on the properties of the aquifer and how the CO2 is injected.
2010Published
Elsevier Ltd.
All rights
reserved
c©2011
⃝
by Elsevier
Ltd.
Keywords: CO2 sequestration; deep saline aquifers; storage capacity; overpressure; CO2 leakage; residual trapping.
1. Introduction
Capturing CO2 and storing it in underground reservoirs will likely be important over the next few decades
because it can help abate anthropogenic CO2 emissions during the transition to emission-free energy sources [1].
Some of the most promising storage reservoirs are deep saline aquifers, which are layers of sandstone or carbonate
rocks filled with salty water and buried 1 to 3 kilometers underground [2]. They are attractive places to sequester
CO2 because they are widespread and their water is typically too salty for drinking or agriculture [3].
In addition to location and salinity, an important measure for evaluating the quality of a deep saline aquifer is
how much CO2 it can hold, called its storage capacity [4]. On way to calculate it is based on the pore volume of an
aquifer and how the injected CO2 would occupy it. For example, one method calculates the capacity as the total
free-phase CO2 that could fit into the pore space [5], while another calculates it as the total CO2 that could be
dissolved in all the water in the pore space [6]. We refer to these estimates as space-limited capacities.
While some studies use space constraints, others use pressure [7,8]. This constraint is based on the observation
that the high pressures caused by injection can fracture an aquifer, potentially creating a path though which CO2 can
escape. If fractures or faults already exist, the high pressure may cause them to slip and generate earthquakes.
1
Corresponding author. Tel.: 1-617-253-7191
E-mail address: juanes@mit.edu.
doi:10.1016/j.egypro.2011.02.457
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Studies that use pressure as a constraint calculate the storage capacity as the maximum amount of CO2 that can be
injected without causing fractures, activating faults, or inducing large earthquakes.
One shortcoming of nearly all of the methods to calculate storage capacity is that they are based on a single
constraint—either pressure or space. Since the most limiting constraint is unknown a priori, it is unclear which
method to use.
In this paper, we begin to address this problem by outlining the conditions under which each type of constraint
dominates in a simple model system. This outline comes from comparing two models that apply to the same system
but are based on the two different constraints. In general, we show that pressure tends to be the dominant constraint
if an aquifer is large and injection occurs over a short time (10s of years), but space tends to be the dominant
constraint if enough time is allowed for injection. We demonstrate these results by applying our models to the Fox
Hills Sandstone.
2. Model system
Our model system exhibits a number of key features, as shown
in Figure 1. The first key feature is scale: we consider
sequestration at the scale of an entire basin since large quantities of
CO2 (100s of millions of metric tons) will have to be stored to
offset emissions. The second key feature is that CO2 is injected
from a line-drive array of wells. These wells are close enough
along the line drive so that the CO2 distribution along the line is
nearly uniform, which allows us to collapse that dimension and
develop two-dimensional models. The third and fourth key features
are that the caprock is sloped and the brine in the aquifer is flowing.
These features cause injected CO2 to migrate. The final key
features are that the aquifer is homogeneous and the boundaries of
the aquifer are impermeable.
Figure 1 Our model system is a deep
saline aquifer at the basin scale, into which
CO2 is injected from a line-drive array of
wells.
3. Space-limited capacity
We calculate the space-limited capacity as the total residual CO2 that can fit in an aquifer without leakage.
Residual CO2 is CO2 that is trapped by capillary forces whenever brine displaces mobile CO2, as at the trailing edge
of a plume (Fig. 2B) [9]. We neglect CO2 that may be trapped in carbonate minerals in our calculation because
mineral trapping takes much longer than residual trapping [10]. We also neglect CO2 that may be trapped via
dissolution into the brine for simplicity. While dissolution is an important trapping mechanism in many cases, our
analysis shows that neglecting it is reasonable when the following conditions hold [11]:
Nf
2U H 2 Á¹b (1 ¡ Sbc )
=
À1
Nd
Vg ®cs (½s ¡ ½b )gk
(1)
¤
2(½b ¡ ½g )krg
sin ¹b H 2 Á2 (1 ¡ Sbc )2
Ns
=
À 1:
Nd
Vg ®cs (½s ¡ ½b )¹g
(2)
where all variables are defined in Table 1. The first equation compares the strength of CO2 migration due to
groundwater flow Nf to the strength of dissolution Nd . The second equation compares the strength of upslope CO2
migration Ns to the strength of dissolution Nd .
The amount of residual CO2 that can fit into an aquifer is controlled by two factors: the fraction of CO2 that can
be trapped in a pore and the fraction of total pore space in the aquifer that will be occupied by this CO2. The first
factor is a function of the porosity Á and the residual gas saturation Sgr . The second factor is controlled by how
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Figure 2 To calculate the space-limited capacity, we model how CO2 migrates in an aquifer. A. During injection, the CO2
migrates nearly symmetrically away from the well array. It begins forming a gravity tongue because the CO2 is much less
viscous than the brine. B. After injection has stopped, the CO2 migrates upslope due to buoyancy or downstream due to
groundwater flow in a more exacerbated gravity tongue, filling a fraction of the pore volume given by (1 ¡ Sbc ). CO2 becomes
trapped at the trailing end at saturation Sgr. C. Eventually the plume becomes completely trapped, reaching a lateral extent Lg.
CO2 migrates in the aquifer. Since it is buoyant and much less viscous than brine, the CO2 will preferentially travel
in a long, thin tongue along the caprock called a gravity tongue [12]. This causes it to infiltrate only a small fraction
of the available pore space as shown in Figure 2.
To determine the effect of gravity tonguing on capacity, we use a simple model for how CO2 migrates [13,14].
The model is an advection partial differential equation and is based on the assumptions that the interface between
the CO2 and brine is sharp and that vertical flow is negligible compared to lateral flow. We solve this equation both
analytically and numerically for the fraction of swept aquifer volume that will be occupied by trapped CO2 [14]. For
the case in which only groundwater flow drives CO2 migration, the fraction is given by:
"fm =
Vaq;g
2¡
=
;
Lg HW
M¡2 + (2 ¡ ¡)(M + ¡ ¡ 1)
(3)
where Lg is the lateral extent of aquifer swept by CO2 (Fig. 2C) and Vaq;g is the volume of aquifer infiltrated by
CO2, not the volume of CO2 itself [13]. This fraction is typically called an efficiency factor. ¡ is the ratio of the
pore volume occupied by residual CO2 to the pore volume initially occupied by CO2, called the trapped coefficient:
¤
¡ = Sgr =(1 ¡ Sbc ). M is the ratio of the mobility of CO2 to the mobility of brine: M = ¹b kgr
=¹g . For the case in
which only slope drives migration, the fraction is given to a good approximation by [14]:
"sm =
Vaq;g
¡
=
:
Lg HW
0:9M + 0:49
(4)
With the efficiency factors known, we calculate storage capacity in three steps. First, we rearrange the
expression for the efficiency factor to solve for the volume of swept aquifer occupied by trapped CO2. Next, we
require that the extent of swept aquifer Lg exactly equal the aquifer length L. This stipulation ensures that the
trapped plume fits exactly inside the aquifer with no leakage. Finally, we convert the volume of aquifer occupied by
CO2 to the mass of CO2 in the pores by multiplying by the porosity Á, the residual gas saturation Sgr , and the CO2
density ½g . The resulting equation for storage capacity is:
Mm = ½g LHW ÁSgr "m:
(5)
4. Pressure-limited capacity
We calculate the pressure-limited capacity to be the total amount of CO2 that can be injected before the pressure
rise creates a tensile fracture in the caprock. While shear failure may occur before this happens, we choose tensile
fracturing as the constraint for simplicity: predicting tensile fracturing requires knowing only the least principle
effective stress in the aquifer, whereas predicting shear failure requires knowing the entire stress tensor [15].
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Table 1 Variables used in this paper.
M
Mm
Mp
Vg;aq
g
Sbc
Sgr
kgr
k
Á
storage capacity
migration-limited storage capacity
pressure-limited storage capacity
aquifer volume infiltrated by CO2
gravitational acceleration
connate brine saturation
residual CO2 saturation
CO2 relative permeability
intrinsic permeability
porosity
H
W
L
Lg
U
groundwater Darcy velocity
cs
caprock slope
®
D
¹b
¹g
½g
½b
½s
aquifer thickness
width of well array
aquifer length
extent of trapped CO2
caprock depth
brine viscosity
CO2 viscosity
CO2 density
brine density
CO2- saturated brine
density
CO2 solubility
(volume fraction)
coefficient of
dissolution flux
"p
"s
T
º
c
Pf rac
P
pemax
¾0
¾T
pressure-limited efficiency
space-limited efficiency
injection time
Poisson’s ratio
aquifer compressibility
fracture pressure
pore pressure
max dimensionless pressure
effective stress
total stress
¾Tv 3
least principal total stress
in vertical direction
least principal total stress
in horizontal direction
¾Th 3
To calculate the pressure that would cause fracturing, we use the effective stress principle:
¾0 = ¾T ¡ P;
(6)
where ¾ 0 is the effective stress, ¾ T is the total stress, and P is the pore pressure. Ignoring the cohesive strength of
the aquifer [15, p.121], a tensile fracture occurs when the least principle effective stress is zero. This indicates that
the fracture pressure Pf rac equals the least principle total stress. When this stress is vertical, we calculate it to be
the weight of the overburden:
Pfrac = ¾Tv 3 = (1 ¡ Á)½r gD + Á½b gD:
(7)
When it is horizontal, we approximate it using Poisson’s ratio º [15, p.281]:
Pf rac = ¾Th 3 =
º
¾v
1 ¡ º T3
(8)
We use a nationwide map of stress in the US to estimate when the least principle stress is vertical or horizontal [16].
Figure 3 To calculate pressure-limited capacity, we model how the pressure in an aquifer rises due to injection. A. We assume
that the rate of injection starts at zero, rises to a maximum Qmax at time T =2, and then ramps back down to zero at time T . B.
Since the model captures single-phase flow and the aquifer is uniform, the pressure rise is uniform across the thickness of the
aquifer. In the lateral direction, the pressure is highest at the well array.
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To determine how much CO2 can be injected before the aquifer pressure reaches Pf rac , we use a simple model
that captures how pressure responds to injection [13]. In this model, the injection rate starts at zero, rises linearly to
a maximum, and then decreases linearly back to zero as shown in Figure 3A. We choose this injection scenario to
parallel how emissions will likely change: in the near future, emissions will probably increase due to increased
energy demands and continued reliance on fossils fuels, and this increase will require sequestering more CO2;
eventually, however, emissions must decrease to stabilize the atmospheric concentration of CO2, and this decrease
means that less will need to be injected.
While models of pressure changes during sequestration can be complex, we use a simplified model. One
simplification is that our model neglects multiphase flow: we model the pressure change due to injecting water
instead of CO2. This simplification causes an overestimate of the pressure rise during injection since water has a
lower compressibility than CO2, but will likely provide reasonable results since gravity tonguing causes the CO2 to
occupy a small fraction of an aquifer’s thickness (Fig. 2B). Another simplification comes from the assumption of
zero lateral strain and constant vertical stress in the aquifer. This assumption allows the flow and poromechanics
problems to be decoupled, reducing the model to a simple diffusion problem [17]. Physically, the problem is a
diffusion problem because it captures how pressure diffuses away from the well array into the aquifer, as shown in
Figure 3B.
We solve the diffusion problem analytically and find that the pressure-limited storage capacity is given by [13]:
s
Mp = 2½g HW
kT c (Pf rac ¡ ½b gz)
;
¹b
pemax
(9)
where pe is a dimensionless parameter that depends on the injection scenario and the boundary conditions. For the
ramp-up, ramp-down scenario shown in Figure 3A, pe = 0:87 if the boundaries are infinitely far away. If the
boundaries are not infinitely far away, the correct value of pe can still be calculated analytically [13].
5. Comparison of pressure and space constraints
The more limiting constraint leads to the smaller capacity. As a result, we can compare the relative severity of
the constraints by comparing the size of the capacities:
R=
p
LÁSgr "m ¹b pemax
Mm
= p
Mp
2 kcT (Pf rac ¡ ½b gD)
(10)
When R > 1, the pressure-limited capacity is smaller so pressure constraints are more important than space
constraints. This tends to occur when the aquifer is shallow and large, the permeability is low but the porosity is
high, and the injection time is short. It also tends to occur when the viscosities of the CO2 and brine are more
similar since the migration efficiency factor "m is inversely proportional to the mobility ratio M . When R < 1,
however, the space-limited capacity is smaller and space constraints are more important. This tends to occur when
the aquifer is deep and small, the permeability is high but the porosity is low, the injection time is long, and the
viscosities are dissimilar.
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6. Pressure and space constraints in the Fox Hills Sandstone.
6.1. Geohydrology of the reservoir
We demonstrate the competition between pressure and space
constraints in the Fox Hills Sandstone. This reservoir lies in the
Powder River Basin in Colorado and Montana, as shown in Figure
4. It consists of continuous marine and non-marine sandstones with
siltstone and minor shale [18]. The relevant geohydrologic data
for the reservoir are listed in Table 2.
The top boundary of the Fox Hills Sandstone is an extensive
caprock called the Upper Hell Creek Confining Layer [19]. It
consists of lower-coastal-plain muddy sandstones. The bottom
boundary is an aquiclude composed of marine shale and siltstone
[18, Fig.50]. The lateral boundaries are at major faults, outcrops,
places where the caprock contains more than 50% sand, and places
shallower than 800m, as shown in Figure 5A.
Figure 4 Depth contours of the Fox Hills
Sandstone in the Powder River Basin [24].
6.2. Capacity calculations
In the Fox Hills Sandstone, the upslope migration of CO2 will likely be much stronger than migration due to
natural groundwater flow. This can be seen by comparing the slope number Ns to the groundwater-flow number Nf
[13,14]:
¤
sin (½b ¡ ½g )gkkrg
Ns
»
=
= 20:
Nf
U ¹g
(11)
As a result, we choose to orient the injection well array parallel to the depth contours in Figure 4 so that our
migration model will capture upslope migration. With the well array in this orientation, we set the length of the
aquifer L to the distance between the two lateral fault boundaries.
Using the aquifer length L and the data in Table 1 in Equation 5, we calculate the space-limited capacity to be 3.5
metric gigatons of CO2. As a check on our assumption of negligible dissolution, we calculate Ns =Nd to be about 90
(Eq.2). We draw the CO2 footprint for this capacity and the corresponding well array in Figure 5B.
Table 2 Data for the Fox Hills Sandstone.
Variable
Sbc
Sgr
kgr
k
Á
U
º
c
Pf rac
Units
mD
radian
cm/yr
GPa-1
GPa
Value
0.4
0.3
0.6
100
0.2
0.02
20
0.3
10
20
Reference
[20]
[20]
[20]
[21]
[19]
[18, Fig 56]
[17 ]
[17,22]
Note
assumed
assumed
assumed
assumed
calculated
calculated
Variable
H
W
L
z
¹b
¹g
½b ¡ ½g
½s ¡ ½b
assumed
Eq. 7
cs
®
Units
m
km
km
m
mPa s
mPa s
kg/m3
kg/m3
Value
100
200
60
1000
0.5
0.04
500
10
0.1
0.01
Reference
[19]
Note
Fig.5A
Fig.5A
[19]
[23]
[24]
[23,24]
[25,26,23]
[26]
[27]
estimated
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Figure 5 A. We set the eastern boundary of the Fox Hills Sandstone where the aquifer becomes shallower than 800m, the
approximate depth at which CO2 changes from a supercritical fluid to a gas. We use this boundary to ensure that CO2 is stored
efficiently in a high-density state. We set the remaining boundaries at large faults, outcrops, and places where the caprock has
more than 50% sand to minimize the possibility of leakage. B. The footprint of residually-trapped CO2 fills a large region of the
aquifer within the established boundaries, extending updip from the well array.
Comparing this capacity to the pressure-limited capacity shows that since the pressure-limited capacity grows as
T 1=2, it is smaller than the space-limited capacity for short injection periods. However, it eventually becomes larger
than the space-limited capacity at long injection periods, as shown in Figure 6. This indicates that pressure
constraints are more limiting for short injection periods, while space-constraints become more limiting for long
injection periods.
Figure 6 For a given reservoir such as the Fox Hills Sandstone, the pressure-limited capacity
grows with injection time. The space-limited capacity, however, is constant, despite the fact
that the CO2 may take thousands or tens of thousands of years to become fully trapped.
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