A simple but rigorous model for calculating CO[subscript
2] storage capacity in deep saline aquifers at the basin
scale
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Citation
Szulczewski, Michael, and Ruben Juanes. “A Simple but
Rigorous Model for Calculating CO2 Storage Capacity in Deep
Saline Aquifers at the Basin Scale.” Energy Procedia 1, no. 1
(February 2009): 3307–3314.
As Published
http://dx.doi.org/10.1016/j.egypro.2009.02.117
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Elsevier
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Final published version
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Thu May 26 05:33:43 EDT 2016
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http://hdl.handle.net/1721.1/96270
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Energy
Procedia
Energy
(2009)
EnergyProcedia
Procedia1 00
(2008)3307–3314
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www.elsevier.com/locate/XXX
www.elsevier.com/locate/procedia
GHGT-9
A simple but rigorous model for calculating CO2 storage capacity in
deep saline aquifers at the basin scale
Michael Szulczewskia, Ruben Juanesa*
a
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139
Elsevier use only: Received date here; revised date here; accepted date here
Abstract
Safely sequestering CO2 in a deep saline aquifer requires calculating how much CO2 the aquifer can store. Since
offsetting nationwide emissions requires sequestering large quantities of CO2, this calculation should apply at the
large scale of geologic basins. The only method to calculate storage capacity at the basin scale, however, is not
derived from multiphase flow dynamics, which play a critical role in CO2 storage. In this study, we explain a new
model to calculate basin-scale storage capacity that is derived from flow dynamics and captures the dynamic
phenomena of gravity override and capillary trapping. Despite the fact that the model is dynamic, it is simple since
it is a closed form expression with few terms. We demonstrate how to apply it on the Fox Hills Sandstone in the
Powder River Basin.
c 2008
2009Elsevier
ElsevierLtd.
Ltd.All
Allrights
rightsreserved
reserved.
©
Keywords: CO2 sequestration; storage capacity; deep saline aquifer; capillary trapping; gravity tonguing; Powder River Basin
1. Introduction
A promising technology for reducing anthropogenic carbon dioxide emissions is called geological carbon
sequestration (GCS) [1,2]. According to the MIT Coal Study, GCS is the critical enabling technology for coal in a
carbon-constrained world [3]. In GCS, CO2 is captured at large sources like coal-burning power plants and stored
away from the atmosphere in deep geologic reservoirs. In this study, we focus on particularly attractive types of
reservoirs called deep saline aquifers since they are widely distributed and have large storage capacities for CO2 [4].
While the collective capacity of deep saline aquifers is large, the safe deployment of CGS to a particular aquifer
requires accurately calculating the storage capacity of the aquifer. This capacity is the result of different physicalchemical mechanisms that trap CO2 in different ways. In a mechanism called structural trapping, the upward
* Corresponding author. Tel.: 1-617-253-7191.
E-mail address: juanes@mit.edu.
doi:10.1016/j.egypro.2009.02.117
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a. Geologic setting.
b. Injection and trapped CO2 footprints.
Figure 1. (a) The geologic setting for which the model applies. Key features include the scale, the presence of
natural groundwater flow, and the line-drive array of injection wells. (b) The footprints of the CO2 plume. The
dark blue footprint is the injection footprint and is measured by Linj. The light blue footprint is the trapped
footprint and is measured by Lmax . The total extent of the plume after it is trapped is measured by Ltotal.
migration of buoyant CO2 is suppressed by low-permeability layers [5]. In another mechanism called capillary
trapping, CO2 breaks up into small ganglia that are immobilized by capillary forces [6,7]. In solution trapping, CO2
dissolves in the formation brine [8]. Lastly, in mineral trapping dissolved CO2 reacts with reservoir rocks and ions
in the brine to precipitate carbonate minerals [9].
While these mechanisms cause CO2 to be trapped for long times, calculating the amount of CO2 that will be
trapped is a major challenge. Currently, calculations suffer from major shortcomings of accuracy, complexity, or
scale [10]. Numerical simulations can calculate capacity from structural, mineral, and solubility trapping with
reasonable accuracy, but these simulations are complex, require detailed geological information about the aquifer,
and are limited to local scales. The only option that can be used at regional and basin scales involves the use of
numbers called capacity coefficients that account only for structural trapping. Capacity coefficients are
multiplicative factors that relate the total pore volume of a reservoir to the pore volume that will be occupied by
trapped CO2 [11]. While in practice the pore volume occupied by CO2 is strongly affected by multiphase flow
dynamics, these coefficients do not rigorously account for critical dynamic phenomena like gravity instabilities. As
a result, current estimates of storage capacity are highly variable and often contradictory [12].
In this study, we demonstrate a new model to calculate storage capacity. This model applies at the basin scale
and is both rigorous and simple. It is rigorous because it is derived from multiphase flow dynamics, and it is simple
because it is a closed-form, analytical expression with few parameters. In addition to providing a way to calculate
capacity, our model provides a visual way of assessing CO2 storage: it shows the total areal extent of the stored
CO2, which we call the hydrogeologic footprint. We demonstrate how to apply this model to calculate the storage
capacity of the Fox Hills Sandstone in the Powder River Basin.
2. Trapping Model
We provide a full derivation of our mathematical model in another paper [13]. In this paper, we briefly explain
the model at the conceptual level and discuss the geologic setting for which it applies. We also review its
assumptions and present the relevant equations.
Our model applies to the geologic setting shown in Figure 1. This setting has three important features. The first
important feature is scale. The model applies to CO2 sequestration at the basin scale, which typically involves
lengths of tens to hundreds of kilometers. The second key feature is the presence of natural groundwater flow. In
our model, CO2 is injected into a deep saline aquifer and, after injection, migrates in the direction of groundwater
flow. The third key feature is the pattern of injection wells. We model injection from a line-drive array of wells for
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3
which flow does not vary greatly in the direction parallel to the line drive. This allows us to model the flow in one
dimension.
The model captures two important multiphase flow phenomena that occur during sequestration. The first
phenomenon is gravity override. Gravity override describes how CO2 migrates to the top of a reservoir both during
and after injection, forming a “tongue” that spreads parallel to the low-permeability caprock. The second
phenomenon is capillary trapping. Capillary trapping describes how CO2 becomes disconnected into immobile
globules. It occurs after injection when brine flows into pore space at the trailing edge of the migrating CO2 plume
[14].
As with any simple model that captures complex phenomena, our model includes a number of assumptions. We
assume that the reservoir is horizontal, homogeneous, and isotropic, and that the injected plume migrates in the
direction of groundwater flow. We assume that fluid viscosities and densities are constant. We assume that there is
a sharp interface between the CO2 plume and the brine (sharp-interface approximation), and that spreading effects
due to a nonzero gravity number can be neglected [13]. Lastly, we assume that the CO2 stored by mineral trapping
and solution trapping can be ignored. This assumption is valid at small time scales because solution trapping and
mineral trapping operate chiefly at larger time scales [15, p.208].
There are two important equations of the model. The equation to calculate the storage capacity is:
·
C=
¸
2M¡2 (1 ¡ Swc )
½CO2 ÁHW Ltotal ;
¡2 + (2 ¡ ¡)(1 ¡ M + M ¡)
(1)
where C is the mass of trapped CO2, ¡ is the trapping coefficient, M is the mobility ratio, ½CO2 is the density of
CO2, Á is the porosity, W is the length of the injection array, H is the net sandstone thickness of the reservoir, and
Ltotal is the total extent of the CO2 plume (Fig.1b). We define the mobility ratio as:
M=
1=¹w
¤ =¹
krg
g
(2)
¤
where ¹w is the viscosity of brine, ¹rg is the viscosity of CO2, and krg
is the endpoint relative permeability to CO2.
We define the trapping coefficient as:
¡=
Srg
1 ¡ Swc
(3)
where Srg is the residual saturation of CO2 and Swc is the connate water saturation.
The term in brackets in Equation 1 is a key feature of our model. It relates total pore volume of an aquifer to the
volume of trapped CO2. We call it the efficiency factor, and it plays a similar role to currently used capacity
coefficients.
The second important equation in our model is used to draw the CO2 footprint. It calculates the distance the
plume has migrated away from the well array when it is completely trapped (Fig.1):
·
Lmax =
¸
(2 ¡ ¡)(1 ¡ M (1 ¡ ¡))
Ltotal
(2 ¡ ¡)(1 ¡ M(1 ¡ ¡)) + ¡2
(4)
The distance the plume travels during injection Linj is then given by:
Linj = Ltotal ¡ Lmax
(5)
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3. Storage Capacity of the Fox Hills Sandstone
3.1. Geohydrologic Setting
The Fox Hills Sandstone occurs in the Northern Great Plains. In this study, we calculate storage capacity for
deep parts of the formation in the Powder River Basin. This basin is an asymmetric foreland basin that lies in
Montana and Wyoming.
The Fox Hills Sandstone is Upper Cretaceous in age. Its composition differs in detail in different areas, but in
general it consists of massive, fine- to medium-grained sandstone with siltstone and minor shale, which are
sometimes interbedded [16, p.T68]. The depth to the top of these rocks, and the net sandstone thickness, is shown in
Figure 2.
The formation is conformably overlain by and intertongued with the Hell Creek Formation in Montana and the
Lance Formation in Wyoming [16, p.T68]. These formations differ only in geography and provide an extensive top
seal called the Upper Hell Creek Confining Layer [18, p.82]. The Fox Hills is conformably underlain by marine
shale and siltstone in the Lewis Shale or Pierre Shale, which form an aquiclude [19, Plate II].
Porosity in the Fox Hills Sandstone is poorly known. We found data for only the West Side Canal Field in the
Green River Basin, in which the porosity is reported to be 0.21 [20, qtd. in 17]. The flow direction over most of the
basin is south to north, as shown in Figure 3. In the southern part of the basin, however, the flow direction is from
west to east.
3.2. Capacity Calculation
The first step in calculating the storage capacity of the Fox Hills Sandstone is identifying the spatial domain over
which to apply the model. We do this by drawing boundaries around the aquifer based on three criteria: the
likelihood of CO2 leakage, the uniformity of the regional flow direction, and the depth of the formation. These
boundaries are shown in Figure 4. To limit leakage, we draw boundaries at outcrops [21, Fig.10], large faults [21,
Fig.10], and places where the caprock contains more than 50% sand [17, Map c8foxhillsg]. While the leakage
properties of faults and sandy parts of the caprock are unknown—faults, for example, may in general be conduits or
barriers for flow—we identify these features as boundaries to be safe since little or no data is available to evaluate
the leakage risk.
In addition to drawing boundaries based on leakage, we draw boundaries where the regional flow direction is
non-uniform since our model assumes a uniform flow direction. Based on this criterion, we draw a boundary in the
b. Net sandstone thickness.
Figure 2. Depth and net sandstone thickness in the Fox Hills Sandstone. (a) Modified from [17, Map
c1foxhills]. (b) Modified from [17, Map c4foxhillsg].
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southern part of the basin where the flow direction abruptly changes, and a
boundary at the northern part of the basin where the streamlines sharply
converge (Fig.3).
We draw the last type of boundary where the top of the reservoir is 800m
deep. Assuming a hydrostatic pressure gradient and a geothermal gradient
of 25°C/km, this is the depth at which CO2 becomes a supercritical fluid.
We define it as a boundary to ensure that CO2 is stored efficiently in a highdensity state.
All of the boundaries constrain both the placement of injection well array
and the migration of the CO2 plume except for the depth boundary. We
choose for this boundary to constrain only the placement of the well array.
This is because using it to constrain plume migration would unnecessarily
limit the portion of the reservoir used for storage: since most of the injected
CO2 is stored in the vicinity of the well array [13], allowing the thin leading
front of the plume to migrate above 800m depth will not strongly affect the
storage efficiency of most of the plume.
After identifying the boundaries of Fox Hills Sandstone, we set values of
the input parameters in the trapping equation (Eq.1). Our methodology
involves two key features. The first key feature is the source of the data we
use to set the parameters. We set some of the parameters based on data from
the formation itself, and set others based on laboratory experiments since the
relevant data does not exist for the formation. The second key feature is how
we handle variability and uncertainty. Since geologic data can be highly
uncertain and the parameters in the model can vary widely at the basin
scale, handling variability and uncertainty is a major challenge for our
model. For parameters set based on experiments, we address this challenge
by using a range of values that covers the range of experimental findings.
For parameters set from reservoir data, we use average values for the
formation taken from the area within the 800m-depth boundary, where most
of the CO2 will be stored.
We set the following parameters based on laboratory data: the connate
water saturation Swc, the residual CO2 saturation Srg , and the endpoint
¤
relative permeability to CO2 krg
. The data we use are from Bennion and
Bachu [22]. We use this data to posit three scenarios consistent with
minimal CO2 trapping, maximum trapping, and average trapping. These
scenarios and the values we use for the parameters are listed in Table 1,
along with the resulting trapping coefficients (Eq.3). We use each of these
scenarios to calculate a minimum, maximum, and average storage capacity.
We set the remaining parameters based on data from the reservoir (Table
2). We set porosity to 0.21, assuming that the only measurement we found
is representative of the formation in the absence of other data. We set the
net sandstone thickness to 120m based on the map in Figure 2. Lastly, we
calculate the density of CO2 and the mobility ratio as functions of
temperature and pressure in the reservoir. We calculate temperature in the
reservoir to be about 66°C using a geothermal gradient of 35°C and an
average formation depth of 1500m [23]. We calculate pressure to be 15
MPa using a hydrostatic gradient. With this temperature and pressure, we
calculate the density of CO2 using an online thermophysical property
calculator provided by MIT [24]. We also use the calculator for the
viscosity of CO2, and use a correlation function to calculate the viscosity of
brine [25]. We then use these viscosities, together with the endpoint relative
permeability to CO2 from our average-trapping scenario (Table 1), to
5
Figure 3. Isopotential contours for
Upper Cretaceous aquifers in the
Powder River Basin. Numbers
represent head in feet, from a
datum of sea level. Modified
from [21, Fig.56]
Figure 4. Boundaries for the Fox
Hills Sandstone.
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Table 1. Trapping scenarios and the corresponding CO2-brine displacement parameters.
¤
krg
Trapping Scenario
Swc
Srg
¡
Less Trapping
0.5
0.5
0.2
0.40
Average Trapping
0.3
0.7
0.4
0.57
More Trapping
0.4
0.6
0.3
0.50
calculate the mobility ratio (Eq.2).
The final parameters to set in our equation are the width of the injection well array W and the total extent of the
CO2 plume Ltotal (Fig.1). The width of the injection well array is constrained by the smallest distance between the
boundaries perpendicular to the flow direction. This constraint restricts CO2 from crossing a boundary during
migration of the plume. We measure it to be about 42 km. The total extent of the plume Ltotal is constrained by the
distance between boundaries parallel to the flow direction. We measure it to be about 299 km.
We now have all of the parameters required to calculate storage capacity using Equation 1. For the averagetrapping scenario, we calculate the storage capacity to be about 5 gigatons of CO2 and the efficiency factor to be
about 1.2%. Table 3 lists the results for the other trapping scenarios.
3.3. Hydrogeologic Footprint
To draw the hydrogeologic footprint, we first calculate the extent of the
trapped plume Lmax using Equation 4. For the average trapping scenario,
we calculate Lmax to be about 253 km. As shown in Figure 5, we draw the
footprint of the trapped plume by measuring out this distance from the well
array along streamlines, since the CO2 will migrate with the regional ground
water flow. We next calculate the extent of the injection plume Linj using
Equation 5. For the average trapping scenario, we calculate Linj to be about
46 km. We draw the footprint for this plume by measuring out the distance
Linj on both sides of the well array (Fig.5). We measure this distance
perpendicular to the array because the pressure gradient from injection
drives flow during the injection phase, and this gradient will predominantly
point perpendicular to the array.
Figure 5. Hydrogeologic footprint
of CO2 storage.
Our model for calculating storage capacity has both advantages and disadvantages. One disadvantage is that its
assumptions are fairly restrictive. For example, it assumes that solubility and mineral trapping are unimportant at
small timescales. Also, it assumes the aquifer is horizontal, which means it neglects migration of CO2 upslope due
to any non-zero dip in the caprock. Another disadvantage is that the uncertainty in the capacity estimates is fairly
large. As shown for the Fox Hills Sandstone, the difference between the upper and lower capacity estimates is about
3 gigatons of CO2 (Table 3).
While the model has shortcomings, it has significant advantages over using capacity coefficients, which is the
only other technique currently available for calculating capacity at the basin scale. One advantage is that it is simple
to apply since it is a closed form expression with few terms. Using capacity coefficients, however, is difficult since
4. Discussion
Table 2. Input parameters in the model.
Parameter
Value
Á
0.21
120 m
H
42 km
W
Ltotal
299.3 km
Average-trapping M
0.26
½CO2
540.5 kg/m3
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Author name / Energy Procedia 00 (2008) 000–000
3313
7
Table 3. Results from the storage capacity calculations.
Scenario
Efficiency Factor (%)
Capacity (gigatons)
Less Trapping
0.8
3.3
Average Trapping
1.2
5.0
More Trapping
1.6
6.4
there are almost no published values of coefficients in the literature and there is no rigorous way of deriving them
[10]. The only published values we found come from the Carbon Sequestration Atlas by the National Energy
Technology Laboratory (NETL), but the derivation of these values is unclear [11]. Another advantage is that our
model produces physically meaningful estimates since it is based on multiphase flow dynamics. Capacity
coefficients, on the other hand, either ignore dynamics or use overly simple multiplicative factors to account for
dynamics. For example, the NETL multiplies the total pore volume of an aquifer by factors between 0.6 and 0.4 to
account for gravity instabilities [11]. The final advantage of our model is that it is based on reservoir-specific
geohydrology. While capacity coefficients should also be reservoir-specific, in practice the NETL uses the same
capacity coefficients for all reservoirs [11].
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