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Energy Procedia 1 ( 2(009) 2549-2556
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Simplified CO2 plume dynamics for a Certification Framework for geologic sequestration projects
Navanit Kumar, Steven Bryant and Jean-Philippe Nicot*
Dept. of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300, Austin, TX 78712, USA
Abstract
A framework for certifying and decommissioning CO2 geologic sequestration sites is a critical requirement for large-scale deployment of CO2 sequestration in brine formations. The certification process should account for the sequestration efficiency of a given volume of a saline aquifer. The sequestration efficiency is determined by maximizing CO2 trapping while minimizing the leakage risk. As part of the development of the Certification Framework, we carried out a large number of compositional simulations to quantify the effect of various reservoir and operating parameters. Porosity, horizontal permeability, permeability anisotropy, formation thickness and dip, pressure, and temperature were systematically varied. Operating parameters such as injection rate, vertical vs. horizontal well and perforation interval were investigated. We then developed several simplified models of CO2 plume behaviour and verified them against sophisticated reservoir simulations.
The simple models captured the following trends: leakage potential increases (1) as the time for the CO2 plume to reach the top seal of the aquifer decreases; (2) as the lateral distance travelled by the plume increases, and (3) as total mobile CO2 increases. We studied one risk parameter in detail, the time for the CO2 plume to reach the aquifer top seal, and showed that it varies systematically with gravity number, defined as the ratio of gravity forces to viscous forces. Likely behaviour of an actual saline aquifer relative to that one risk parameter is easily captured by interpolation within the catalogue of detailed simulations for different reservoir and operational parameters. We illustrate the application of these simplified models to assess risks of leakage for a hypothetical sequestration project in a gas storage reservoir for which extensive characterization is available.
© 2009) Elsevier Ltd. All rights reserved.
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1. Introduction
Uncertainties are associated with the injection and storage of CO2 in the deep subsurface especially in aquifers. Regulators will need guidelines for commissioning or decommissioning a geological site for CO2 sequestration that account for these uncertainties in a quantitative fashion. A suitable framework for certifying and decommissioning sites is therefore a critical requirement for large-scale deployment of CO2 sequestration. The certification process should account for the sequestration efficiency of a given volume of a saline aquifer. By sequestration efficiency we mean maximizing CO2 trapping while minimizing the leakage risk. In this paper we will consider leakage risk to
* Corresponding author Tel.: 512-471-3259; fax: 512-471-9695. E-mail address: steven_bryant@mail.utexas.edu.
doi:10.1016/j.egypro.2009.02.019
increase as the time for the CO2 plume to reach the top seal of aquifer decreases; as the lateral distance traveled by the plume increases, and as total mobile CO2 increases.
For quantification of risk the system is divided into compartments (Oldenburg and Bryant [1]). One compartment is the saline aquifer in which CO2 is stored. Other compartments are formations of economic or environmental importance into which CO2 could leak and thereby contaminate existing resources. These compartments can be subsurface, e.g. hydrocarbon reservoirs or underground sources of drinking water, or at surface, e.g. local sites where leakage occurs, and distant sites affected due to wind from leakage location. Conduits for leakage from source to compartments or from one compartment to another may be well(s) or fault(s).
The CO2 leakage risk (CLR) in each compartment is defined as
CLR = Impact x Total Probubility (1)
Impact is a consequence to a compartment and evaluated by proxy as CO2 concentration or CO2 flux into the compartment. The total probability is the product of the following probabilities:
a) Fault or well intersecting a compartment: For leakage to occur into a compartment there should be a conduit from the source compartment to leakage compartment.
b) Fault or well intersecting CO2 plume: This is the probability of CO2 coming in contact with the leakage conduit. When CO2 is injected in saline aquifer, it travels some lateral distance due to viscous and/or gravity forces and may thereby come in contact with conduits.
c) Fault or well being conductive: This probability quantifies whether the fault or well is conductive or sealed. As indicated schematically in Fig. 1[a], we thus have
Total Probability = Probability (u) X Probability (b) X Probability (c). (2)
2. Response Variables
Ideally CO2 injection operations will keep indefinitely the CO2 in the injection formation and will not allow any leak to any resources or atmosphere. Thus the probability of intersection of migrating CO2 plume with probable leakage conduits such as faults or abandoned wells needs to be minimized. To define the leakage potential of an aquifer we consider three response variables extracted from the output of simulations of CO2 storage in aquifer. These are 1) Total mobile CO2 in the aquifer, 2) Maximum lateral distance traveled from the injector (i.e. extent of the edge of the CO2 plume) and 3) Time the plume takes to reach the top seal. These are indicated in Fig. 1[b].
Injector
[a] [b]
Figure 1[a]: Schematic showing different probabilities: (a) probability of fault or well intersecting a compartment. (b) probability of fault or well intersecting CO2. (c) probability of fault or well being conductive. [b] Schematic showing aquifer system with a vertical injector in center. Well is perforated in bottom half section of thickness. Three response variables (time to hit top seal, maximum lateral extent and total mobile gas) are shown.
Total mobile CO2 is the CO2 in gas phase which is mobile or has potential to be mobile. This is the CO2 which has not been trapped by dissolution, residual trapping or mineralization. Any CO2 held beneath top seals, anticlines,
unconformities or faults is considered here as mobile as it would leak if the sealing structures were to lose integrity. For the purposes of this work this means CO2 held at saturations exceeding the residual phase saturation.
Maximum lateral distance is the distance the CO2 plume travels in horizontal or dipping direction from the injector. In the simulation it is considered as the farthest point from the injector reached by the CO2 plume within 1000 years after injection begins. The farther the plume travels, the greater its chance of intersecting leaky faults or abandoned wells.
Time to reach top seal is zero if CO2 is injected across the entire thickness of an aquifer. If CO2 is injected at the bottom of the aquifer, it will move vertically until it reaches the top seal. Then the plume moves laterally under the top seal. This movement can be rapid and extensive. Thus the smaller the time to reach top, the greater the leakage risk.
3. Simulation Catalog
As part of the development of the Certification Framework, we carried out several hundred compositional simulations to quantify the effect of various reservoir and operating parameters. Porosity, horizontal permeability, permeability anisotropy, formation thickness and dip, and depth were systematically varied (Kumar [2]). Operating parameters such as injection rate, vertical vs. horizontal well and perforation interval were also investigated. The risk parameters (time to hit top, maximum lateral extent and total mobile gas) were extracted from these simulations. The goal of simulations was to create a catalog, from which reasonable estimates of risk factors could be obtained if certain basic characteristics of the storage target formations were known.
The simulation models included in the framework are representative of field situations, but they are not exhaustive. The simulations capture the CO2 plume behavior in the source compartment (saline aquifer). This can be combined with appropriate leakage models (e.g. Chang [3]) to assign CLR to a geological site.
3.1. Parameterization Using Gravity Number
Gravity number is the dimensionless ratio of gravity forces to viscous forces in a reservoir. The gravity number determines the shape of the CO2 plume in aquifer. Thus it is convenient to parameterize the plume behavior in terms of gravity number, defined as follows:
N = kvApgcos« (3)
where kv = vertical permeability, Ap = density difference between brine and CO2 at aquifer temperature and pressure, a = dip angle, f = CO2 viscosity, and u = flow velocity. Here the velocity is taken as the Darcy velocity of CO2 at sand face, measured at reservoir conditions:
= Qrc (4)
A 2^rwhp
Using gravity number to characterize CO2 sequestration efficiency confers the advantage of combining the effects of many of the reservoir and operating parameters. Essential features of a plume can be predicted just by computing the gravity number. Thus if one sequestration project has been intensively modeled and its efficiency estimated, then a good estimate of the efficiency of a second project can be obtained by comparing the gravity numbers for the two cases. The usefulness of these correlations is in developing simplified models of sequestration efficiency, which are needed for the development of regulatory frameworks for geologic CO2 sequestration.
One risk parameter, time to hit the top seal, is studied in detail below. A plot of time to hit the top vs. gravity number shows a reasonable trend if the time to hit top seal is normalized by a characteristic time t*:
= (H - h1)h2fw0 (5)
where, H = formation thickness, h1= distance to top perforation in vertical well from aquifer bottom or distance of center of horizontal well from bottom, h2 = perforation interval, rw = wellbore radius, 0 = porosity, and Qrc = injection rate at reservoir conditions.
These variables are shown in Figure 2[a]. The characteristic time, t is the time the plume would take to hit top seal if it were traveling at constant velocity v equal to the average velocity at sandface.
(¡>Aw 2nrjh1^
where v = radial velocity coming out of well and. I„= circumferential area of well.
l.E+09 l.E+08 l.E+07 l.E+06 * l.E+05 ~ l.E+04 l.E+03 l.E+02 l.E+0l l.E+00
l.E-08 l.E-07 l.E-06 l.E-05 l.E-04 l.E-03 l.E-02 l.E-0l l.E+00 Gravity Number
Figure 2[a]: Schematic for vertical and horizontal well showing the parameters used in characteristic time. [b]: Plot of dimensionless time to hit top seal vs gravity number. The data points are from simulation carried out by varying porosity, permeability, permeability anisotropy, thickness, depth, perforated interval. It includes all the cases in simulation catalog including horizontal wells. The characteristic time t* differs for each case, see Eq. 5.
The minimum distance traveled by plume tip to reach top seal is denoted by d:
d = (H - h) (7)
From above
Int = d = 2nrwh2<i>(H - K) (8)
Eq. 5 follows from Eq. 8, dropping the constant factor of
Thus t/t* is the ratio of actual time taken by the plume to the time taken when it travels at constant velocity v in vertical direction. When the gravity number is large, the plume travels almost vertically and t/t* is closer to l. When gravity number is small, the plume travels more in lateral direction, and t >> t*. Thus dimensionless time (t/t*)
should vary inversely with gravity number. Plotting these values for the catalog simulations confirms this trend, Fig. 2[b].
4. Using simulation catalog for estimating risk parameters for actual aquifer
The simulation catalog contains cases for low, medium and high values of the properties listed in Table 1. Most aquifers will not have all properties similar to any one case in catalog. In order to predict the risk parameters for an actual case we can estimate the risk parameters from the closest catalog case using some simplified models. In this section we discuss the methodology of extrapolating the risk parameters.
Table 1—Reservoir and Operating Parameters for Fulshear Case and Closest Catalog Case
Property Fulshear Aquifer Closest Catalog Case
Porosity 0.25 0.25
Permeability, md 136 100
Thickness, ft 50 100
Permeability anisotropy 0.04 0.03
Dip 1 1
Depth, ft 7,000 10,000
Well type Vertical Vertical
Injection rate 0.8 Mt/yr 0.8 Mt/yr
Perforation interval Fully perforated Fully perforated
Period of injection 30 yrs 30 yrs
Gravity number 0.001 0.00085
CO2 density, lb/ft3 38 47
CO2 viscosity, cp 0.06 0.085
CO2 solubility in aqueous phase, mole fraction 0.021 0.025
4.1. Time to hit the top seal
The gravity number and characteristic time (t*) are readily calculated for the actual aquifer. The trendline in Fig. 2[b] can then be used to predict the time to hit the top seal.
4.2. Lateral extent
The lateral extent of the plume at the end of injection period can be estimated from the closest catalog case by assuming that the shape of the plume stays the same. This assumption is valid only when the closest catalog case has gravity number similar to that of the actual case. We correct for the actual volume injected:
XR aH afiaS g.avg.aPco2a = ( 9a / qdb R dbH dbfidbSg , avg , dbPco2db ( '
which can be re-written as
R 2 - R 2 H db $db Sg,avg,db Pco2,db qa (10)
a db rr , <-.
a Ta g,avg,a r co-2 a
where Ra and Rdb are the lateral extent in actual aquifer case and catalog case respectively. Similarly H is the thickness, q is the injection rate, 0 is the porosity, S&avg is the average gas saturation behind the Buckley-Leverett saturation front (dependent on relative permeability, calculated from Welge's construction, Burton et al. [4]) and p is the density of CO2 which is dependent on the pressure and temperature. In the above case the injection periods are assumed identical.
If the injection periods differ, say t1 for actual case and t2 for the catalog case, the lateral extent of plume in the catalog is first estimated at time t1. From the Buckley-Leverett theory in radial system the radial distance r travelled by the brine-displacement shock front increases with the square root of time:
where t is the time period of injection. So the radial extent of plume in case of catalog case after time t1 is calculated as
Rdb,t1 Rcib,t2\l t
K (11)
where Rdbt1 and Rdb,t2 are the lateral extent of the plume in catalog case at time t1 and t2 respectively. After getting Rdb,a, Equation 10 can be used to find the lateral extent after time t1 in the actual case. If the gravity number in these two cases differs significantly (order of magnitude), then the shape of plume will be different. For example in a gently dipping reservoir if the gravity number is low the plume will be symmetric around the injector during injection period. At higher gravity number the plume will travel preferentially up dip and is asymmetric around the injector. Thus a catalog case of similar gravity number is required for correct estimation.
After injection stops the plume travels under gravity. The plume velocity is proportional to the following quantity:
OC^Apsina (i2)
From the most similar catalog case the distance travelled by plume over certain period of time like 100 years and 1000 years is extracted. The distance travelled by the plume under gravity will be the additional distance the plume travels after injection is stopped. By taking the ratio of plume velocity which is the ratio of parameters in Eq. 12 the distance travelled by plume under gravity in actual case can be calculated.
US.u = sm«a VS,u = R (13)
Ugdb kh,db APdb sma
db Mg,db
where subscripts 'a' and 'db' are actual and catalog case. The distance travelled under gravity in the actual case is thus
Lg,u=Ru Lg,db
where, Lgu Lgddb are the lateral distance travelled by plume under gravity (after injection is stopped) in actual and simulation catalog case.. The total lateral distance (Lu) then will be the sum of the distance travelled during injection period and travelled under gravity.
Lu= Ru + Lg,u
4.3. Total mobile gas
The dissolution and residual phase trapping of CO2 depend on the volume of rock and brine contacted by CO2 plume. In the dipping reservoir the plume will travel a longer distance and thus trap a larger amount of CO2. Pressure and temperature also affect the solubility of CO2. With increase in pressure the solubility of CO2 in brine increases whereas with increase in temperature it decreases.
The trapped CO2 is broken into two contributions: the amount dissolved into brine and amount trapped as residual phase. This allows for an estimate of total trapping for an actual aquifer from catalog simulations. During the injection period in most of the regions of aquifer, drainage process occurs as CO2 displaces brine. The major trapping mechanism in that case is by dissolution of CO2 in brine. It is important that the gravity number of catalog case be similar to the actual aquifer case so that the plume shape is similar in both cases.
4.4. Definition of trapped CO2
The total mobile gas is expressed as percentage of total injected gas: MG =100-TG, where, MG= % mobile gas and TG = % trapped gas. Thus the trapped gas TGdb,1 in the catalog case after the injection period can be calculated as TG/bi = 100-MGdbi where MG/biis the percent mobile gas after injection period in catalog case.
4.5. Trapping by dissolution during injection period
Trapping by dissolution of CO2 into the aqueous phase in actual case can be estimated from the catalog case by
RdbHdb&dl
1 - S.
g ,avg1
1 - S.
g,avg 2 y
where, TGai and TGdb,i are the trapped gas in the actual case and catalog case at the end of injection period. Xco2,1 and Xco2,2 are the solubility of CO2 in aqueous phase in actual case and catalog case. Solubility is expressed in terms of mole fraction of CO2 in aqueous phase. This is dependent on pressure and temperature which can be different for actual and catalog case. TGdb i can be calculated as TGdbi = 100-MGdbi where MGdb iis the percent mobile gas after injection period in catalog case. Then TGa i is calculated from Equation 14. The mobile gas in actual case after injection period is given by MGai = 100 - TGai.
4.6. Trapping after injection is stopped
After injection is stopped the plume travels under gravity. Plume travels in vertical or updip direction where it comes in contact with more unsaturated brine and further dissolution takes place. Also due to countercurrent movement of brine, imbibition takes place and CO2 is also trapped as residual gas. The trapping as residual saturation is dependent on relative permeability and the maximum trapped gas saturation. In the simulation catalog cases mentioned in Kumar, 2008, the injection period is 30 years. Percentage mobile gas is listed for 30 years, 100 years and 1000 years. After 30 years the plume migrates under gravity. The additional trapping (total trapping after 100 or 1000 years minus trapping after 30 years) in catalog case under gravity is given by,
TGdb t - TGd
where, TGdb,t is the total trapped gas after 100 years or 1000 years (depending on when the trapped gas is required for actual case) given by
TGdbt = 100 -MG,
where MGdb,t is the total mobile gas after 100 years or 1000 years in simulation catalog.
The farther the plume travels the more it will come in contact with rock and brine, thus the trapping during migration under gravity is proportional to the lateral distance travelled under gravity.
TGa,g = TG^
Lg ,aHa V Lg,dbHdb y
(1 — S ) X
^ g ,avg ,a> co2 a
(1 - S,
co7 db
V gt,avg,db y
where, Sgt,avg is the trapped gas saturation when imbibition starts at a saturation of Sg,avg.. It can be obtained from Land's model of hysteresis as shown below
S - S S - S S - S S - S
^gt ,max ^gr g ,max ^ gr u gti u gr u gi u gr
In this equation if Sgi = Sg,avg, then Sgti=Sgt,avg (Sgr=0), as there is no residual gas saturation at the start and Sgt,Nax is the characteristic property of rock.
After calculating TGa,g from Equation 15, total trapped gas in actual case can be calculated as TGat= TGai + TGag and total Mobile Gas as ' MGa,t = 100 - TGat
In the following sections the above mentioned simulation catalog is applied to predict the response variables for an actual aquifer. To check the validity of the estimation procedure the response variables are then compared with those obtained from simulating the actual aquifer case.
5. Comparison of simplified models with actual simulations
A case study of the application of the Certification Framework (CF) was carried out on a hypothetical geologic CO2 storage project targeting the down-dip water leg of the Fulshear natural gas storage reservoir southeast of Katy, Texas (Oldenburg and Bryant [1]). The detailed properties of aquifer are shown in Table 1. The simulation from catalog having properties closest to that in aquifer was selected as catalog case. The simplified models described above were applied to estimate the response variables. Then a direct simulation was carried out using the Fulshear aquifer parameters and the estimated response variables are compared with actual simulation results. The comparison is tabulated in Table 2.
Table 2—Comparison of Response Variables from Catalog Case, Expected Fulshear Case from Simplified Models, and Actual Fulshear Simlation Case
Closest Cutulog Estimated Fulsheur Cuse Direct Simulation Cuse from Simplified Models of Fulsheur Cuse
Lateral extent after 30 yrs 4,750 7,500 8000
Lateral extent after 1000 yrs 13,250 31,800 29500
Mobile gas after 30 yrs (% of injected) 70 68.5 66
Mobile gas after 1000 yrs (% of injected) 19 9.9 9.3
6. Conclusion
A simulation catalog has been created by varying a large number of reservoir and operating parameters to cover essentially a large variety of saline aquifers. The response variables (time to hit the top seal, maximum lateral extent and total mobile gas) can be obtained from these simulations. In order to obtain response variables for actual aquifers, simplified models discussed in this paper can be used. These response variables determine the CO2 sequestration efficiency of aquifer.
Acknowledgements
The CO2 Capture Project Phase 2 (CCP2) supported this work.
References
1. Oldenburg, C.M., Bryant, S.L., "Certification Framework for Geologic CO2 Storage", Presented at NETL CCS conference, May 2007
2. Kumar, N, "CO2 Sequestration: Understanding the plume dynamics and estimating risk", MS Thesis, The University of Texas at Austin, 2008.
3. Chang, K., "A Simulation Study of Injected CO2 Migration in the Faulted Reservoir", MS thesis, The University of Texas at Austin, 2007.
4. Burton, M., Kumar, N., Bryant, S.L., "Time -Dependent Injectivity During CO2 Storage in Aquifers", paper SPE 113937 presented at SPE Improved Oil Recovery symposium in Tulsa, April 2008.
