Applying fractional flow theory to evaluate CO2 storage capacity of an aquifer

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Applying Fractional Flow Theory to Evaluate CO2 Storage Capacity of an Aquifer Rouzbeh Ghanbarnezhad Moghanloo, Younas Dadmohammadi, Yuan Bin, Shadi Salahshoor

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S0920-4105(14)00373-8 http://dx.doi.org/10.1016/j.petrol.2014.11.013 PETROL2853

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Received date: 30 July 2011 Accepted date: 12 November 2014 Cite this article as: Rouzbeh Ghanbarnezhad Moghanloo, Younas Dadmohammadi, Yuan Bin, Shadi Salahshoor, Applying Fractional Flow Theory to Evaluate CO2 Storage Capacity of an Aquifer, Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2014.11.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Applying Fractional Flow Theory to Evaluate CO2 Storage Capacity of an Aquifer

Rouzbeh Ghanbarnezhad Moghanloo, Younas Dadmohammadi; Yuan Bin; Shadi Salahshoor The University of Oklahoma *Corresponding author: Rouzbeh G. Moghanloo The University of Oklahoma [email protected]

Abstract In this paper, an application of fractional flow theory is used to evaluate CO2 storage capacity of an aquifer because of two trapping mechanisms: capillary snap-off and gas dissolution. The capillary snapoff and CO2 dissolution into the resident aqueous phase are two major trapping mechanisms of the CO2 sequestration in geological formations over intermediate time-scale. In practice, numerical simulations are used to assess the CO2 storage capacity of a geological formation and evaluate various trapping mechanisms; however, the simulations are complex and time-consuming and they require detailed inputs. Whereas, the presented method requires limited inputs and provides fast results in agreement with the simulation that makes it suitable tool to compare and screen the CO2 storage potential of various formations. The notion of optimal solvent-water-slug size is adopted as the ultimate CO2 storage capacity for a given permeable medium. A combined graphical solution of multiple geochemical front propagation and fractional flow theory is used to determine the CO2 storage capacity of one-dimensional (1D) models; i.e. the largest slug of injected CO2 that is trapped because of the capillary trapping and the CO2 dissolution. Injecting larger amount of CO2 than the optimum slug size causes the CO2 breakthrough (over capacity) while smaller slugs leaves the aquifer unfilled (under-capacity). We use numerical simulation to validate the accuracy of the predicted optimal slug size. Next, we incorporate gravity override as the governing two-dimensional (2D) phenomenon affecting the storage capacity. The impact of 2D effects is applied via a multiplying factor that reduces the ultimate storage capacity and depends on the reservoir aspect ratio and buoyancy number. In practice, the 1

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proposed method provides an efficient screening method to assess the CO2 storage capacity of aquifers and significantly reduces the simulation costs while providing an interesting insight. Keywords: CO2 storage capacity, fractional flow theory, gravity override Introduction CO2 capture and geological storage (CCGS) is a promising technology for long-term storage of CO2 to mitigate its accumulation in the atmosphere and detrimental impacts on climate. However, a general lack of knowledge about an accurate storage capacity of deep saline aquifers stands in the way of immediate full-scale implementation of CCGS (IPCC 2005; Bradshaw et al. 2007; Bachu et al. 1994). Our focus in this study is to present a new screening tool to examine various geological formations for their CO2 storage capacity. Evaluation of the CO2 storage capacity in saline aquifers is very complex as there are multiple trapping mechanisms acting simultaneously at different rates. In the context of CO2 storage in aquifers, the involved trapping mechanisms are: 1. Structural (hydrodynamic) trapping, the upward migrating buoyant CO2 is suppressed by an impermeable cap rock (Bachu et al. 1994) 2. Capillary snap-off trapping, injected CO2 breaks up into immobile ganglia (Kumar et al. 2005; Juanes et al. 2006) 3. Solubility trapping, CO2 dissolution in an aqueous phase (Ennis-King and Paterson 2005; Riaz et al. 2006) 4. Mineral trapping, dissolved CO2 reacts with rock minerals and leads to carbonate minerals precipitation (Gunter et al. 1997) 5. Local capillary trapping, accumulation of the upward migrating buoyant CO2 beneath of a region with larger capillary entry pressure than average (Saadatpoor et al. 2010) This study is mainly focused on the two trapping mechanisms that are likely to be effective on an intermediate time-scale: capillary snap-off and dissolution trapping (Sifuentes et al. 2009; Juanes et al.

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2009). Injected CO2 in an aquifer displaces the resident water under a drainage mechanism (assuming the gas phase is nonwetting). Resident or post-injection water displaces CO2 through an imbibition process (Fig.1). The hysteresis in the gas relative permeabilities causes snap-off at the pore scale and, subsequently, trapping of the gas phase. In addition, CO2 dissolves into brine at any contact between the aqueous and gas phases. However, the effects of various rock types on trapping is outside the scope of the presented analytic model. Numerical simulations are used to calculate the CO2 capacity with reasonable accuracy. However, the simulation results are complex, as they require detailed geological information of the aquifer, in addition, the level of uncertainty associated with simulation inputs and, thus, the inaccuracy of results increases as the system becomes more complicated. That is where a simple analytical model is somehow preferred to conduct the comparison-based studies. Szulczewski et al. (2009) introduced an analytical model to predict the basin-scale CO2 storage capacity of an aquifer while considering gravity override and capillary trapping; however, their model does not account for the solubility of CO2 in the brine as well as mineral trapping. We adopt the notion of the optimal solvent-water-slug size as defined by Walsh and Lake (1989) for CO2 oil recovery; we use the graphical solution of combined geochemical fronts propagation and fractional flow theories (Noh et al. 2007) to define the CO2 storage capacity of aquifers. According to Walsh and Lake (1989), the optimal solvent slug size, expressed in total pore volume (P.V.), occurs when the fastest waves of the chase water (the imbibition front, in our study) and injected CO2 (drainage front) coincide at the outlet. The outlet here is the distant boundary of the aquifer. Similarly, the optimal slug is defined as the largest slug size that leaves immobile CO2 at the outlet. Larger and smaller slugs of CO2 than the optimal are unfavorable and represent over and under capacity conditions. It is notable that our study is limited to capillary snap-off and dissolution mechanisms. For verification, we compare the analytical and the simulation results. At the next part of paper, we present a systematic approach to predict the storage capacity of the systems affected by gravity override.

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Description We consider CO2 injection into an aquifer (drainage process), which is filled up initially with 100% brine, followed by a post-flood aqueous phase injection (imbibition process) under the following assumptions, most of which are common in the fractional flow theory: 1. The flow is one-dimensional governed by Darcy’s law for multiphase flow. 2. Capillary and dispersion effects (dissipation) are negligible; i.e. conservation of an individual component leads to a first-order strictly hyperbolic partial differential equation. 3. The permeable medium is homogeneous. Fractional flow of each phase does not depend on position other than through a saturation change. 4. There are two flowing phases (the aqueous and non-aqueous or gas phase). 5. Mixing in the fluid phases is ideal; i.e. assuming constant partial molar volume and no change in total volume upon mixing and transfer of components from one phase to another. 6. Viscosities, aquifer pore volume, and densities are independent of pressure. Relative permeabilities are monotonic and differentiable. 7. Local-equilibrium applies; i.e. mutual solubility of CO2 and water in the aqueous and gaseous phases is assumed to be in local thermodynamic equilibrium. 8. Neither sorption nor any chemical reaction occurs. 9. Injected CO2 is dry; i.e. contains no water vapor at the inlet. Fig. 2 shows a schematic of typical gas saturation profile for a brine displacing CO2 as followed by an imbibition displacement. As dry CO2 is injected, the residual water around the injection well is vaporized into the gaseous phase and eventually if the injection lasts enough, region J develops (Zuluaga 2008). In this study, we disregard the region J as its length of influence is negligible compared to the aquifer length.

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Mathematical Model The governing equations are the material balances for each component i: 0

(1)

where, tD, dimensionless time: tD = injected pore volumes and xD is the dimensionless distance. For our specific case, the overall composition and the fractional flux of CO2 are: ,

,

,

,

(2)

Using the method of characteristics, Noh et al. (2007) derived an analytical solution for 1D two-phase semimiscible displacement (CO2 displacing water and vice versa are considered as semimiscible displacements because of the substantial solubility of CO2 and water in the aqueous and gaseous phases, respectively). The solution occurs in the form of spreading or sharpening waves; for step-change boundary conditions the latter is also known as shock. The drainage part of the gas saturation profile (between regions I and J) consists of two shocks: at the leading edge between I and II and at the trailing edge between J and II where a series of spreading wave connect the two shocks. During the drainage process, the gaseous phase displaces the residential brine while CO2 dissolves in the brine (semimiscible). The specific velocity of the leading shock (fastest wave of the injected CO2) is: I II II II

II II

,

,

,

,

II

II

,

(3)

,

The fractional flux of the gaseous phase is defined as: (4)

where Ng is the buoyancy number defined as the following:

6

(5)

for horizontal displacements where Ng is zero, the graphical interpretation of Eq. (3) is a tangent line emanating from the retardation point ( D I → II , D I → II ) to the drainage gas fractional flow curve (depicted in Fig. 5). Retardation point as defined in lake (1989) represents phase dissolution; the velocity of drainage front is hindered by dissolution of CO2 into water phase and, hence, is smaller than a case with no dissolution. During the imbibition section of the gas saturation profile, where an aqueous phase (ground water flow or post flood injected water) displaces the existing plume of CO2, a leading shock occurs between regions J and III and a trailing shock between III and K. However, we discard the region J as its length of influence is negligible compared to the aquifer length. This region is water dried-out zone (% 100 CO2) and can be ignored except when near wellbore phenomena (including but not limited to injectivity) are studied. The existence of region J is trivial as the injected CO2 is under-saturated gas with respect to water (assumption 7) and because local equilibrium applies (assumption 9). However, the slope of any shock or wave emanating from % 100 CO2 to regions II or III is less than the velocity of imbibition front (vcw); therefore, it will be quickly overtaken by imbibition front. In other words, region J will vanish, in the presence of imbibition wave. Furthermore, we replace region II with a sharpening wave associated with the average saturation behind the CO2 front (SIIg|Ave). In other words, we assume an analogous constant-state region (Lake 1989) with saturation equal to the SIIg|Ave to be the downstream of the imbibition displacement. Therefore, the shock between the region III and the surrogate constant-state region represents the fastest sharpening wave of the imbibition process. The specific velocity of the imbibition front (VCW) is the slope of the tangent line emanating from SIIg|Ave located on the imbibition fractional flow curve (shown in Fig. 5).

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Fig. 3 illustrates three possible conditions that may occur based on location where the fastest wave of chase water meets the fastest wave of the injected CO2. As shown in Fig. 3-c, the optimal condition takes place when the two shocks coincide at the outlet; i.e. they breakthrough simultaneously. The optimal CO2 slug size is then calculated as: (6) The suggested CO2 slug size is expressed as the fraction of the total aquifer P.V. This quantity may also be interpreted as the storage efficiency (Bachu et al. 2007). To account for the gravity effects owing to the lower density of the injected CO2 than the resident brine and to model the upward migrating CO2, a non-zero buoyancy number is required in Eq. (5). The graphical procedure to determine the specific velocity of the drainage front in non-horizontal displacements differs from the horizontal displacement as sufficiently large buoyancy number (can be obtained by very small injection rate) are characterized by gas fractional flows greater than unity. Therefore, the graphical solution involves no tangent lines, as they would lead to non-physical results. The physical explanation of gas fractional flows greater than unity is that countercurrent flows would occur under certain initial and injection conditions. For more details on modeling of the gravitydominated flows in 1D permeable media, see Walsh (1991) and G.Moghanloo (2012). For sufficiently large buoyancy number, the gas fractional flow curve intersects the line representing fg=1; From Eq. (4) and noting that fg=1, the uniform CO2 saturation behind the drainage front is given by: II

(7)

The specific velocity of the drainage front is equal to the slope of the line connecting the retardation point and SgII .

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Simulation Approach To confirm the analytical solution, we perform a set of 1D displacement simulations and present the comparison between the results. There are 256×1×1 grid blocks in the x-y-z directions, respectively. Fig. 4 shows the relative permeability functions used in the simulations. Capillary pressure is ignored except insofar as it determines the relative permeability. The hysteresis curves for gas relative permeability are needed as input both for simulation and the analytic model. The models are initially fully saturated with brine. The outlet of the base case model is maintained at a constant bottom-hole pressure of 2300 psi. The injection well (for both CO2 and the post-flood displacements) is set at a constant rate constraint. The porosity and the permeability of all models are 0.15 and 500 md, respectively. The temperature and the salinity of the base case model are 130˚F and 5000 ppm, respectively. The PVT properties of gas and brine (density, viscosity, solubility, and z compressibility factor) are calculated internally in the numerical simulator by the Peng-Robinson equation of state. The viscosity of brine and CO2 are 0.517 and 0.052 cp, respectively. For the base case model, the retardation factor is -1.03 leads to a fast CO2 shock located at Sg= 0.42 and yields a specific velocity of 0.196; however, the fastest chase water shock (imbibition front) emanates from (0.52, 0.92) to (0.29, 0.06) that yields a specific velocity of 3.55 (Fig. 5). The CO2 storage capacity of the base model is 0.226 P.V. from Eq. (6). Under such circumstances, the CO2 and the imbibition shocks collide at the outlet. In the simulations, this situation is translated to the maximal injected CO2 slug expressed in terms of the aquifer P.V. that yields no CO2 in the state of gaseous phase (free-gas) at the outlet. Fig. 6 illustrates the gas saturation profiles obtained by the simulations for three cases: (1) under capacity, (2) over capacity, and (3) optimum at a specified time. Under optimal condition, the injected CO2 is spread out over the entire aquifer owing to the capillary snap-off and the dissolution trapping mechanisms while never being found in the form of free-gas at the outlet. For the under capacity (under

9

optimal) case a relatively small amount of CO2 is spread over the entire length of the aquifer and is entirely trapped. Fig. 7 confirms that a CO2 slug size of 0.225 is the largest that yields no free gas at the outlet, which is consistent with the value obtained from Eq. (6). Tables 1-3 indicate the results of the sensitivity analysis conducted to study the effects of different water salinities, aquifer pressures, and temperatures on the CO2 storage capacity. The storage capacity varies by changing the CO2 solubility as it also observed in previous studies (Kumar et al. 2005). However, the solubility trapping is slow and time-dependent process and is a function of the amount of mixing that occurs between the free-gas and the CO2-unsaturated aqueous phase; therefore, it contributes less in the early stage of the CO2 sequestration (less than 10% in this study). Next, we investigate the effect of buoyancy on the storage capacity of vertically gravity-dominated displacements. We use the base case model tilted 90 degree such that the injection well now located at the bottom and the outlet at the top. Smaller injection rates than the base case model is used to study gravity-dominated displacements (such as upward slowly migrating CO2) as the buoyancy number is the ratio of gravity to viscous forces. Fig. 8 indicates the CO2 storage capacity as a function of the buoyancy number. The capacity decreases as the buoyancy number increases in agreement with the simulation results obtained by Ide et al. (2007). The results are consistent with the fact that greater gas saturation during the drainage process yields larger residual gas saturation owing to the following imbibition displacement (Fig. 9). The simulation results confirm the storage capacities obtained with the proposed procedure; however, the advantages of using the graphical solution are simplicity and speed.

Prediction of the storage capacity of the systems affected by gravity override The gravity override reduces the CO2 storage capacity of 2D systems compared to that of 1D models presented earlier. Since injected CO2 has less density than the resident aqueous solution, it would displace water upward until it reaches to an impermeable layer/cap rock; after being stopped by the

10

impermeable layer, CO2 would displace the water just underneath that layer. The injection may proceed until the pressure exceeds the maximum allowable limit (to avoid possible CO2 escape; i.e. fault activation, fracturing the rock along the weakest stress). Here, we do not consider the extra CO2 (after injected CO2 has reached the aquifer boundaries) that can be stored owing to compressibility of the system as our analytic model is based on incompressible fluids. Following Stones (1982), the segregation velocity can be obtained by considering incompressible fluids and the same pressure gradient for upward flowing gas and downward flowing water phases; Dacry law for gas and water phases can be written as: ,

8

.

9

Eliminating pressure gradient from the above equations while equating uw and ug (as a result of incompressible assumption) give, ∆

.

10

Fig. 10 illustrates an element of upward flowing CO2 within segregation zone; the flux of CO2 passing through any horizontal surface of this element after having steady state established (sufficiently time after CO2 reaches to the top of formation) is equal to total volume of CO2 injected underneath that surface. ,

11

where w is the width of the formation. Using Eq. (11), the segregation length (distance from injector beyond which the horizontal velocity is zero; i.e. no displacement occurs in x-direction) can be calculated as: Lg =

uinjection usegregate

H

(12)

11

where H is the height of formation. The segregation zone can also be interpreted as the swept area; using triangular shape analogy for the sweep efficiency, 1 2

.,

13

where L is the length of aquifer. Substitution of Eq. (12) into Eq. (13) gives: 1 2

.,

14

Fig. 11 shows the sweep efficiency as a function of the formation aspect ratio (

) for gravity-

dominated flow in an aquifer with excellent vertical communication (vertical equilibrium; see Lake (1978) for more detail). As inferred from the plot, the greater the aspect ratio, the smaller the sweep efficiency for the aquifer is realized, consistent for all buoyancy numbers. Therefore, CO2 storage capacity for 2D system will be only a fraction of what earlier discussed for 1D system since, 2

.

.

,

(15) where the second term represent the sweep efficiency.

Conclusions The main outcome of the analytical developments presented here is a procedure that predicts the CO2 storage capacity of aquifers owing to capillary snap-off and dissolution. •

The predicted value of the CO2 storage capacity of a saline formation obtained from the fractional flow theory is consistent with the simulation results.

•

The simplicity of the solution yields an efficient and quick method to investigate the impact of uncertainty in the parameters (such as the gas solubility) on the CO2 storage capacity.

•

Dimensionless characteristic of the solution with respect to the size of the closed aquifers overcomes the scale-dependency of the previous solution as pointed out by Juanes (2010).

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•

The developed graphical procedure is an ideal solution for prompt evaluation of large databases to determine the most attractive CO2 storage geological formations based on the two trapping mechanisms that are effective in intermediate time-scale.

•

The CO2 storage capacity of 2D system is only a fraction of that of 1D solution for formations with large aspect ratio; because the larger the aspect ratio, the smaller the sweep efficiency (Fig. 11).

•

The dissolution does not seem as effective as capillary snap-off trapping; its contribution is maximum up to % 10 of that of capillary trapping mechanism.

Nomenclature Ng = buoyancy number ppm = parts per million D I → II

= retardation factor

Fi = overall flux of component i fj = fractional flow of phase j CTi= overall concentration of component i ,

= the volume fraction of CO2 in the phase j

Sj = saturation of the phase j tD = dimensionless time; injected volume expressed in the aquifer P.V. Uinj = injection volumetric rate (ft3/d) tDS = CO2 slug size expressed in the aquifer P.V. VCW = the specific velocity of the imbibition front VCS = the specific velocity of the drainage front SgII

= the gas saturation behind

μj = the viscosity of phase j (cp)

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ρj = the mass density of phase j (lb/ft3) g = standard gravity constant (32.174 ft/s2) α = aquifer dip angle krj = the relative permeability of phase j kz=permeability in z-direction kx= permeability in x-direction Lg= segregation length xD = dimensionless distance RL = formation aspect ratio

Subscripts aq.= the aqueous phase g= the gaseous phase Superscripts -=upstream

Acknowledgements The Authors also thank the Computer Modeling Group Ltd. (CMG) support for the simulation software. References Bachu, S., W. D. Gunther, and Perkins, E. H. 1994. Aquifer Disposal of CO2: Hydrodynamic and Mineral Trapping. Energy Conv. Manag. 34 (4): 269-279. Bachu, S., Bonijoly, D., Bradshaw, J., Burruss, R., Holloway, S., Christensen, N. P. and Mathiassen, O. M. 2007. CO2 Storage Capacity Estimation: Methodology and Gaps. Intl J. Greenhouse Gas Control. 1 (4): 430–443. Ennis-King, J., and Paterson, L. 2005. Role of Convective Mixing in the Long-Term Storage of Carbon Dioxide in Deep Saline Formations. SPE J. 10 (3): 349–356.

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Gunter, W. D., Wiwchar, B., and Perkins, E. H. 1997. Aquifer Disposal of CO2-Rich Greenhouse Gases: Extension of the Time Scale of Experiment for CO2-Sequestering Reactions by Geochemical Modeling. Miner. Pet. 59 (2): 121–140. Bradshaw, J., Bachu, S., Bonijoly, D., Burruss, R., Holloway, S., Christensen, N. P., and Mathiassen, O. M. 2007. CO2 Storage Capacity Estimation: Issues and Development of Standards. Intl. J. Greenhouse Gas Control 1: 62-68. Cinar, Y., Riaz, A., Tchelepi, H.A. 2009. Experimental Study of CO2 Injection into Saline Formations. SPEJ. 14(4):588-594. Kumar, A., Ozah, R., Noh, M., Pope, G. A., Bryant, S., Sepehrnoori, K., and Lake, L. W. 2005. Reservoir Simulation of CO2 Storage in Deep Saline Aquifers. SPE J. 10 (3): 336–348. Ghanbarnezhad Moghanloo, R. 2012. Modeling the Fluid Flow of Carbon Dioxide through Permeable Media. PhD Dissertation, the University of Texas at Austin Lake, L. W. 1989. Enhanced Oil Recovery. Englewood Cliffs, New Jersey: Prentice Hall. Nghiem, L. 2002. Compositional Simulator for Carbon Dioxide Sequestration. Computer Modeling Group Ltd. Juanes R., Spiteri, E. J., Orr, F. M. Jr., and Blunt, M. J. 2006. Impact of Relative Permeability Hysteresis on Geological CO2 Storage. Water Resource. Research. 42: W12418. Juanes, R., and MacMinn, C. W. 2010. The Footprint of the CO2 Plume during Carbon Dioxide Storage in Saline Aquifers: Storage Efficiency for Capillary Trapping at the Basin Scale. Transp Porous Med. 30: 19-30. IPCC. 2005. Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press. IPCC. 2007. Climate Change: The Physical Science Basis. Fourth assessment report. Riaz, A., Hesse, M., Tchelepi, H. A., and Orr, F. M. Jr. 2006. Onset of Convection in a Gravitationally Unstable, Diffusive Boundary Layer in Porous Media. J. Fluid Mech. 548: 87–111.

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Saadatpoor, E., Bryant, S. L., and Sepehrnoori, K. 2010. New Trapping Mechanism in Carbon Sequestration. Transp Porous Med. 82 (3): 3-17. Sifuentes, W., Blunt, M. J., and Giddins, M. A. 2009. Modeling CO2 Storage in Aquifers: Assessing the Key Contributors to Uncertainty. Paper SPE presented at the Offshore Europe Oil & Gas Conference & Exhibition, Aberdeen, UK, 8-11 September. Stone, H.L. Vertical Conformance in an Alternating Water-Miscible Gas Flood. SPE paper 11130 presented at the 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME; New Orleans, LA, Sept. 26-29. Szulczewski, M. and Juanes, R. 2009. A Simple but Rigorous Model for Calculating CO2 Storage Capacity in Deep Saline Aquifers at the Basin Scale. Energy Procedia (Proc. GHGT-9) 1 (1): 3307– 3314. Taku Ide, S., Jessen, K., Orr, F. M. J. 2007. Storage of CO2 in Saline Aquifers: Effects of Gravity, Viscous, and Capillary Forces on Amount and Timing of Trapping. International Journal of Greenhaouse Gas Control I. 1 (4):481-491 Walsh, M. P. and Lake, L.W. 1989. Applying Fractional Flow Theory to Solvent Flooding and Chase Fluids. J. Petroleum Science and Eng. 2 (4): 281-303. Walsh, M.P. and Moon G.M. 1991. An Analysis of Gravity-Dominated, Immiscible Flows in Dipping Reservoirs. Paper SPE presented at the Production Operations Symposium, Oklahoma City, Oklahoma, April 7-9. Zuluaga, E., and Lake, L. W. 2008. Modeling of Experiments on Water Vaporization for Gas Injection using Traveling Waves. SPE J.13 (2): 248-256.

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Table 1: -Sensitivity analysis on the salinity of the brine

Brine salinity, ppm 1000

Retardation factor -1.032

CO2 storage capacity 0.225

CO2 mole fraction in aqueous phase 0.021

5000

-1.033

0.225

0.021

10000

-1.035

0.225

0.020

20000

-1.039

0.223

0.020

30000

-1.042

0.223

0.019

40000

-1.044

0.223

0.018

50000

-1.045

0.223

0.018

Table 2: Sensitivity analysis on the aquifer pressure

Aquifer pressure, psi 1600

Retardation factor -1.028

CO2 storage capacity 0.21

CO2 mole fraction in the aqueous phase 0.019

μCO2, cp 0.040

2000

-1.032

0.223

0.021

0.046

2600

-1.033

0.225

0.021

0.051

3000

-1.042

0.23

0.022

0.063

3500

-1.048

0.235

0.023

0.069

CO2 mole fraction in the aqueous phase

μCO2, cp

0.024

0.067

Table 3:- Sensitivity analysis on the aquifer temperature

Aquifer temperature, ˚F

Retardation point

100

-1.041

CO2 storage capacity 0.235

110

-1.041

0.23

0.023

0.062

120

-1.040

0.227

0.022

0.056

130

-1.033

0.225

0.021

0.051

140

-1.031

0.225

0.021

0.049

150

-1.029

0.223

0.020

0.044

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Figure 1: Trapping mechanism depicted as the consequence of an imbibition displacement followed by an initial drainage

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Figure 2: Schematic of the gas saturation profile in a set of semimiscible displacements where injected CO2 is followed by an aqueous phase. Five distinct regions occur at the early stage of the displacement: (1) region I is the initial condition with 100% water saturation, (2) part II is a drainage semimiscible displacement where a gaseous phase displaces an aqueous phase with mutual solubility of CO2 and water, (3) section J is the CO2 injection condition, (4) part III is similar to region II but it is an imbibition displace of a gaseous phase displaced by an aqueous phase, (5) K illustrates the post-CO2 water injection that represents an imbibition displacement. Water injection is because of injection or when a regional ground water flow pushes the CO2 slug farther into the aquifer. Note that saturations propagate at various specific velocities causing waves interference and disappearance of the J condition. SIIg|Ave represents the average gas saturation of the region II.

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(a) Typical MOC solution

(b) Over-capacity

20

(c) Optimal

(d) Under-capacity Figure 3: Part (a) shows the typical form of the method of characteristics (MOC) solution when CO2 displacing water is followed by an aqueous phase. The slope of each line on the distance-time diagram is the specific velocity of the concentration attributed to that wave. To evaluate possible conditions a surrogate shock representing region II is defined. Parts b-d illustrate three different conditions: under capacity, optimum, and over capacity according to when the fastest imbibition front meets the fastest drainage shock: Part (b) Over-capacity condition: the imbibition front with specific velocity of VCW intersects the drainage front with the velocity of VCS beyond the aquifer length. In other words, the imbibition front does not catch-up to the fastest drainage wave and there is extra CO2 than the aquifer capacity. Part (c): Optimal condition: the imbibition front catches-up to the fastest drainage shock at the aquifer boundary and leaves all injected CO2 as the trapped. Part (d): Under-capacity condition: the imbibition front catches the fastest drainage shock before the aquifer end and part of the aquifer will remain unfilled.

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1

Relative Permeability

0.75

0.5 krg_Drainag e krw_Draina ge

0.25

0 0

0.25

0.5 Gas Saturation, Sg

0.75

1

Figure 4: Relative permeability curves for the aqueous and gaseous phases. The pink line is the imbibition curve for the gas phase.

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II Sg Ave .

J

0.92

Sg

Gas Fractional Flow, fg

Sg|f (0.42, -0.84)

II

Ave.(0.52,

0.92)

0.72

0.52

VCS

Imbibition

VCW

Drainage

0.32

0.12

(0.29,0.06) -0.08 -0.08

I &K

0.12

0.32

0.52

0.72

0.92

Gas Saturation, sg

(-1.03,-1.03) Figure 5: Graphical procedure to predict the CO2 storage capacity of the aquifer. The slope of a tangent-line emanating from the retardation point (fw, sw)=(-1.03,-1.03) to the drainage fractional flow curve of the gaseous phase is Vcs and the slope of the tangent line from SIIg|Ave. to the imbibtion curve determines the Vcw. Using Eq. (6) the total pore volume, which ultimately is occupied by the injected CO2 owing to the residual (snap-off) and dissolution trapping, is 0.226. The retardation point is outside this plot.

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F Figure 6: Gas saturation profiile for three possible condition ns at tD=0.5. Th he red curve illlustrates the op ptimal condition n for which in njected CO2 is trapped t evenly along the aquiffer. The over caapacity conditioon (green line) leads l to existencce of free gas att the outlet; h however, if a sm maller CO2 slu ug size than the optimal is in njected before the t imibition process p occurs, the drainage front f never r resaches the ou utlet ; i.e. the aquifer a has nott been filled to capacity. Therrefore, simulatiion results suggest that the CO C 2 storage c capacity of the quifer is 0.225 5 of the total pore p volume. There T is a slow dissolution shoock at the rearr bank of the CO C 2 plume c corresponding t the dissolutio to on of the capillaary trapped CO2 into the fresh water.

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F Figure 7: The cu umulative CO2 production forr the optimal an nd above optimal cases. Simulaation results sh how that the larrgest slug of C 2 that yields no free-gas as the CO t outlet is 0.2225 of the total pore p volume (pu urple line). Injeecting more thaan the optimal size s leads to the production of o CO2; in otheer words, the prresence of CO2 in the form of free-gas at the outlet indicatess that the aquiffer capacity i volumee. iss less than the injected

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F Figure 8: CO2 sttorage capacity y as a function of o the buoyancyy number. The CO2 storage cap pacity of the aq quifer decreasess as the d displacement beecomes more grravity-dominateed.

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F Figure 9: Gas saaturation profille during the drrainage displaceement (CO2 disp placing the brin ne) for differentt buoyancy num mber. L Larger buoyanccy number yield ds smaller gas saturation and eventually e smalller residuals beecause of the capillary trappingg m mechanism.

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Figure 10: Volume balance in steady state segregated zone

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1.E+00 0

Sweep Efficiency

1.E‐01 1 1.E‐02 2 1.E‐03 3 1.E‐04 4 Ng=0.06

Ng=0.6

Ng=6

1.E‐05 5 10

100 Form mation Aspecct Ratio, RL

1000

Figure 11: Sw weep efficiency as a a function off formation aspect ratio for varrious buoyancyy number

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We d develop an analytical solution to dettermine CO2 storage cap pacity of an aaquifer  

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The ssolution provvides a fast aapproach to screening vvarious geolo ogical formations 

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Increasing the bu uoyancy num mber reduces the CO2 sto orage capaccity of aquifeers 

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The laarger the aspect ratio off the formattion. the smaaller the storrage capacitty