Dissolution Trapping of Carbon Dioxide in Reservoir Formation Brine – A Carbon Storage Mechanism

Carbon Capture and Storage (CCS) is a method to reduce anthropogenic greenhouse gas emissions thereby mitigating global warming. In CCS, carbon dioxide (CO2) is captured from fossil fuel-fired power plants or other large point-source emitters, purified, compressed and injected deep underground into subsurface formations at depths of or greater than 800m. At such depths CO2 is in a supercritical (sc) state increasing storage capacity (IPCC 2005). In CCS, there are four main mechanisms which keep the buoyant CO2 underground: 1. Structural/stratigraphic trapping – here an impermeable caprock prevents the CO2 from flowing upwards, 2. Capillary trapping, where micrometer-sized disconnected CO2 bubbles are formed and held in place by local capillary forces in the rock pore-network, 3. Dissolution trapping, where CO2 dissolves in the formation brine and sinks in the reservoir as the CO2-enriched brine has an increased density, 4. Mineral trapping, where the dissolved CO2 reacts with the formation brine, forms carbonic acid which dissociates generating protons, 3 HCO − and 3 CO − ions; these species subsequently react with the formation brine and/or host rock to form solid minerals which trap the CO2 very safely. The focus of this text is on dissolution trapping; how much CO2 dissolves under which geothermal conditions and what happens to the CO2-enriched brine, which is slightly denser than the original formation brine, in the formation. Important open questions in this context are: How fast are these mass transfer processes in real geological porous media under realistic CCS conditions? Are there means of accelerating CO2 dissolution? How do separate gas and/or oil phases (oil and/or gas reservoirs) in the reservoir affect CO2 dissolution processes and reservoir fluid dynamics? How does the pressure drop due to CO2 dissolution affect injectivity and storage capacity of CO2?


Introduction
Carbon Capture and Storage (CCS) is a method to reduce anthropogenic greenhouse gas emissions thereby mitigating global warming. In CCS, carbon dioxide (CO 2 ) is captured from fossil fuel-fired power plants or other large point-source emitters, purified, compressed and injected deep underground into subsurface formations at depths of or greater than 800m. At such depths CO 2 is in a supercritical (sc) state increasing storage capacity (IPCC 2005). In CCS, there are four main mechanisms which keep the buoyant CO 2 underground: 1. Structural/stratigraphic trapping -here an impermeable caprock prevents the CO 2 from flowing upwards, 2. Capillary trapping, where micrometer-sized disconnected CO 2 bubbles are formed and held in place by local capillary forces in the rock pore-network, 3. Dissolution trapping, where CO 2 dissolves in the formation brine and sinks in the reservoir as the CO 2 -enriched brine has an increased density, 4. Mineral trapping, where the dissolved CO 2 reacts with the formation brine, forms carbonic acid which dissociates generating protons, 3 HCO − and 2 3 CO − ions; these species subsequently react with the formation brine and/or host rock to form solid minerals which trap the CO 2 very safely. The focus of this text is on dissolution trapping; how much CO 2 dissolves under which geothermal conditions and what happens to the CO 2 -enriched brine, which is slightly denser than the original formation brine, in the formation. Important open questions in this context are: How fast are these mass transfer processes in real geological porous media under realistic CCS conditions? Are there means of accelerating CO 2 dissolution? How do separate gas and/or oil phases (oil and/or gas reservoirs) in the reservoir affect CO 2 dissolution processes and reservoir fluid dynamics? How does the pressure drop due to CO 2 dissolution affect injectivity and storage capacity of CO 2 ?

Geological background of dissolution trapping
The International Panel on Climate Change (IPCC) (2005) has suggested several possible geological storage media, including deep saline aquifers, oil or gas reservoirs and unmineable www.intechopen.com coal seams. In case of CO 2 storage in coal, a benefit is that additional methane is produced which is adsorbed on the coal surface and displaced by CO 2 (so-called enhanced coal-bed methane (ECBM) production). However, CO 2 injection leads to the highly detrimental effect of coal swelling which strongly deteriorates injectivity as observed from laboratory and pilot field studies (Reeves and Oudinot, 2005). This text focuses on aquifers and oil/gas reservoirs and will not discuss ECBM any further as low permeability and swelling characteristics limit the scale of exploitation of coalbeds as potential CO 2 storage sinks. In terms of CO 2 storage, deep saline aquifers -too saline for drinking water or agricultural usage -are most promising, because they are geographically widespread and have large potential storage capacities. Published storage capacity estimates especially for aquifers vary widely based on the assumptions made. This is an active area of research with the objective to provide accurate basic information so that effective CCS schemes can be planned in order to store the large quantities of anthopogenic CO 2 emitted (circa 30 Gt CO 2 /a, IPCC 2007). To focus on dissolution trapping, the topic of this chapter, the main problem associated with it is addressed straight away: it is the slow speed of CO 2 dissolution and the two-phase (CO 2 and brine) reservoir flow dynamics -as long as the CO 2 is in a separate supercritical state it tends to flow upwards because of buoyancy forces, and it can potentially leak to the surface. Mass transfer of CO 2 from the supercritical phase into the aqueous phase is the timedetermining step in dissolution trapping which therefore also determines leakage risk. In fact CO 2 is only stored safely once it is dissolved in the aqueous phase (or precipitated as a solid). Hence the study of CO 2 dissolution is an essential aspect of CCS risk assessment. Mass transfer and solubilities of CO 2 into brine are functions of pressure, temperature, salinity, local CO 2 concentration and subsequent chemical reactions (formation and dissociation of carbonic acid and following rock dissolution/precipitation). Moreover interfacial areas scCO 2 -brine play a vital role in the mass transfer kinetics, and they are closely related to the two-phase flow dynamics in the reservoir. All these aspects will be discussed in this chapter. In addition several reservoir scale computer simulations will be presented which analyze fluid flow and CO 2 storage in CCS schemes. In this context it is worth noting that CO 2 is a naturally abundant species in the subsurface. Rumble et al. (1982) suggested two possible chemical reactions between calcite and quartz which formed this naturally occuring CO 2 over geological times. A result of this is that CO 2 content in oil or gas reservoirs can be very high. In gas reservoirs CO 2 content can reach concentrations larger than 90 mol% and in oil reservoirs CO 2 content can be as high as 70-80 mol% (Badessich et al. 2005). As an example Ballentine et al. (2001) state that the CO 2 concentration in gas fields in Texas varies from 3% to 97% depending on the geographical location. In summary dissolution trapping is a feasible mechanism to store large quantities of CO 2 , and if a route could be found to quickly dissolve scCO 2 into brine CO 2 emissions could be dramatically, rapidly and economically reduced this way, maybe even solving the climate change problem caused by CO 2 gas emitted from large point-sources. However, although CO 2 contributes the largest chunk to greenhouse gas emissions, other gases such as CH 4 , CO, N 2 O, halogenated carbons, etc., also need to be eliminated to completely stop global warming. One route for disposing these gases may also be dissolution into formation brines.

Reservoir fluid dynamics
In actual ongoing CCS projects large quantities of CO 2 are injected deep underground. The largest injection time for a pure CCS project has been achieved in Norway in the Sleipner www.intechopen.com project, where 1 Mt CO 2 /a are injected into the Utsira sandstone formation in the Norwegian sector of the North Sea at 800m depth (Iglauer 2011). This project started in 1996, and reservoir CO 2 monitors confirm reservoir simulations which predict that the CO 2 rises upwards and accumulates beneath the caprock (Hesse et al. 2008). CO 2 from this rising CO 2 -plume dissolves in brine as it migrates upwards Garcia 2002, Bachu andAdams 2003). The CO 2 -enriched brine has a slightly higher density than the original brine (Ennis-King and Paterson 2005, Moortgat et al. 2011). This leads to gravitational flow instabilities in the reservoir (Riaz et al. 2006, Pau et al. 2010, and it is believed that the CO 2 -rich brine sinks in the reservoir over hundreds to millions of years (Bachu 2000, Ennis-King and Paterson 2005, Lindeberg and Wessel-Berg 1997 in the form of thick and thin fingers (cp. Figures 1 and 2), however this is an active area of research and it has been suggested that this mechanism is considerably faster (Moortgat et al. 2011). Again, this storage mechanism is very safe, but if the dissolution process is a very slow process then that means that the leakage risk is high in the short term (= initial several hundreds of years) since the CO 2 may escape before it can dissolve.

Thermodynamics of CO 2 dissolution into formation brine
It has been reported that 0.9-3.6 mol% of CO 2 can be dissolved in brine, depending on pressure, temperature and brine composition (Rumpf et al. 1994, Koschel et al. 2006. The advance of the fastest finger front is shown for different permeabilities (represented by different lines) (from Riaz et al. 2006 with permission from Cambridge University Press) 2003, Kiepe et al. 2002). Before analyzing these relationships in more depth, it should be pointed out that CO 2 and brine are a reactive system, CO 2 reacts with water to form carbonic acid which subsequently dissociates (scheme 1) through a proton-relay mechanism that is catalyzed by several water molecules (Adamczyk et al. 2009) (2009) studied these reactions at atmospheric pressure and found that the slowest step in scheme 1 is the forward reaction of (b), the hydration of CO 2 (aq) resulting in H 2 CO 3 . The dehydration of H 2 CO 3 is also relatively slow, with a dehydration rate constant of k de = 18 s -1 (Pocker and Bjorkquist 1977). The deprotonation rate in scheme (c) is k off = 7 10 s -1 (Pocker and Bjorkquist 1977) and the associated pK a value is 3.45. Note that this pK a value published by Adamczyk et al. (2009) is considerably different from the normally assumed pK a = 6.35 for the CO 2 (aq)/H 2 O system at atmospheric pressure conditions. The protonation rate of scheme (c) then results in k on = k off /K a . The K value at 50.66 MPa for the reaction in scheme (d) is 5.13 x 11 10 − (Hirai et al. 1997) In addition, one consequence of an increase in CO 2 solubility with increasing pressure (or decreasing temperature or salinity) is that the aqueous phase increasingly acidifies because more CO 2 is present in the aqueous phase and reaction (b) is shifted to the right side according to Le-Chatelier's principle. It can therefore be expected that the pK a value of scheme (c) drops further at increased CO 2 pressure. In laboratory measurements pH values between 3.2-3.6 were observed within a temperature range between 300-343 K, a pressure range between 4-11 MPa and a salinity range 1-4 M NaCl solutions (Schaeff and McGrail 2004). In siliclastic and carbonate gas fields however pH values between 5-5.8 have been observed (Gilfillan et al. 2009); the discrepancy between lab and field data is most likely caused by complex geochemical buffering reactions, e.g. with carbonate host rock or carbonate based cements. The increased proton concentration in the brine has significant implications for geochemical reactions (Stumm andMorgan 1996, Gauss 2010) generally leading to more rock dissolution and higher dissolution rates. When the pH value has increased again to sufficiently high levels CO 2 can be trapped as a solid phase -so-called mineral trapping (IPCC 2005, Gauss 2010). This could in principle also be engineered in the future although the physical and chemical phenomena associated with this process are highly complex and coupled. Such reactions bring a range of problems and advantages with them: • It is possible that too much rock is dissolved and high permeability channels are formed; this is especially a problem in carbonates (Egermann et al. 2005, Luquot andGouze 2009). Injected CO 2 will preferentially flow through such channels, which are also termed "wormholes". This reduces reservoir sweep efficiency which again decreases capillary trapping as only low initial CO 2 saturations are achieved. Low initial CO 2 saturations however result in low residual CO 2 saturations 2011a,b;Al-Mansoori et al. 2010;Iglauer 2009). In addition such high permeability flow paths increase the risk of CO 2 leakage, especially if caprock material is affected. • Should so much host rock be dissolved that the mechanical rock integrity is affected, then this can result in wellbore instability or even landmass subsidence.

•
In case of precipitation of solid minerals due to geochemical reactions (when the pH value has increased again) rock permeability can be significantly reduced, e.g. by blockage of small pore throats (which determine the permeability value). This can result in serious injectivity problems, e.g. injection rates may have to be reduced dramatically which may render CCS schemes ineffective.

•
Rock dissolution increases permeability and enhances injectivity rendering CCS schemes more economical.

•
Precipitation of CO 2 in solid minerals (after chemical reactions) is the safest form of CO 2 storage in CCS as the CO 2 cannot escape to the surface anymore. This trapping mechanism is believed to take between thousands to billions of years (IPCC 2005, Xu et al. 2003).

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In light of the new results published by Adamczyk et al. (2009) it is important to note that carbonic acid has a considerable acidity as it acts like a carboxylic acid on nanosecond timescales; this may have significant implications for geochemical reactions, rock surface alterations and associated possible rock wettability changes. Rock wettability strongly influences multi-phase fluid dynamics and capillary trapping.
On an important side issue these chemical reactions also happen in the oceans when CO 2 gas in the atmosphere dissolves in seawater thereby reducing its pH value. With the increasing CO 2 concentration in the atmosphere (from 190 ppm in 1750 to 380 ppm in 2005, IPCC 2005) more carbonic acid is formed in the oceans and the seawater pH value decreases with possible massive effects on sea life, starting with the sensitive but all important sea plankton. Therefore disposing anthropogenic CO 2 by dissolving it into the ocean seems to be a risky enterprise, as the pH value would drop further and locally reach substantially lower numbers.

Effect of pressure on CO 2 solubility in brine
CO 2 solubility (mole fraction of CO 2 per mass unit of brine) in formation brine is a strong function of pressure as shown in Figure 3. The data curve (open diamonds) in Figure 3 was computed with Duan and Sun (2003) and Duan et al. (2006)'s online CO 2 solubility calculator. The temperature was held constant at 323 K and brine salinity was 1 mol NaCl/kg brine. CO 2 solubility rapidly increases when pressure is raised from 0.1 MPa to 10 MPa, then the increase flattens out although a slight solubility increase follows. Three experimentally measured points at CCS pressure conditions are also added to the graph.   Nighswander et al. (1989), Li et al. (2004) and Kiepe et al. (2002) 4.2 Effect of temperature on CO 2 solubility in brine CO 2 solubility decreases with increasing temperature as shown in Figure 4. Experimental data relevant for CCS and simulated data are displayed.  Moreover, the type of dissolved salt has an influence on CO 2 solubility. Yasunishi and Yoshda (1979) studied CO 2 solubilites at atmospheric pressure in a wide variety of salt solutions, these salts included NaCl, KCl, Na 2 SO 4 , MgCl 2 , CaCl 2 , K 2 SO 4 , MgSO 4 , BaCl 2 , AlCl 3 , Al 2 (SO 4 ) 3 among others. They found that for the same electrolyte concentration, KCl solutions can absorb more CO 2 than NaCl solutions, while CaCl 2 and MgCl 2 solutions absorb approximately the same amount of CO 2 . Monovalent NaCl or KCl solutions with the same salt concentration absorb more CO 2 than their divalent CaCl 2 or MgCl 2 counterparts. For example Yasunishi and Yoshda (1979) measured at atmospheric pressure and 298 K that a 4.216 mol/L NaCl solution absorbs L = 0.3144 (L is the Ostwald coefficient, L = V g /V l with V g = volume of CO 2 absorbed and V l = volume of absorbing brine) while a 4.131 mol/L KCl solution absorbed L = 0.4703. For a 3.955 mol/L MgCl 2 solution they measured L = 0.1648. Chloride salt solutions absorbed more CO 2 than the corresponding sulphate solutions (that was tested for 32 Na , K , Al and Mg where Y CO2,brine = CO 2 solubility in brine (mass fraction) Y CO2,pureH2O = CO 2 solubility in pure water (mass fraction) S = salinity of brine (weight percent) Sun (2003, 2006)

Theoretical model for computing CO 2 solubilities
Here T is the temperature, p the pressure, R is the universal gas constant, m is the molality of components dissolved in water, y CO2 is the mole fraction of CO 2 in the vapour phase, F CO2 is the fugacity coefficient of CO 2 , 2 (0) l CO μ is the standard chemical potential of CO 2 in the liquid phase, CO2-Na is the interaction parameter between CO 2 and Na + and CO2-Na-Cl is the interaction parameter between CO 2 and Na + , -Cl . The fugacity F CO2 can be calculated via a fifth-order virial equation of state (equation 3). The coefficients c i are stored in a look-up table (Duan et al. 2006) The mole fraction of CO 2 in the vapour phase y CO2 can be computed with equation (4) ( ) where p H2O is the water vapour pressure which can be estimated with the empirical equation (5) where t = (T-T c )/T c and T c and p c are the critical temperature and critical pressure of water (T c = 647.29 K, p c = 22.085 MPa).

Effect of injection depth on CO 2 solubilities
In a deep saline aquifer or oil reservoir high pressures and elevated temperatures are found.
The pore pressure at depth is usually assumed to be equal to the hydrostatic pressure; a typical hydrostatic pressure gradient is 10.35 MPa/1000m (Dake 2007). In addition a geothermal gradient exists, the reservoir temperature increases with depth. Average typical geothermal gradients are 25-30 K/1000 m (Fridleifsson et al. 2008). Average temperatures and pressures at depth are listed in Table 2, they were calculated assuming typical pressure and temperature gradients and a surface temperature of 293 K. The surface temperature needs to be adjusted for each specific geographical location, e.g. average temperature is low in Norway (average temperature throughout the year is around 281 K) while average yearly temperature is high in Saudi Arabia (298 K). As stated above CO 2 solubility decreases with increase in temperature, but increases with increase in pressure. In Table 2 CO 2 solubilities calculated with Duan's web based CO 2solubility calculator (Duan et al. 2003(Duan et al. , 2006) are shown. The pressure effect over compensates the temperature effect so that CO 2 solubility increases with reservoir depth up to a depth of approximately 900m when it reaches a plateau. With regard to storage of CO 2 in a supercritical phase optimal CCS conditions are conditions where the CO 2 density CO2 is maximal, because then a maximum mass of CO 2 can be stored in the same rock pore space. Thermodynamically CO2 increases with pressure but decreases with temperature. CO2 as a function of depth increases monotonically as the pressure effect also over compensates the temperature effect (Table 2).

Effect of presence of oil (CCS in oil reservoirs)
CO 2 can also be injected into depleted oil reservoirs although storage capacities are much smaller than in aquifers (IPCC 2005). It is estimated that 50 Gt of CO 2 can be stored in this way worldwide (Firoozabadi and Cheng 2010) which is roughly 1.5 times of what is emitted per year. So this is clearly not the solution to mitigate global warming, however CO 2 solubility in oil is very high, up to 60-80 mol% of CO 2 can be dissolved (De Ruiter et al. 1994, Kokal and Sayegh 1993, Emera and Sarma 2006, Firoozabadi and Cheng 2010. CO 2 solubility generally increases with pressure and it is higher at lower temperatures. If the temperature is below the critical CO 2 temperature (T c = 304.13 K), then CO 2 solubility increases until the CO 2 liquefaction pressure is reached (circa 5.88 MPa), then it levels off  Span and Wagner (1996). ** 1 mol/kg NaCl brine, calculated with Duan et al.'s (2003Duan et al.'s ( , 2006 calculator. Table 2. Variation of temperature, pressure, CO 2 solubility and CO 2 density with depth In case of heavy oils CO 2 dissolves into the oil phase while some light oil fractions are extracted into the CO 2 phase. Depending on the oil and thermophysical condition, vapourliquid, liquid-liquid, liquid-supercritical fluid, liquid-liquid-vapour phase behaviours are observed. The densities of CO 2 -saturated oil increase at lower temperature (294 K) while they decrease at higher temperature (e.g. 413 K) (Kokal and Sayegh 1993). This makes CO 2 a very efficient solvent for crude oil extraction in tertiary oil recovery processes (Green andWillhite 1998, Blunt et al. 1993). The dissolved CO 2 reduces oil viscosity significantly which improves the mobility ratio oil-injected fluid (for improving production) and results in a much better reservoir sweep efficiency. The flow of oil in the reservoir is improved by the improved oil relative permeability, which leads to increased oil production. In addition, CO 2 which dissolves into the oil causes oil swelling (up to 50-60%, Firoozabadi and Cheng 2010) which also leads to enhanced oil production. One side effect of CO 2 addition to crude oil is that large asphaltene molecules precipitate (crude oil is a very complex fluid (cp. Moreover there is a very important reservoir engineering aspect associated with depleted oil reservoirs; reservoir pressure is low (because of oil production) and CO 2 can be injected at fairly high rates and comparatively large quantities of CO 2 can be stored. It is important not to exceed the fracture pressure of the caprock which would result in catastrophic leakage of www.intechopen.com CO 2 . Exceeding the capillary entry pressure of CO 2 into the caprock should also be avoided (then CO 2 will also flow through the caprock although very slowly because of the very low permeability of the caprock shale) resulting in potential CO 2 leakage to the surface. Estimates suggest that many millions of tons of crude oil are produced yearly via enhanced oil recovery with CO 2 (CO 2 -EOR) (Firoozabadi and Cheng (2010)). Crude oil production could be further increased if more CO 2 would be used but such CO 2 -EOR schemes should have a CO 2 storage element. In principle oil would be a very good storage medium for CO 2 (provided that the oil does not migrate upwards after CO 2 -takeup, so ideally the process would be designed in such a way that oil density increases), but of course oil is an economically valuable commodity and will be produced, so oil production schemes need to be combined with CCS schemes and optimized, essentially as much oil as possible needs to be recovered while storing as much CO 2 as possible.
Reservoir simulations can calculate such CO 2 -EOR recovery/injection schemes over several years (Qi et al. 2008, one complication here is the three-phase flow and the associated complex fluid thermodynamics occurring in the reservoir. This includes mass transfer of CO 2 into the oil and aqueous phases. In summary, most of the current CCS schemes which are online are actually EOR processes because of profitability. Example projects are the Weyburn-Midale project in Canada, which started in the year 2000. 1.8 Mt/a of CO 2 are injected into a depth of 1500m into a depleted oil reservoir (PTRC 2011, Pentland 2011. 225 m 3 of CO 2 produce 0.12 m 3 extra crude oil there. Another CO 2 -EOR project is underway in the Salt Creek field in Wyoming, USA; here 2.09 Mt of CO 2 are injected yearly and more than 1.2 x 6 10 m 3 of incremental crude oil have been recovered so far and it is planned to store 50 Mt of CO 2 in total (Andarko 2010, Pentland 2011).

Effect of presence of gas (gas reservoirs or oil reservoirs with a gas cap)
CO 2 can also be injected into depleted gas reservoirs in order to produce additional gas, this is called enhanced gas recovery (EGR). The injected CO 2 increases reservoir pressure which supports gas production. As in the case of oil reservoirs or indeed aquifers the caprock failure stress must not be exceeded. Natural gas is a mixture of various components (cp .  Table 4); the exact composition varies with the location of the gas fields and it is determined by the original hydrocarbon generation (Dandekar 2006). In the reservoir, the CO 2 flood front mixes with the natural gas by dispersion and diffusion. In parallel to the CO 2 -gas mixing process, CO 2 also equilibrates with the formation brine, similar to the mixing processes occurring in deep saline aquifers. The main advantage of CO 2 -EGR is profitability as in CO 2 -EOR, and an optimum between additional gas production and CO 2 sequestration needs to be found. There are several CO 2 -EGR pilot units where these processes are tested, e.g. in the Lacq demonstration project in southwest France, 5 10 t of CO 2 will be injected and stored in a depleted gas field at a depth of 4500m (Total 2011). A thorough study of nine natural gas fields (including sandstone and carbonate reservoirs) concludes that the main trapping mechanism over millennial timescales is dissolution trapping. At most 18% of injected CO 2 is stored as a solid mineral phase (Gilfillan et al. 2009) and mineral trapping is predicted to happen only for siliclastic reservoirs. In the case of oil reservoirs with a gas cap, the mixing thermodynamics are a combination of CO 2 -gas mixing, CO 2 dissolution in oil and CO 2 dissolution in brine. These complex www.intechopen.com processes are topic of current research (DaVega 2011). These mixing processes result in three-phase flow in the reservoir (oil, gas and water flow as separated phases); in addition it is possible that additional phases are formed (e.g. a second immiscible oil phase or a solid asphaltene phase) which can further complicate fluid dynamics at the pore-scale and in the whole reservoir. Depending on rock surface wettabilities CO 2 dissolution into brine can be slowed down, e.g. in case of a water-wet surface water covers the rock surface, and an oil layer may separate the brine from the CO 2 (Piri and Blunt 2005). This oil layer then essentially acts as a barrier through which the CO 2 has to pass in order to reach the brine and to be stored there safely by the dissolution trapping mechanism. Helium, He 0 -5 Table 4. Typical composition of natural gas (McCain 1990). Apart from methane and ethane traces of medium sized hydrocarbons can be found. In addition, natural gas can contain significant amounts of H 2 S, CO 2 or N 2 -up to 90 mol% (Firoozabadi and Cheng 2010). Such non-hydrocarbon gases usually need to be separated out of the production stream in order to achieve sellable gas quality

Kinetics of CO 2 dissolution into formation brines
Dissolution kinetics of CO 2 into brine in a reservoir are driven by four main factors, namely molecular diffusion of CO 2 into brine, dispersion during flow, convection of CO 2 -saturated (heavier) brine in the reservoir and flow of the scCO 2 phase in the reservoir. These mechanisms are described in more detail in the following paragraphs.

Molecular CO 2 diffusion into reservoir brines.
Molecular diffusion in natural groundwater systems is usually a time-dependent unsteadystate process. This is described by Fick's second law (equation 7). The driving force behind molecular diffusion is the concentration gradient, essentially the entropy of the system is increased by molecular diffusion. 10 − m 2 /s (Mazarei andSandall 1980, Unver andHimmelblau 1964) were reported. Based on these datasets, Renner (1988) (1988) indicated that water viscosity and CO 2 viscosity were highly correlated with the diffusion coefficient, but molecular weight of CO 2 , molar volume of CO 2 , pressure or temperature were not statistically significant. However Renner states in his paper and Renner's data show that D CO2-H2O increases with an increase in pressure. Therefore it can be expected that CO 2 diffusion processes under CCS conditions are faster than at atmospheric pressure conditions -which is positive news for dissolution trapping as it minimizes leakage risks by absorbing the mobile CO 2 faster in the aqueous phase. Hirai et al. (1997)  10 − m 2 /s). Their results fit perfectly with the empirical equation (9) suggested by Wilke and Chang (1955). ι is an association parameter equal to 2.26 for water. The experimental data measured by Shimizu et al. (1995) (D CO2-H2O is approximately 1.8 x 9 10 − m 2 /s at 286 K and 9-13 MPa) is however 40% larger than predicted by equation (9) 10 − k 2 = 0.135607 k 3 = 1.84220 k 4 = 2.41943 x 3 10 − k 5 = 0.858204 T r,2 = reduced temperature p r,2 = reduced pressure µ = viscosity c 2 = solvent molar density (the solvent is defined here as the dominant component) The advantage of Mutoru et al.'s (2010) model is that it incorporates the temperature and pressure effects on the total dipole moment of water and the induced dipole moment of CO 2 . In addition, it can predict D CO2-H2O over the complete range from infinitely diluted CO 2 to infinitely diluted H 2 O. From equation (10) it is clear that temperature has a stronger influence on D CO2-H2O than pressure. This is due to the strong dependence of the viscosity and the solvent molar density on the temperature. However, pressure influences are also strong as pressure determines equilibrium compositions (Mutoru et al. 2010). An interesting perspective on CO 2 dissolution into brine is the consideration of the CO 2 droplet diameter (Hirai et al. 1997). Especially in the context of residual trapping; here the rising CO 2 plume is split into a large number of small disconnected CO 2 clusters at the trailing edge of the plume due to natural water influx or chase brine injection . The drop diameter is expected to have a highly significant effect on CO 2 dissolution speed. A strong enhancement of CO 2 dissolution is expected for such small CO 2 bubbles as their CO 2 -brine surface area is significantly increased compared with that of a single-cluster CO 2 plume. The dissolution rate of CO 2 can be described by equation (12) (Hirai et al. 1997).
where V = volume of the scCO 2 droplet, A = surface area of the scCO 2 droplet k = mass transfer coefficient C 0 = surface concentration of the droplet C ∞ = concentration at infinity The mass transfer coefficient k is expressed in equation (13) (13) small CO 2 droplets dissolve faster than large ones (assuming that D CO2-H2O is a constant). Essentially this is a formal description of how residual trapping enhances dissolution trapping. More research in this area would certainly improve understanding of the relation between residual and dissolution trapping. Suekane et al. (2006) studied such mass transfer processes of scCO 2 dissolution into pure water in packed glass beads (measurement conditions were 313 K, 8.3 MPa, 70 µm bead diameter) and developed relation (14) 0.92 0.029 Re Sh′ = with the modified Sherwood number Sh'. Sh' can be calculated with equations (15) and (16).
where k is the total mass transfer rate (= kA) and L is the length of the glass bead pack. Equation (16) is the solution of the one-dimensional steady state mass balance equation (17) with the boundary conditions C = 0 at x = 0.
Another interesting suggested correlation for D CO2-H2O has been put forward by Bahar and Liu (2008); they measured D CO2-H2O at 17.8 MPa and 356 K in 2 wt% NaCl brines and developed an empirical correlation between D CO2-H2O and the pressure p, temperature T, molecular weight MW, volume V and viscosity µ of the liquid (equation 18  Bahar and Liu (2008) found that D CO2-H2O is higher for unsteady-state systems, and that the duration of the unsteady-state system strongly depends on the pressure and temperature.

Effect of temperature on CO 2 diffusion in water
As stated in equation (10), temperature has a clear effect on D CO2-H2O . Unver and Himmelblau (1964) developed an empirial equation (19) for the dependence of D CO2-H2O on temperature for atmospheric pressure within a temperature range between 279-338 K. D increases monotonically with temperature T (equation 19).
( ) A = 0.95893, B = 0.024161, C = 0.00039813 are constants for CO 2 , A, B and C adopt different values for other gases. D is given in m 2 /s. Again, diffusion-dominated CO 2 dissolution is more effective at higher temperatures.

Effect of pressure on CO 2 diffusion in water
According to measurements conducted by Wilke-Chang (1955), Shimizu et al. (1995) and Hirai et al. (1997) D CO2-H2O (approximately 1.5 x 9 10 − m 2 /s) is quasi independent of pressure in the tested range of circa 9-40 MPa. Their measurements were all performed at 286 K. However, Renner's (1988) measurements show that D CO2-H2O increases with pressure, this is supported by Mutora et al.'s (2010) analysis. Renner (1988) measured diffusion coefficients of CO 2 in decane D CO2-C10 at a temperature of 311 K and in a pressure range 1.54-5.86 MPa. The results for D CO2-C10 ranged from 1.97-11.8 x 9 10 − m 2 /s. An increase in pressure led to an increase in D CO2-C10 and measured diffusion coefficients in a vertical sandstone core were significantly higher than in a horizontal core; this might have been due to convective forces in the vertical core. Renner developed the empirical-statistical equation (20) for D CO2-HC estimates.

CO 2 diffusion into oil
where V CO2 is the molar volume of CO 2 . Model equation (10) can also estimate the diffusion coefficients of CO 2 -hydrocarbon (HC) systems D CO2-HC ; predictions can be made for small alkane molecules (e.g. methane, ethane, butane) and polar H 2 S.

Water diffusion into scCO 2 phase
Although not essential for CO 2 storage, it is noted for completeness that water diffuses and dissolves into the scCO 2 phase. Water solubility in scCO 2 is low, it increases with pressure. For a pressure range from 8.31-20.54 MPa at 313 K water mole fractions between 0.00053-0.00596 were measured, for a pressure range between 2.51-10.20 MPa at 323 K the water mole fraction measured ranged between 0.00251-0.0120 (Sabirzyanov et al. 2002). Measured diffusion coefficients of water in CO 2 D H2O-CO2 are reported to be much higher than diffusion coefficients of CO 2 into water. Values between 1.5 x 8 10 − to 1.8 x 9 10 − m 2 /s were published for a pressure range between 7-20 MPa and a temperature of 298 K (Espinoza and Santamaria 2010). However the investigated temperature was lower than the expected temperature at CCS storage depths. The cited numbers could therefore be slightly different for actual CCS conditions. In addition, the semi-empirical model equation (10) can also estimate D H2O-CO2 diffusion coefficients. www.intechopen.com

Dispersion of dissolved CO 2 due to flow through a porous medium
In addition to diffusion, dispersion occurs when a solute flows through a porous medium. This can essentially be understood as an unsteady irreversible mixing process of two miscible fluids which have different solute concentrations (e.g. brine saturated with CO 2 = fluid 1, and brine undersaturated with CO 2 = fluid 2). Dispersion can therefore influence CO 2 mass transfer as it changes the CO 2 concentration gradient. Dispersion is caused by several effects (Bear 1972(Bear , Özgür 2006(Bear , 2010: 1. The flow velocity profile in a pore (the flow velocity has a maximum in the middle of a pore). 2. Different flow velocities in different pores (the pores in a geological rock have a pore size distribution and therefore different flow resistances to fluids according to their size; faster flow happens in the pores with a larger diameter). 3. The complex tortuosity of the pores in the rock; some pores are longer and fluid flow takes longer. 4. Interactions of the solute with the rock matrix/rock surface. 5. Chemical reactions, e.g. ion exchange, of the solute with species in the brine or on the rock surface. Bear (1972) distinguishes between mechanical dispersion and hydrodynamic dispersion. He defined hydrodynamical dispersion as the sum of mechanical dispersion plus molecular diffusion. The dispersion described above -and all dispersion mentioned in this text -is the same as Bear's mechanical dispersion. At reservoir scale dispersion can be described by equation (21) where D dis is the dispersion coefficient, u is the average pore flow velocity and α the dispersivity (Bear, 1972;Özgür, 2006).
The dispersivity α is a property of the reservoir and it depends on the heterogeneity of the porous medium and the length of flow. Schulze-Makuch (2005) reviewed 307 datasets and suggested α L = c 0.5 L ( w h e r e α L is the longitudinal dispersivity, L is flow distance and c varies between 0.01 m for sandstones and unconsolidated material and 0.8 m for carbonates). A detailed discussion of dispersion and dispersivities is given by Bear (1972).

Convection of CO 2 -enriched brine in the reservoir
Convection -here defined as flow at the reservoir scale induced by gradients in density, concentration or heat -can potentially move large quantities of dissolved CO 2 through the formation. A resistance threshold has to be overcome for convection to commence, this threshold can be assessed with the Rayleigh number Ra (equation 22) (Riaz et al. 2006).
where K = permeability Δ = density difference (between brine with high CO 2 concentration and brine with low CO 2 concentration) g = gravitational constant H = reservoir depth www.intechopen.com D = diffusion coefficient µ = brine viscosity φ = porosity Above a critical Rayleigh number Ra c convection will occur; Ra c is a function of the boundary conditions of the system (Weatherill et al. 2004), e.g. for a homogenous reservoir where the horizontal boundaries are impermeable and perfect heat conductors Ra c = 4 2 (Lindeberg and Wessel-Berg 1997). One mechanism which can trigger convective flow is dissolution of CO 2 into brine, which can increase brine density by 1% under CCS conditions (Ennis-King and Paterson 2005). Based on an expression suggested by Garcia (2001Garcia ( ) Özgür (2006 developed an equation (23) with which the effect of aqueous CO 2 concentration on brine density can be estimated. = dissolved CO 2 mass fraction V m,brine = apparent molar volume of CO 2 in brine M = molecular weight of CO 2

Reservoir scale dissolution trapping
In the context of reservoir flow where dissolved CO 2 molecules are transported, convection, dispersion, diffusion and maximum CO 2 solubilities can all play a significant role. This is an active field of research, and three literature examples are presented where CO 2 solute transport was modelled at reservoir scale. Interesting conclusions extracted from these computations are that dissolution trapping is favourably done in a high permeability reservoir. Moreover CO 2 dissolution can significantly reduce reservoir pressure (the pressure is increased by CO 2 injection, but only a maximum reservoir pressure is tolerable, the fracture pressure), improving injectivity, i.e. CO 2 can be injected at a faster rate, and more CO 2 can be stored in total -provided that CO 2 dissolves at an adequate rate or CO 2 injection is slow enough. Özgür (2006, 2010)  , Peclet number = ratio between transport by convection/transport by molecular diffusion (Bear 1972(Bear ) Özgür (2006(Bear , 2010 solved the diffusion-convection equation (25)  The solution for equation (25) is then (Lake 1989) Özgür (2006, 2010) also conducted numerical modelling studies, and found that convection rate strongly increases with increasing permeability and dissolution trapping is strongly accelerated thereby. In diffusion dominated systems the dissolution rate is very slow, however, and only after 7 10 years the considered aquifer was completely saturated with CO 2 . Higher dispersivity generally supports dissolution trapping. It is moreover interesting to note that the mixing zone length Δz D (which is defined as the distance between the points C D = 0.1 and C D = 0.9 in the reservoir, Lake 1989) reaches a value of 0.9 in diffusion dominated systems only after a threshold (when convection sets in) is reached. In convection dominated systems, porosity decreases Δz D , while dispersivity slightly increases Δz D . Lindeberg and Wessel-Berg (1997) modelled the onset of convection in aquifers into which CO 2 has been injected. The water column in such aquifers can be unstable because of the density gradient introduced by molecular CO 2 diffusion into the brine. In their simulation they solved the Darcy equation, heat conduction equation, equation of continuity and energy equation (details are described very thoroughly by Bear (1972)). They also included the equation of diffusion (27) so that diffusive mass transfer was considered.

The Lindeberg/Wessel-Berg model (1997)
where j is the volume flux. They calculated the Rayleigh numbers for an array of model reservoirs, spanning a temperature range from 303-363 K, a pressure range from 10-30 MPa, a permeability range from 100-2000 mD, while the porosity was a constant 30%. Variations in pressure and temperature resulted in brine density variations between 1013.5-1036 kg/m 3 and molecular diffusion coefficients between 2.2-6.3 x 9 10 − m 2 /s. The brine density difference Δ was 14.42 kg/m 3 due to difference in dissolved CO 2 concentration, while Δ was only 2.847-2.910 kg/m 3 due to differences in temperature. In Lindeberg and Wessel-Berg's model the water column is stable if only thermal gradients are considered, Ra lies then in the range 3.53-29.3 and no convection occurs (Ra c = 39.5 in this case). However, if molecular CO 2 diffusion is considered (resulting in a significantly higher Δ ), convection is predicted to occur. Lindeberg and Wessel-Berg define a stability criterion S which is the sum of the temperature and concentration effect on convective stability. S is analogous to Ra, and for infinite CO 2 dilution or an infinite molecular diffusion coefficient S becomes equal to Ra. The computed S values range from 1046-24204, and they are much higher than Ra c . This means that convection will occur in aquifers under CCS conditions, which strongly enhances dissolution trapping and storage security. This convection is caused by the concentration gradient, not the temperature gradient. Lindeberg and Wessel-Berg (1997) suggest improvements for their model, especially a more sophisticated description of the concentration gradient should be implemented (they used a linearized concentration gradient). Moreover the Soret effect should be considered. Riaz et al. (2006) conducted a linear analysis and numerical simulations of the stability of the diffusive boundary layer (i.e. the brine layer adjacent to the scCO 2 phase into which the CO 2 diffuses) in a semi-infinite domain. Their calculations are based on Boussinesq-flow in a horizontal porous layer. The model neglects dispersion and geochemical reactions and assumes a homogenous and isotropic porous medium. Riaz et al. (2006) describe a critical time t c (equation 28) which is a criterion for the onset of gravitational instability. For times larger than t c convection will occur.

The Riaz model (2006)
( ) www.intechopen.com t c influences the penetration depth of the diffusive boundary layer (t), which again influences Ra c = Ra( (t)). t c can vary over several magnitudes, mainly because permeability can span several magnitudes in a geological formation. For a permeability increase from 1 mD to 3 Darcy Riaz et al. (2006) calculated a t c decrease from 2000 years to below 10 days, and associated with that (t) changed from 55 m (for 1 mD permeability) to 0.07 m.
The model also demonstrates that Ra has a strong influence on the finger-like flow in the reservoir, including finger thickness and shape. In terms of the numerical model they found that grid size plays an important role and a fine grid is required to resolve disturbances at small times. Correct identification of such early disturbances is necessary to obtain reliable results. One important conclusion they make is that dissolution trapping is strongly enhanced in high permeability reservoirs. They estimate that the onset of gravitational instabilitiesessentially induced by molecular diffusion mass transfer processes -occurs after several hundreds of years for typical aquifers with average permeability. It should be noted that these estimates are quite rough because of the assumptions made.

Summary of reservoir models
There are other reservoir models described in the literature, e.g. Ennis- King and Paterson (2005) conclude that anisotropy of the reservoir has a strong effect on dissolution trapping, but this is beyond the scope of this book chapter and the reader is encouraged to check current research; this is an active area of research. The simulation results are very important for CCS assessments and project planning, but it must be emphasized that more experimental research should be conducted, in the laboratory and especially at field scale to evaluate the quality of the model predictions. In addition, it is important to stress the approximative character of these models, real field situations are much more complex, e.g. it is not clear whether Fick's law can describe diffusion in the field or whether very heterogeneous pore structures (for instance in carbonate reservoirs) enhance convection or slow it down.

Multiphase flow in the reservoir -flow of the scCO 2 phase
The flow of the scCO 2 phase affects the dissolution process as it determines interfacial areas and overall position of the CO 2 in the reservoir. Reservoir models predict that the injected CO 2 phase rises upwards and is stopped by the caprock (Qi et al. 2009, Juanes 2006, Hesse 2008. This behaviour has been confirmed experimentally in the Sleipner formation by seismic imaging (Iglauer 2011). Small residual CO 2 clusters at the trailing edge of the rising CO 2 plume -trapped by capillary forces , Juanes et al. 2006) -strongly increase CO 2 -brine interfacial areas. Hence CO 2 dissolution speed is predicted to be accelerated, especially if combined with convective flow of saturated/undersaturated brine. However experimental reservoir monitoring data is needed to confirm these predictions. Optimal conditions would be to bring undersaturated brine continuously into contact with residual micrometer-sized CO 2 bubbles while removing saturated or highly CO 2 -enriched brine simultaneously. Engineering this dissolution phenomenon can be a promising topic for future research. Moreover, and most likely even more significant in the short term -thereby strongly affecting the economics of CCS schemes are the fluid dynamics associated with CO 2 injection. CO 2 injectivity and CO 2 -wellbore effects can strongly impact CCS schemes. For example, flow in the reservoir is strongly influenced by changes in rock morphology and wettability, which can result in changes of relative permeabilites and capillary pressures of CO 2 and brine. Relative permeability and capillary pressures however strongly influence multi-phase fluid flow in the reservoir. As an example, there is evidence that wettability (Espinoza andSantamaria 2010, Chiquet et al. 2007) and rock pore morphology -especially carbonates (Luquot and Gouze 2009) are changed by scCO 2 . More research work is required in this area to completely understand these changes and improve CCS risk assessment.

Conclusions
In summary it is clear that dissolution trapping is a potential solution for storing large quantities of anthropogenic CO 2 thereby reducing carbon emissions. More research is required, especially field testing with integrated monitoring to check how the CO 2 behaves under realistic injection and reservoir conditions in the medium-to-long term. The major advantages of dissolution trapping are that very substantial amounts of CO 2 can be stored very safely. The risk is that CO 2 dissolves too slowly so that a significant part of CO 2 is still in a mobile separate supercritical phase (separated from the brine phase) which is buoyant and could escape to the surface. There are however two other CCS mechanisms, structural and residual trapping which prevent or at least reduce the CO 2 leakage risk. It must also be guaranteed that no drinkable-water aquifers are contaminated with CO 2 or any harmful species mobilized by CO 2 injection (e.g. dissolution of heavy metal ions by the acidic brine generated), which may then be transported into drinking water reservoirs.