**5. Kinetics of CO2 dissolution into formation brines**

Dissolution kinetics of CO2 into brine in a reservoir are driven by four main factors, namely molecular diffusion of CO2 into brine, dispersion during flow, convection of CO2-saturated (heavier) brine in the reservoir and flow of the scCO2 phase in the reservoir. These mechanisms are described in more detail in the following paragraphs.

### **5.1 Molecular CO2 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.

$$D\frac{\partial^2 c}{\partial z^2} = \frac{\partial c}{\partial t} \tag{7}$$

where

246 Mass Transfer - Advanced Aspects

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 CO2 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 CO2 (Piri and Blunt 2005). This oil layer then essentially acts as a barrier through which the CO2 has to pass in order to reach the brine

> **Component mole %**  Methane, CH4 70-98 Ethane, C2H6 1-10 Propane, C3H8 trace - 5 Butanes, C4H10 trace - 2 Pentanes, C5H12 trace - 1 Hexanes C6H14 trace – 0.5 Heptanes C7H16 trace – 0.5

Carbon dioxide, CO2 trace – 5

Hydrogen sulphide, H2S trace – 3

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 H2S, CO2 or N2 – up to 90 mol% (Firoozabadi and Cheng 2010). Such non-hydrocarbon gases usually need to be separated out of the production stream in order

Dissolution kinetics of CO2 into brine in a reservoir are driven by four main factors, namely molecular diffusion of CO2 into brine, dispersion during flow, convection of CO2-saturated (heavier) brine in the reservoir and flow of the scCO2 phase in the reservoir. These

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

to achieve sellable gas quality

increased by molecular diffusion.

**5. Kinetics of CO2 dissolution into formation brines** 

**5.1 Molecular CO2 diffusion into reservoir brines.** 

mechanisms are described in more detail in the following paragraphs.

Nitrogen, N2 trace - 15

Helium, He 0 - 5

and to be stored there safely by the dissolution trapping mechanism.


A limited number of measurements of the CO2 diffusion coefficient in water DCO2-H2O at high pressure have been conducted. Renner (1988) measured DCO2-H2O for 0.25 N NaCl brine at 311 K for a pressure range 1.54-5.86 MPa and recorded DCO2-H2O values in the range 3.07- 7.35 x <sup>9</sup> 10<sup>−</sup> m2/s. More measurements at atmospheric pressure were conducted and DCO2- H2O values between 1.8 x <sup>9</sup> 10<sup>−</sup> – 8 x <sup>9</sup> 10<sup>−</sup> m2/s (Mazarei and Sandall 1980, Unver and Himmelblau 1964) were reported. Based on these datasets, Renner (1988) developed an empirical-statistical expression (equation 8).

$$D\_{CO\_2-H\_2O} = 6391\ \mu\_{CO\_2}^{-0.1584} \mu\_{H\_2O}^{6.911} \tag{8}$$

where

μCO2 = CO2 viscosity

μH2O = H2O viscosity

Renner's analysis (1988) indicated that water viscosity and CO2 viscosity were highly correlated with the diffusion coefficient, but molecular weight of CO2, molar volume of CO2, pressure or temperature were not statistically significant. However Renner states in his paper and Renner's data show that DCO2-H2O increases with an increase in pressure. Therefore it can be expected that CO2 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 CO2 faster in the aqueous phase.

Hirai et al. (1997) measured DCO2-H2O via laser-induced fluorescence at 286 K and 29.4 and 39.3 MPa (DCO2-H2O = 1.3 x <sup>9</sup> 10<sup>−</sup> and 1.5 x <sup>9</sup> 10<sup>−</sup> m2/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) (DCO2-H2O is approximately 1.8 x <sup>9</sup> 10<sup>−</sup> m2/s at 286 K and 9-13 MPa) is however 40% larger than predicted by equation (9). Hirai's data and the Wilke-Chang equation both indicate that DCO2-H2O increases slightly with pressure.

$$^{1}D\_{\text{CO}\_{2}-H\_{2}O} = 7.4 \cdot 10^{-8} \left( \mu M\_{H\_{2}O} \right)^{0.5} T \left/ \left( \mu\_{\text{CO}\_{2}} V\_{\text{CO}\_{2}}^{0.6} \right) \right. \tag{9}$$

More recently, Mutoru et al. (2010) developed a semi-empirical model for calculating diffusion coefficients for infinitely diluted CO2 and water mixtures (equation 10) based on 187 experimental data points. The subscript 1 denotes CO2 and the subscript 2 denotes water. However, in case of water diffusing into the CO2 phase, subscript 1 denotes water and subscript 2 CO2.

$$D\_{CO\_2-H\_2O} = \frac{k\_1 \left(M\_{12} \varepsilon\_{12}\right)^{k\_2} T\_{r,2}^{k\_3}}{p\_{r,2}^{k\_4} \left(\mu\_2 c\_2\right)^{k\_5}}\tag{10}$$

Dissolution Trapping of Carbon Dioxide in

Sh = Sherwood number (= <sup>2</sup> 2 2 *CO CO H O*

ν

Sc = Schmidt number (= *CO H O* 2 2

Re = Reynolds number (= *CO*<sup>2</sup> *u d*⋅

diameter) and developed relation (14)

with the boundary conditions C = 0 at x = 0.

*CO*<sup>2</sup> *d* = CO2 droplet diameter

= kinematic viscosity

u = flow velocity

where

ν

where ˆ

Reservoir Formation Brine – A Carbon Storage Mechanism 249

According to equation (13) small CO2 droplets dissolve faster than large ones (assuming that DCO2-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

Suekane et al. (2006) studied such mass transfer processes of scCO2 dissolution into pure water in packed glass beads (measurement conditions were 313 K, 8.3 MPa, 70 µm bead

with the modified Sherwood number Sh'. Sh' can be calculated with equations (15) and (16).

<sup>ˆ</sup> <sup>2</sup> *kd Sh*

<sup>ˆ</sup> ln 1 *u C <sup>k</sup> L C*<sup>∞</sup> ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠

Equation (16) is the solution of the one-dimensional steady state mass balance equation (17)

( )( ) <sup>ˆ</sup> *dC u kA C C k C C*

Another interesting suggested correlation for DCO2-H2O has been put forward by Bahar and Liu (2008); they measured DCO2-H2O at 17.8 MPa and 356 K in 2 wt% NaCl brines and developed an empirical correlation between DCO2-H2O and the pressure p, temperature T,

7

0.5 1.3678 10 *CO T MW <sup>D</sup>*

Bahar and Liu (2008) found that DCO2-H2O is higher for unsteady-state systems, and that the duration of the unsteady-state system strongly depends on the pressure and temperature.

As stated in equation (10), temperature has a clear effect on DCO2-H2O. Unver and Himmelblau (1964) developed an empirial equation (19) for the dependence of DCO2-H2O on

molecular weight MW, volume V and viscosity µ of the liquid (equation 18).

2

**5.1.1 Effect of temperature on CO2 diffusion in water** 

*k* is the total mass transfer rate (= kA) and L is the length of the glass bead pack.

0.92 *Sh*′ = 0.029Re (14)

*dx* =− − = − <sup>∞</sup> <sup>∞</sup> (17)

<sup>−</sup> = ⋅ (18)

1.47 2.2

*V p*μ

*<sup>D</sup>* ′ <sup>=</sup> (15)

(16)

*kd D* <sup>−</sup> <sup>⋅</sup> )

ν)

*D* <sup>−</sup> )

understanding of the relation between residual and dissolution trapping.

where

$$M\_{12} = \left(\frac{1}{M\_{H\_2O}} + \frac{1}{M\_{CO\_2}}\right)^{-1} \tag{11}$$


c2 = 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 CO2. In addition, it can predict DCO2-H2O over the complete range from infinitely diluted CO2 to infinitely diluted H2O. From equation (10) it is clear that temperature has a stronger influence on DCO2-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 CO2 dissolution into brine is the consideration of the CO2 droplet diameter (Hirai et al. 1997). Especially in the context of residual trapping; here the rising CO2 plume is split into a large number of small disconnected CO2 clusters at the trailing edge of the plume due to natural water influx or chase brine injection (Iglauer et al. 2010).

The drop diameter is expected to have a highly significant effect on CO2 dissolution speed. A strong enhancement of CO2 dissolution is expected for such small CO2 bubbles as their CO2-brine surface area is significantly increased compared with that of a single-cluster CO2 plume.

The dissolution rate of CO2 can be described by equation (12) (Hirai et al. 1997).

$$d\left(\rho\_{\rm CO\_2}V\right)/dt = -kA\left(\mathbb{C}\_0 - \mathbb{C}\_\alpha\right) \tag{12}$$

where


The mass transfer coefficient k is expressed in equation (13) for high Schmidt (Sc) numbers

$$\text{Sh} = 1 + \left(\text{Sc} + 1 / \text{Re}\right)^{1/3} 0.752 \,\text{Re}^{0.472} \tag{13}$$

where

248 Mass Transfer - Advanced Aspects

12

*M*

2 2

1 1 *H O CO*

<sup>−</sup> ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

*M M*

c2 = 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 CO2. In addition, it can predict DCO2-H2O over the complete range from infinitely diluted CO2 to infinitely diluted H2O. From equation (10) it is clear that temperature has a stronger influence on DCO2-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

An interesting perspective on CO2 dissolution into brine is the consideration of the CO2 droplet diameter (Hirai et al. 1997). Especially in the context of residual trapping; here the rising CO2 plume is split into a large number of small disconnected CO2 clusters at the trailing edge of the plume due to natural water influx or chase brine injection (Iglauer et al.

The drop diameter is expected to have a highly significant effect on CO2 dissolution speed. A strong enhancement of CO2 dissolution is expected for such small CO2 bubbles as their CO2-brine surface area is significantly increased compared with that of a single-cluster CO2

( ) ( ) <sup>2</sup> *CO* / <sup>0</sup> *d V dt kA C C*

The mass transfer coefficient k is expressed in equation (13) for high Schmidt (Sc) numbers

=− − <sup>∞</sup> (12)

( )1 3 0.472 *Sh Sc* =+ + 1 1 /Re 0.752Re (13)

strong as pressure determines equilibrium compositions (Mutoru et al. 2010).

The dissolution rate of CO2 can be described by equation (12) (Hirai et al. 1997).

ρ

1

(11)

where

M = molecular mass ε1 = dipole moment

Tr,2 = reduced temperature pr,2 = reduced pressure

k1 = 7.23389 10<sup>−</sup> k2 = 0.135607 k3 = 1.84220 k4 = 2.41943 x <sup>3</sup> 10<sup>−</sup> k5 = 0.858204

µ = viscosity

2010).

plume.

where

V = volume of the scCO2 droplet, A = surface area of the scCO2 droplet

C0 = surface concentration of the droplet

k = mass transfer coefficient

*C*∞ = concentration at infinity

ε12 = ratio of dipole moments, ε1/ ε<sup>2</sup>

Sh = Sherwood number (= <sup>2</sup> 2 2 *CO CO H O kd D* <sup>−</sup> <sup>⋅</sup> ) Sc = Schmidt number (= *CO H O* 2 2 ν *D* <sup>−</sup> ) Re = Reynolds number (= *CO*<sup>2</sup> *u d*⋅ ν ) *CO*<sup>2</sup> *d* = CO2 droplet diameter

ν= kinematic viscosity

u = flow velocity

According to equation (13) small CO2 droplets dissolve faster than large ones (assuming that DCO2-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 scCO2 dissolution into pure water in packed glass beads (measurement conditions were 313 K, 8.3 MPa, 70 µm bead diameter) and developed relation (14)

$$Sh'=0.029\,\text{Re}^{0.92}\tag{14}$$

with the modified Sherwood number Sh'. Sh' can be calculated with equations (15) and (16).

$$Sh' = \frac{\hat{k}d^2}{D} \tag{15}$$

$$
\hat{k} = \frac{\mu}{L} \text{Im} \left( \mathbf{1} - \frac{\mathbf{C}}{\mathbf{C}\_{\text{eq}}} \right) \tag{16}
$$

where ˆ *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.

$$
\mu \frac{d\mathbf{C}}{d\mathbf{x}} = -kA\left(\mathbf{C} - \mathbf{C}\_{\infty}\right) = \hat{k}\left(\mathbf{C} - \mathbf{C}\_{\infty}\right) \tag{17}
$$

Another interesting suggested correlation for DCO2-H2O has been put forward by Bahar and Liu (2008); they measured DCO2-H2O at 17.8 MPa and 356 K in 2 wt% NaCl brines and developed an empirical correlation between DCO2-H2O and the pressure p, temperature T, molecular weight MW, volume V and viscosity µ of the liquid (equation 18).

$$D\_{CO\_2} = 1.3678 \cdot 10^{-7} \frac{T^{1.47} MW^{2.2}}{V^{0.5} p\mu} \tag{18}$$

Bahar and Liu (2008) found that DCO2-H2O is higher for unsteady-state systems, and that the duration of the unsteady-state system strongly depends on the pressure and temperature.

#### **5.1.1 Effect of temperature on CO2 diffusion in water**

As stated in equation (10), temperature has a clear effect on DCO2-H2O. Unver and Himmelblau (1964) developed an empirial equation (19) for the dependence of DCO2-H2O on

Dissolution Trapping of Carbon Dioxide in

several effects (Bear 1972, Özgür 2006, 2010):

pore).

takes longer.

rock surface.

where

K = permeability

 CO2 concentration) g = gravitational constant H = reservoir depth

same as Bear's mechanical dispersion.

Reservoir Formation Brine – A Carbon Storage Mechanism 251

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 CO2 = fluid 1, and brine undersaturated with CO2 = fluid 2). Dispersion can therefore influence CO2 mass transfer as it changes the CO2 concentration gradient. Dispersion is caused by

1. The flow velocity profile in a pore (the flow velocity has a maximum in the middle of a

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;

3. The complex tortuosity of the pores in the rock; some pores are longer and fluid flow

5. Chemical reactions, e.g. ion exchange, of the solute with species in the brine or on the

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

At reservoir scale dispersion can be described by equation (21) where Ddis is the dispersion coefficient, u is the average pore flow velocity and α the dispersivity (Bear, 1972; Özgür, 2006).

> *D u dis* = α

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 αL = c 0.5 L (where αL 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 – here defined as flow at the reservoir scale induced by gradients in density, concentration or heat – can potentially move large quantities of dissolved CO2 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).

> *K gH Ra D* ρ

Δρ = density difference (between brine with high CO2 concentration and brine with low

φ μ (21)

<sup>Δ</sup> <sup>=</sup> (22)

**5.4 Dispersion of dissolved CO2 due to flow through a porous medium** 

faster flow happens in the pores with a larger diameter).

4. Interactions of the solute with the rock matrix/rock surface.

**5.5 Convection of CO2-enriched brine in the reservoir** 

temperature for atmospheric pressure within a temperature range between 279-338 K. D increases monotonically with temperature T (equation 19).

$$D = \left(A + BT + CT^2\right) \cdot 10^{-9} \tag{19}$$

A = 0.95893, B = 0.024161, C = 0.00039813 are constants for CO2, A, B and C adopt different values for other gases. D is given in m2/s. Again, diffusion-dominated CO2 dissolution is more effective at higher temperatures.

#### **5.1.2 Effect of pressure on CO2 diffusion in water**

According to measurements conducted by Wilke-Chang (1955), Shimizu et al. (1995) and Hirai et al. (1997) DCO2-H2O (approximately 1.5 x <sup>9</sup> 10<sup>−</sup> m2/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 DCO2-H2O increases with pressure, this is supported by Mutora et al.'s (2010) analysis.

#### **5.2 CO2 diffusion into oil**

Renner (1988) measured diffusion coefficients of CO2 in decane DCO2-C10 at a temperature of 311 K and in a pressure range 1.54-5.86 MPa. The results for DCO2-C10 ranged from 1.97-11.8 x <sup>9</sup> 10<sup>−</sup> m2/s. An increase in pressure led to an increase in DCO2-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 DCO2-HC estimates.

$$D\_{CO\_2-HC} = 10^{-9} \mu\_{\odot\_{CO\_2}}^{-0.4562} M\_{\odot\_{CO\_2}}^{-0.6898} V\_{\odot\_{CO\_2}}^{-1.706} p^{-1.831} T^{4.524} \tag{20}$$

where VCO2 is the molar volume of CO2.

Model equation (10) can also estimate the diffusion coefficients of CO2-hydrocarbon (HC) systems DCO2-HC; predictions can be made for small alkane molecules (e.g. methane, ethane, butane) and polar H2S.

#### **5.3 Water diffusion into scCO2 phase**

Although not essential for CO2 storage, it is noted for completeness that water diffuses and dissolves into the scCO2 phase. Water solubility in scCO2 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 CO2 DH2O-CO2 are reported to be much higher than diffusion coefficients of CO2 into water. Values between 1.5 x <sup>8</sup> 10<sup>−</sup> to 1.8 x <sup>9</sup> 10<sup>−</sup> m2/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 DH2O-CO2 diffusion coefficients.

temperature for atmospheric pressure within a temperature range between 279-338 K. D

A = 0.95893, B = 0.024161, C = 0.00039813 are constants for CO2, A, B and C adopt different values for other gases. D is given in m2/s. Again, diffusion-dominated CO2 dissolution is

According to measurements conducted by Wilke-Chang (1955), Shimizu et al. (1995) and Hirai et al. (1997) DCO2-H2O (approximately 1.5 x <sup>9</sup> 10<sup>−</sup> m2/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 DCO2-H2O increases with pressure, this is

Renner (1988) measured diffusion coefficients of CO2 in decane DCO2-C10 at a temperature of 311 K and in a pressure range 1.54-5.86 MPa. The results for DCO2-C10 ranged from 1.97-11.8 x <sup>9</sup> 10<sup>−</sup> m2/s. An increase in pressure led to an increase in DCO2-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

9 0.4562 0.6898 1.706 1.831 4.524 <sup>10</sup> *CO HC CO CO CO D M*

Model equation (10) can also estimate the diffusion coefficients of CO2-hydrocarbon (HC) systems DCO2-HC; predictions can be made for small alkane molecules (e.g. methane, ethane,

Although not essential for CO2 storage, it is noted for completeness that water diffuses and dissolves into the scCO2 phase. Water solubility in scCO2 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

Measured diffusion coefficients of water in CO2 DH2O-CO2 are reported to be much higher than diffusion coefficients of CO2 into water. Values between 1.5 x <sup>8</sup> 10<sup>−</sup> to 1.8 x <sup>9</sup> 10<sup>−</sup> m2/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

*V p T* −− − − −

<sup>−</sup> = (20)

2 2 22

mole fraction measured ranged between 0.00251-0.0120 (Sabirzyanov et al. 2002).

μ

( ) 2 9 *D A BT CT* 10<sup>−</sup> =+ + ⋅ (19)

increases monotonically with temperature T (equation 19).

**5.1.2 Effect of pressure on CO2 diffusion in water** 

empirical-statistical equation (20) for DCO2-HC estimates.

supported by Mutora et al.'s (2010) analysis.

where VCO2 is the molar volume of CO2.

**5.3 Water diffusion into scCO2 phase** 

also estimate DH2O-CO2 diffusion coefficients.

**5.2 CO2 diffusion into oil** 

butane) and polar H2S.

more effective at higher temperatures.
