Bentheimer Sandstone

Article pubs.acs.org/EF

Wettability Evaluation of a CO2/Water/Bentheimer Sandstone System: Contact Angle, Dissolution, and Bubble Size N. Shojai Kaveh,*,† E. S. J. Rudolph,‡ P. van Hemert,† W. R. Rossen,† and K.-H. Wolf† †

Department of Geoscience and Engineering, Delft University of Technology, Delft 2628CN, The Netherlands Fakultaet III, Institut fuer Lebensmitteltechnologie und Lebensmittelchemie, Technische Universität Berlin, 14195 Berlin, Germany

‡

S Supporting Information *

ABSTRACT: The success of CO2 storage in deep saline aquifers and depleted oil and gas reservoirs is largely controlled by interfacial phenomena among fluid phases and rock pore spaces. Particularly, the wettability of the rock matrix has a strong effect on capillary pressure, relative permeability, and the distribution of phases within the pore space and thus on the entire displacement mechanism and storage capacity. Precise understanding of wettability behavior is therefore fundamental when injecting CO2 into geological formations to sequestrate CO2 and/or to enhance gas/oil production. In this study, the contact angles of Bentheimer sandstone/water/CO2 or flue gas have been evaluated experimentally using the captive-bubble technique in the pressure range from 0.2 to 15 MPa. The experiments were conducted using different compositions of aqueous phase with respect to CO2, i.e., unsaturated and fully saturated. It has been shown that a reliable contact-angle determination needs to be conducted using a pre-equilibrated aqueous phase to eliminate dissolution effects. In the fully saturated aqueous phase, the Bentheimer sandstone/water system is (and remains) water-wet even at high pressures against CO2 and/or flue gas. In these systems, the data of the stable contact angle demonstrate a strong dependence on the bubble size, which can be mainly explained by the gravity (buoyancy) effect on bubble shape. However, the surface nonideality and roughness have significant influence on the reliability of the contact-angle determination. The results of this study prove that in order to avoid the dependency of the contact angle on the bubble size in these systems, the effect of gravity (buoyancy) on bubble shape has to be considered by calculation of the Bond number; for systems characterized by Bond numbers less than 0.9, the influence of the bubble radius on the contact angle becomes insignificant. The experimental results show that, in contrast to quartz, the phase transition of CO2 from subcritical to supercritical has no effect on the wettability of the Bentheimer sandstone/water system, which originates from differences in the surface charges of quartz and Bentheimer sandstone. In an unsaturated system, two dissolution regimes are observed, which may be explained by density-driven natural convection and molecular diffusion.

1. INTRODUCTION To reduce CO2 emissions into the atmosphere, different scenarios are proposed to capture and store carbon dioxide (CO2) in geological formations (CCS). Storage strategies include CO2 injection into deep saline aquifers,1,2 depleted gas and oil reservoirs,3−5 and unmineable coal seams.6 Even though the volumetric CO2 storage capacity is the highest in aquifers, CO2 storage by means of CO2-enhanced gas and oil recovery (CO2-EGR and CO2-EOR) is more economically viable. In reservoir engineering, it has been well-identified that interfacial interactions, i.e. ,wettability, capillarity, interfacial tension, and mass transfer, control the flow behavior and the displacement in porous media. Particularly, wettability has been known as one of the most important factors determining the residual saturation, the capillary-pressure, and the relativepermeability functions.7,8 This means that the process of CO2 storage in hydrocarbon reservoirs and in deep saline aquifers is influenced by gas/liquid/rock interfacial interactions.9−11 The relation between the interfacial interactions (interfacial tension, capillarity, and wettability) is represented by the Young− Laplace equation: Pc = Pnw − Pw =

where Pc is the capillary pressure, Pnw and Pw are the pressures in the nonwetting and wetting phases, respectively, γaq,CO2 is the interfacial tension between the aqueous phase and the CO2-rich phase, R is an effective pore radius corresponding to the narrowest pore throat along the entire CO2 flow path,12 and θ is the contact angle related to the reservoir wettability (determined through the densest phase, here the aqueous phase; Figure 1). The capillary pressure can be positive or negative, depending on the wetting phase; i.e., the contact angle is smaller or greater than 90°. To identify the secure strategy for CO2 injection, not only the wettability and its relation to fluid distribution but also the physics of the trapping mechanisms need to be understood. Capillary trapping occurs when CO2 is immobilized in the rock pores by capillary forces. This process depends on the interfacial tension (IFT) between the CO2-rich and the aqueous phase (brine), wettability of the rock, and the poresize distribution (eq 1).13,14 In the literature, a large amount of data related to research with respect to CO2 storage in depleted gas reservoirs and aquifers can be found. Current focus is on geochemical modeling, aquifer and reservoir simulation, long-term reservoir integrity, and risk assessment. Only a very Received: January 7, 2014 Revised: April 28, 2014 Published: May 1, 2014

2γaq,CO cos θ 2

R © 2014 American Chemical Society

(1) 4002

dx.doi.org/10.1021/ef500034j | Energy Fuels 2014, 28, 4002−4020

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2. THEORETICAL REVIEW 2.1. Wettability and Contact-Angle Determination. Wettability of reservoir rocks is determined by a complex relationship of interfacial interactions between the rock, composed of a wide variety of minerals, and the reservoir fluids that occupy the irregular pore space. Experimentally, the wettability is only determined in the laboratory because no experimental method exists for in situ measurements. Different techniques, either quantitative or qualitative, have been developed to evaluate the wettability of a rock/fluid system, namely, the Amott test, the USBM test, and contact-angle measurements. The Amott and USBM methods give a quantitative value of the wettability of a core only at atmospheric conditions. The contact-angle method allows the determination of the wettability of a specific surface also at high pressures and elevated temperatures.22 To avoid complications due to surface roughness and heterogeneity during the experiments and data processing, the experimental determination of the contact angle is commonly conducted on idealized and polished surfaces. The wettability determination on a polished surface leads to an “apparent contact angle” determination. However, the average of these contact angles can be used as an index for the wettability of the surface. Therefore, experimentally determined contact angles are widely used to characterize the wettability of complicated systems, in particular at high pressures and elevated temperatures.12,14,19 For the characterization of the surface wettability by means of the contact angle, Young’s equation is applied. The Young’s contact angle, θY, is a unique contact angle at equilibrium. However, in practice, many metastable states of a droplet/bubble on a solid exist, which might lead to an inequality of the experimentally determined contact angle, θ, with the Young’s contact angle, θY. In general, the difference in the receding, θr, and advancing contact angle, θa, is called the contact angle hysteresis and results from surface roughness and/or heterogeneity.23 On ideal surfaces, there is no contact-angle hysteresis, and the experimentally determined contact angle is equal to θY. The contact angle between the three phases (θ in Figure 1) determines whether a reservoir rock is water-wet (θ < 75°), intermediate-wet (75° 2100. The calculation of 4013


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aqueous phase to eliminate dissolution effects. Due to dissolution, the bubble size continuously changes, so that a reliable and reproducible contact-angle determination is not guaranteed. (b) Experiments in the fully saturated system show that Bentheimer sandstone is (and remains) water-wet against either CO2 or flue gas, even at supercritical pressures. However, all contact angles of the flue gas bubbles are smaller than those of CO2. The data for the apparent contact angle of these systems show a strong dependence on the bubble size. (c) Analysis of the experimental data shows that although the surface nonideality and roughness influence on the reliability of the contact-angle values and its variation with the bubble size, however, it is not a major controlling factor on this variation in the system at hand. This dependency can be mainly explained by the effect of gravity (buoyancy) on bubble shape. The influence of the bubble radius on the contact angle of the CO2 system becomes insignificant for bubble diameters smaller than 2.3 mm (Bond numbers less than 0.9). (d) The results of this study confirm previous findings by Vafaei and Podowski30,31 that axisymmetric droplets are sizedependent and cannot satisfy the original Young equation. In addition, it is in a good agreement with results of Sakai and Fujii,38 which shows that the apparent contact angle on rough surfaces can be changed by gravity. (e) According to the results of this study, it can be concluded that in order to avoid the dependency of the contact angle on the bubble size in these systems, the effect of gravity (buoyancy) on bubble shape has to be considered by calculation of the Bond number. (f) To identify the effect of pressure, only results with Bond numbers smaller than 0.9 (negligible dependency to the bubble size) were considered. From this, it is deduced that there is no significant effect of pressure on the contact angle of the Bentheimer/CO2/water system. This inconsistency between the results of Bentheimer and quartz originates from differences in surface charges of Bentheimer and quartz. Even if Bentheimer sandstone is mainly composed of quartz, a low content of clay (i.e., 2.5% Kaolinite and so on) changes the surface charge of particles considerably. (g) Results obtained from unsaturated aqueous phase experiments provide important information on the interfacial interactions and mass transfer between the aqueous and CO2 phases. In the unsaturated system, the change in contact angle is influenced by a number of mechanisms such as dissolution and bubble-size variation, rather than by the wetting properties of the surface alone. (h) For experiments in the unsaturated aqueous phase, two dissolution regimes were observed. Analysis of the data showed that this behavior cannot be caused by wettability alterations of the surface from strongly to less water-wet, but by bubble volume reduction due to CO2 dissolution in the aqueous phase. (i) In the CCS field application, the amount of capillarytrapped CO2 depends on the wettability of reservoir rocks. Results of this study show that there is no significant effect of pressure on the wettability of the Bentheimer/water/CO2 or flue gas system. Even at high pressure, the Bentheimer sandstone remains water-wet to either CO2 or flue gas.

Figure 15. Bubble radius as a function of time at 0.58 MPa and a constant temperature of 318 K. Blue triangles display experimental data, and the red line gives the description with Fick’s law (see also Appendix 4) assuming a bulk phase of pure water (no CO2 initially dissolved in the aqueous phase) and using a molecular diffusion coefficient of CO2 in water, D, at 318 K from ref 61.

this dimensionless number for the system at hand (Appendix 5) reveals that diffusive transport is accelerated by density-driven natural convection in regime I. Considering the dimensions and conditions of the system at hand, it is expected that the entire bubble dissolves quickly by natural convection since Ra > 2100. However, after a certain time, known as the transition time, dissolution becomes less convection-dominated and more diffusion-dominated. The density difference in regime II is smaller, but according to this criterion (Ra > 2100), natural convection should occur in regime II as well. Nonetheless, the results indicate that the rate of mass transfer is what one would expect for diffusion with no convection. The reason for this sudden change observed in the mass-transfer rate is not clear yet. It might be attributed to the formation of a CO2-saturated water film around the bubble due to the capillary condensation, which reduces the driving force (concentration gradient) and the mass-transfer rate at the interface. This phenomenon cannot be studied by available experimental data from this study and needs to be investigated further. Based on the slow dissolution rate of regime II, this regime is mainly considered to be a diffusion-dominant process. Due to the formation of a CO2-saturated water film, the dissolution of the bubble in this regime takes longer than the dissolution of the bubble in the pure water phase. These findings are in good agreement with the experimental results of Farajzadeh.63

5. CONCLUSION In this work, wettability of the Bentheimer sandstone/water/ CO2 and/or flue gas system has been experimentally evaluated using the captive-bubble technique in a pressure range from 0.2 to 15 MPa (from 2 to 150 bar). The CO2 experiments were conducted using different water/CO2 mixtures, i.e., unsaturated and fully saturated, in order to evaluate the dissolution effects and wetting properties for short and long periods. All contactangle determinations were performed using natural rock surfaces which had not been treated chemically. The results of these experiments do contribute to a better understanding of wettability and the displacement behavior of fluids in sandstone reservoirs. The results are summarized as follows: (a) A reliable contact angle determination should be conducted using a pre-equilibrated (fully saturated or quasi-saturated)

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APPENDIX 1: SYNTHETIC MINERAL RECONSTRUCTION AND XRD ANALYSIS OF BENTHEIMER SANDSTONE Tables 2 and 3 list synthetic mineral reconstruction and XRD analysis of Bentheimer sandstone, respectively. 4014


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bubble with time (Figure 16c). After introducing the CO2 bubble, mass transfer occurs between the bubble and the aqueous phase. The driving force for this process is the difference in chemical potentials of each specific component in the two coexisting phases. The time required to reach a stable bubble size depends on the chemical potential gradients in the two phases. Since adding a CO2 bubble to the equilibrated system only slightly disturbs the equilibrium, the mass transfer between the bubble and the aqueous phase is negligible and does not affect the contact angle so that the wetting properties of the substrate are determined. For such a system, any variation of the contact angle with time can be attributed to surface heterogeneity and roughness. According to Figure 16, the contact angle variation is proportional to the change in bubble volume which shows the dependency of the contact angle on the bubble size in the system at hand. These observations are in agreement with the results discussed in section 4.2. In Table 4, the basic parameters allowing the direct comparison of experiments in the unsaturated, quasi-saturated, and fully saturated system at 0.58 MPa are given. θmin is the contact angle of the initial bubble with the radius of Rio. In the unsaturated system, the CO2 bubble disappeared after 2700 s. In the quasi-saturated system the bubble first shrank and then became stable after 4800 s. In the fully saturated system, the stable bubble was obtained after 180 s. In the two latter systems, Rfinal and θfinal are the bubble radius and the contact angle after establishing the equilibrated bubble. From the data at hand, it can be concluded that a reliable contact-angle determination should be conducted in a preequilibrated (fully saturated or quasi-saturated) aqueous phase to eliminate dissolution effects. Dissolution affects the contactangle determination due to the constantly changing bubble size; this means that the system continuously changes its conditions, thereby changing the contact line and the contact angle.

Table 2. Synthetic Mineral Reconstruction of Bentheimer Sandstone mineral

concn wt (%)

quartz kaolinite montmorillonite orthoclase dolomite calcite hematite rutile pyrite calcium phosphate halite (NaCl)

91.70 2.50 0.18 4.86 0.26 0.15 0.16 0.03 0.01 0.07 0.03

Table 3. XRD Analysis of Bentheimer Sandstone

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compd name

concn wt (%)

absolute error (%)

Al2O3 CaO Cl Co3O4 Cr2O3 Fe2O3 K2O MgO Na2O NiO P2O5 PbO SO3 SiO2 SrO TiO2 ZnO ZrO2

1.931 0.208 0.020 0.001 0.005 0.172 0.827 0.064 0.022 0.002 0.030 0.003 0.020 96.616 0.002 0.072 0.002 0.004

0.04 0.01 0.004 0.0008 0.002 0.01 0.03 0.008 0.004 0.001 0.005 0.002 0.004 0.001 0.008 0.001 0.002

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APPENDIX 3: THEORETICAL ANALYSIS OF GAS CAPTIVE BUBBLE ON A HORIZONTAL SUBSTRATE The following theoretical analysis and derivations are based on the analytical model of Vafaei and Podowski,31 which allows the calculation of liquid droplet volume from a given contact angle (and radius of the contact area). In their approach, the droplet is circular in all its horizontal cross-sections. This assumption does not apply to vertical sections. This model has been adapted for a captive gas bubble system surrounded by the aqueous phase by considering the effect of buoyancy force on the bubble contour. Forces in the z-direction acting on an axially symmetric captive bubble, as shown in Figure 17, should be considered. The force balance for a slice between z and z + dz is

APPENDIX 2: EVOLUTION OF THE BUBBLE RADIUS AND CONTACT ANGLE WITH TIME FOR DIFFERENT PHASE CONDITIONS To determine whether the system is in the one-phase or twophase region, the phase diagram of the CO2/water system is used from the literature (Figure 4). Figure 16 shows the evolution of the bubble radius and contact angle with time at 0.58 MPa for different phase conditions and overall compositions of the CO2/water system. The data show that, for pre-equilibrated systems, the bubble dissolution rate is smaller than the dissolution rate in the unsaturated system. For an unsaturated system (one-phase region), the amount of CO2 in the system is smaller than the maximum amount which can be dissolved in the aqueous phase at a given temperature and pressure. Hence, when adding a CO2 bubble, the bubble dissolves completely in the aqueous phase (Figure 16a). In the quasi-saturated system, the bubble initially dissolves slowly and the bubble size decreases. When equilibrium is established, the bubble size remains constant (Figure 16b). The time to reach equilibrium depends on the initial composition of CO2 in the water-rich phase. In the fully saturated system, equilibrium is already established when injecting CO2 into the system. Still, releasing CO2 in the equilibrated system causes a slight disturbance, which can be recognized by an initial volume reduction of the

dFg − dFb + Fp(z) − Fp(z + dz) − Fσ sin θ(z) + Fσ sin(θ + dθ )(z + dz) − 2πrPL dr = 0

(A3.1)

where the individual forces are gravity force: dFg = ρg gπr 2(z) dz

(A3.2)

buoyancy force: dFb = ρl gπr 2(z) dz 4015

(A3.3)


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Figure 16. Evolution of bubble radius (shown as blue triangles at right y-axis) and contact angle (shown as red squares at left y-axis) over time at 0.58 MPa and 318 K in (a) unsaturated, (b) quasi-saturated, and (c) fully saturated aqueous phase. The error bars in these panels are given based on the standard error of the values.

surface tension force:

Table 4. Parameters Characterizing the Experiments at 0.58 MPa in the Unsaturated, Quasi-saturated, and Fully Saturated System

Fσ (z) = 2πr(z)γlv

(A3.5)

where the vertical pressure distribution is given by

aqueous-phase condition

R0 (mm)

θ0 (deg)

Rfinal (mm)

θfinal (deg)

time (s)

unsaturated (fresh water) quasi-saturated with CO2 fully saturated with CO2

1.18 1.02 1.23

17 17.3 16.7

0 0.62 1.21

35.1 26.06 20.4

2700 4800 180

p(z) = ρg gz + PL +

2γlv R0

(A3.6)

where PL is the pressure determined in the aqueous phase; γlv is the liquid−vapor interfacial tension at pressure PL; R0 is the bubble radius at apex, and ρg is the density of the bubble. By accounting for the individual forces, eq A3.1 gives πr 2(z)(ρl − ρg )g =−

d dr [πr 2(z) p(z) − 2πr(z)γlv sin θ(z)] − 2πrPL dz dz (A3.7)

Integrating both sides of eq A3.7 yields Vb =

δ

π r 2 dz =

2πγlvR2 ⎛ 1 sin θ ⎞ − ⎜+ ⎟ Δρg ⎝ R 0 R ⎠

(A3.8)

where δ is the location of the apex, Δρ is the density differences between the bubble and aqueous phase, and R is the radius of the contact circle. Data of the contact angle (θ), the radius of the curvature at the apex (R0), and the radius of the contact circle (R) are obtained using the numerical method from the Young−Laplace description of the bubble profile. Δρ and γlv

Figure 17. Force balance in the z-direction for a captive bubble.

pressure force: Fp(z) = πr 2(z) p(z)

∫0

(A3.4) 4016


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are determined experimentally at the specific pressure and temperature.

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r = R io

APPENDIX 4: STEADY-STATE DIFFUSION THROUGH THE BUBBLE VARIABLE AREA In this section we follow the derivation for steady-state diffusion through the spherical bubble variable area into an infinite body of liquid65 and then scale the mass flux by the fraction of the full spherical surface represented by the CO2 bubble against the solid surface. Diffusion of CO2 from a CO2rich bubble into the aqueous phase is described using Fick’s first law.65 A mass balance is written at a thin spherical shell with the thickness of Δr around the bubble (Figure 18). Since

at r → ∞

(A4.6)

at t = 0

(A4.7)

By assuming a spherical shape for the bubble (truncated by the solid surface), π Vb = rb3[2 + 3 cos θs − cos3 θs] (A4.8) 3 Ab = 2πrb 2(1 + cos θs)

(A4.9)

Integrating eq A4.4 with boundary conditions (eq A4.5 and A4.6) yields s b W = 2π (1 + cos θs)D(CCo − CCo )r 2 2 b

(A4.10)

W is the constant molar rate of mass transfer (molar flux × area, eq A4.4) and is equal to the rate of dissolution of the bubble at any instant: W=−

d mb d = − (ρCO Vb) 2 dt dt

(A4.11)

Combining eqs A4.8, A4.10, and A4.11 gives −π[2 + 3 cos θs − cos3 θs]ρCO rb 2 2

drb dt

s b )r = 2π (1 + cos θs)D(CCO − CCO 2 2 b

Figure 18. Mass balance in the r-direction for a captive bubble through the variable area.

Integrating eq A4.12 with initial condition (eq A4.7) yields 2

rb = R io

the bubble dissolves in the liquid phase, the diffusion area cannot be considered to be constant and changes along the diffusion direction (r) and also with time.65 In this case, at any instant in time, t, the CO2 bubble radius is rb. A steady-state mass balance (zero accumulation rate) on the spherical shell (Δr) gives65 −

d (AbNCO2) = 0 dr

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APPENDIX 5: RAYLEIGH NUMBER CALCULATION FOR A CAPTIVE-BUBBLE SYSTEM The onset of natural convection in the porous medium is determined by the Rayleigh number (Ra), which is dependent on the properties of the fluids and geometry of the system:

(A4.2)

where NCO2 is the molar flux of CO2, Ab is the gas−liquid interfacial area, and W is the constant molar rate of mass transfer. In this case, it is assumed that water diffusion into the CO2-rich phase (bubble) is negligible because of the small diffusion coefficient of water into CO2. Therefore, the system is considered as diffusion of CO2 through nondiffusing water. According to Fick’s law

Ra =

(A4.3)

where D is the CO2 diffusion coefficient into water. It should be noted that D depends on temperature but not greatly on pressure (D = 3.07 × 10−9 m2/s at 318 K).59 Combining eq A4.2 and A4.3 yields − A bD

dCCO2 dr

=W

(A4.4)

Ra =

In this case, initial and boundary conditions are s CCO2 = CCo 2

at r = rb

k ΔρgL ϕμD

(A5.1)

where k is the permeability of the porous medium, Δρ is the density difference between the boundary layer fluid and that far away, g is the local gravitational acceleration, L is the characteristic length scale of convection, ϕ is the porosity, μ is the dynamic viscosity, and D is the diffusivity of the characteristic that is causing the convection. In porous media the interfaces will be unstable for Rayleigh numbers above 4π2 ≈ 40.66 For bulk solutions eq A5.1 converts to

dCCO2 dr

s b ⎞ − CCO (CCO )D ⎛ 2(1 + cos θs) 2 2 ⎜ ⎟t −2 3 ρCO ⎝ (2 + 3 cos θs − cos θs) ⎠ 2

It is assumed that the CO2 concentration in the bulk (CbCO2) far from the bubble is zero. In this model, the bubble geometry is assumed to be spherical. This may have caused an error in calculations, in particular for larger bubbles. The average deviation for the volume of bubbles compared to spheres, at 0.58 MPa, was 5.31%.

which yields

NCO2 = −D

2

(A4.13)

(A4.1)

AbNCO2 = constant = W

(A4.12)

ΔρgL3 μD

(A5.2)

In these systems, density-driven natural convection occurs when Ra > 2100.

(A4.5) 4017


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Accordingly, for the captive-bubble system at 0.58 MPa and 318 K, eq A5.2 gives Ra =

(1060 − 1000 kg/m 3) × (9.8 m/s2) × [(2 × 10−2)3 m 3] [0.65 × 10−3 kg/(m·s)] × [3 × 10−9 (m 2/s)]

= 24 × 108 > 2100

Therefore, the calculation of this dimensionless number for the system at hand reveals that diffusion is accelerated by density-driven natural convection in regime I. The density difference in regime II is smaller, but according to this criterion, natural convection should occur in regime II as well. Nonetheless, the results indicate that the rate of mass transfer is what one would expect for diffusion with no convection (section 4.2, Figure 15). Nomenclature

Ab = gas−liquid (bubble) interfacial area Bo = Bond number CCO2 = CO2 concentration CsCO2 = CO2 concentration at the bubble interface CbCO2 = CO2 concentration in the aqueous phase (bulk) 1 CbCO = CO2 concentration in the bulk phase in regime I b2 2 CCO2 = CO2 concentration in the bulk phase in regime II D = CO2 molecular diffusion coefficient into water D1 = effective diffusion coefficient in regime I D2 = effective diffusion coefficient in regime II Fb = buoyancy force Fg = gravity force Fp = pressure force Fσ = surface tension force g = local gravitational acceleration H = contact-angle hysteresis L = characteristic length scale of convection NCO2 = molar flux of CO2 mb = bubble mass MD = bubble maximum diameter p(z) = vertical pressure distribution Pa = characterization factor of the surface roughness Pb = total pressure in the bubble Pc = capillary pressure PL = pressure of the aqueous phase Pnw = pressure of the nonwetting phase Pw = pressure of the wetting phase R = contact radius; the radius of the contact circle rb = bubble radius R0 = radius of curvature at apex Ri0 = initial radius of bubble at apex R02 = radius of bubble at apex at transition time Rfinal = bubble radius after establishing the equilibrated bubble Ra = Rayleigh number t = time V = volume of a droplet Vb = volume of a bubble W = constant molar rate of CO2 θ = apparent contact angle (experimentally determined contact angle) θY = Young’s contact angle θa = advancing contact angle θr = receding contact angle θs = contact angle for a spherical droplet/bubble θ∞ = contact angle for the bubble with infinite radius of the solid−liquid contact circle

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θmin = contact angle of the bubble with the initial bubble radius of Rio θmax = last accurate detectable contact angle θfinal = contact angle after establishing the equilibrated bubble ϕ = porosity of the porous medium μ = dynamic viscosity ρCO2 = density of CO2 in the bubble pressure ρg = density of the gas phase (bubble) ρl = density of the liquid phase Δρ = density difference between the bubble and aqueous phase γaq,CO2 = interfacial tension between the aqueous phase and the CO2-rich phase γw,cCO = interfacial tension between water and CO2 γlv = interfacial tension between the aqueous phase and the gas phase γwg = interfacial tension between CO2 and water γsv = surface energy between the solid and the gas phases γsl = surface energy between the solid and the aqueous phases σ = line tension δ = bubble height; location of the apex

ASSOCIATED CONTENT

S Supporting Information *

Text describing information concerning line-tension determination for a CO2/water/Bentheimer system and a figure showing contact angle versus bubble radius or inverse length of the contact line at two different pressures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.:+31152789671. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research reported in this work is carried out as a part of the CATO2 project (CO2 capture, transport, and storage in The Netherlands). This research is conducted in the Laboratory of Geoscience and Engineering at Delft University of Technology. We gratefully thank the technical staff of the Laboratory, particulary J. Etienne, M. Friebel, K. Heller, and J. van Meel. We also thank Dr. Cas Berentsen and Amin Ameri for their constructive input during this study.

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REFERENCES

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