# Quantitative Investigation on the Contributing Factors to the Contact Angle of the CO2/H2O/Muscovite Systems Using the Frumkin-Derjaguin Equation

Authors: Masashige Shiga; Masaatsu Aichi; Masao Sorai
Journal: Geofluids
 (2020)

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## Abstract

It is significant to understand the values and trends of the contact angle of CO2/brine/mineral systems to evaluate and model the sealing performance of CO2 Geo-Sequestration (CGS). It has been reported that the contact angles of the CO2/brine/muscovite systems increase as pressure increases from ambient conditions to reservoir conditions. This trend suggests a decrease in seal integrity. In this paper, we studied its mechanisms and the contributing factors by calculating the Frumkin-Derjaguin equation, which is based on the thermodynamics of the interfacial system. Results show that a decrease of pH is a critical factor for the wettability alteration at a lower pressure range (0.1 MPa to 3.0 MPa). In contrast, the increase of CO2 density and the decrease in the interfacial tension of CO2/brine are significant for the wettability change at a higher pressure range (3.0 MPa to 10.0 MPa). Also, sensitivity analysis shows that the contact angle is sensitive to the interfacial tension of CO2/brine and the coefficients of hydration forces.


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## Body

## 1. Introduction

CO2 Geo-Sequestration (CGS) and CO2-EOR (enhanced oil recovery) are crucial strategies to pursue sustainable development. Reservoir rocks and caprocks typically consist of fine mineral particles from micrometer to nanometer sizes [1]. In such porous media, the interfacial phenomena have crucial roles in the multiphase fluid flow because of the high specific surface area. Wettability is a critical factor because it directly influences sealing performance in CGS and the oil-recovery rate in CO2-EOR [2].Contact angleθ is an indicator of wettability. Many measurements of CO2/brine/mineral systems have been carried out using muscovite, quartz, and calcite, which are essential minerals for caprock or reservoir rock. It has been reported that the contact angle of the CO2/brine/muscovite systems increases as pressure (of CO2 or an experimental system) increases [3–6]. Although the absolute values are different among these studies, the overall trend is consistent with each other. Increases in the contact angle may decrease the sealing performance and the storage potential. As a key mechanism of this trend, changes in pH and CO2 density are suggested by previous studies [3–5]. However, these effects have not been quantitatively studied.The contact angle is determined by the balance of one interfacial tension and two interfacial energy terms: CO2/brine, brine/mineral, and CO2/mineral. Then, it is worth paying attention to the properties of each interface in order to understand the mechanism of the change in contact angle. The thermodynamic model on these interfaces is helpful to quantitatively evaluate which property contributes to the change in the contact angle. Establishing a quantitative model helps interpret and estimate differences in sealing performance at different physical properties and conditions.Several studies have calculated the contact angle for oil/brine/mineral systems at the thermodynamic equilibrium [7–9] based on the Frumkin-Derjaguin equation [10, 11]. In the thermodynamic equilibrium state, brine in the wetting phase forms a thin adsorption film. The disjoining pressure acting on the water film consists of van der Waals forces, electrostatic forces, and hydration forces (structural forces).In this study, by using the Frumkin-Derjaguin equation, we studied the mechanisms of the change of the contact angles of the CO2/brine/muscovite systems by increasing pressure and investigated the contributing factors quantitatively.


## 2. Materials and Methods

### 2.1. Contact Angle Calculation by the Frumkin-Derjaguin Equation

Contact angleθ is determined by the balance of three interfacial tensions (IFT) or surface energy in the case of fluid/solid interfaces. It is formulated with Young’s equation (equation (1)), showing the mechanical equilibrium of IFT and surface energy:
(1)Cosθ=γCM−γBMγBC,where γBC, γCM, and γBM are IFT of brine/CO2, interfacial energy of CO2/mineral, and interfacial energy of brine/mineral, respectively. θ is zero when γCM−γBM+γBC≥0, while the system has a finite value of θ when γCM−γBM+γBC<0. The latter means the partial wetting state. Young’s equation is valid in the mechanical equilibrium condition. In order to formulate a contact angle in the thermodynamic equilibrium condition, however, it is necessary to consider the effect of water adsorption. γCM decreases because H2O adsorbs to lower the free energy of the system. By adsorption of H2O, the distance between CO2 and the mineral increases. The force acting between two interfaces (CO2/brine and brine/mineral) of the film balances the capillary pressure. This force acting on the film per unit area is a disjoining pressure and is related to the stability of the film [7]. Finally, a contact angle is calculated by equation (2), called the Frumkin-Derjaguin equation [7, 10, 11]:
(2)Cosθ=1+1γBC∫0Πheqh′dΠ′=1−1γBC∫∞heqΠhdh−heqΠheq,where h is the film thickness, heq is the film thickness in thermodynamic equilibrium, and Π is the disjoining pressure.


### 2.2. Formulation of Disjoining Pressure

Disjoining pressure is modeled considering the DLVO theory and structural forces [7]. The DLVO theory describes the balance between van der Waals forces and electrostatic forces. Hydration forces are non-DLVO forces and represent short-range forces between hydrophilic surfaces or hydrophobic surfaces, which are essential in the stability of colloid particles or a soap film [12]. Disjoining pressure Π is formulated by these three terms shown in equation (3). h means the thickness of the water film between the CO2 phase and the mineral phase.
(3)Πh=ΠvdWh+Πeleh+Πhydh.The integration ofΠh is defined as follows:
(4)Wh=−∫∞hΠhdh,Wh=WvdWh+Weleh+Whydh.


#### 2.2.1. Van der Waals Forces

(5)ΠvdWh=−A6πh3.The coefficientA of the van der Waals interaction is the Hamaker constant. When A>0, this interaction acts as attractive forces. As shown in equation (6), the Hamaker constant of CO2 and H2O can be calculated from the Lifshitz theory using experimental data of the refractive index and the relative permittivity. Aii means the constant for material i is interacting across a vacuum.
(6)Aii=34kBTεi−1εi+12+3h′νe162ni2−12ni2+13/2,where kB is the Boltzmann constant, T is the temperature, εi is the relative permittivity of material i, h′ is the Planck constant, νe is the main electronic absorption frequency, ni is the refractive index of material i, and the material numbers of minerals, CO2, and H2O are 1, 2, and 3, respectively. The Hamaker constant of muscovite is determined from experimental data, as summarized in Table S1. Several existing studies [13–18] reported the value around 1.0×10−19 J. This value is used in this study for A11. Finally, the Hamaker constant of the water film sandwiched between the CO2 phase and the mineral phase (A132) is calculated from A11, A22, and A33 based on the mixing rule:
(7)A132=A12+A33−A13−A23=A11−A33A22−A33=A11−A33A22−A33.Values ofεi and ni at conditions for the calculation of equation (6) followed existing studies [19–23]. In this calculation, A11 is assumed to be constant with increasing pressure. The changes in the optical properties εi and ni of minerals are usually negligible within the pressure and temperature ranges in this study. For example, the optical properties of sapphire change less than 0.5% when the pressure increases from 0.0 Pa to 10.0 GPa [24].


#### 2.2.2. Electrostatic Forces

The contribution from the electrostatic forces is calculated from equation (8) [25–27]. The constant potential (CP) model or the constant charge (CC) model is used to formulate the interaction of two dissimilar surfaces in electrolyte solutions. These models assume that the surface electrical potential or surface charge is constant when two surfaces approach. Each of them is calculated from the minus sign and the plus sign of equation (8), respectively. In reality, both potential and charge are likely to change as the interfaces approach each other. Between these two models, different contact angles can be obtained from one single pair of surface potentials ϕBC and ϕBM. Therefore, in this work, in order to evaluate the effect of the model, calculations are conducted by both CP and CC models:
(8)Πeleh=12ε0εκΦBM2±1+FΦ2κcschhD2+2κFΦcschhDcothhD,where
(9)κ=e2∑Cizi2ε0εkT,hD=κh,Fϕ=ϕBCϕBM.e is the elementary charge, Ci is the concentration of i (molecules/m3), and zi is the valence of ion i.ε0 is the permittivity of vacuum, ε is relative permittivity, and κ is reciprocal Debye length. ϕBC and ϕBM are surface electrical potentials of brine/CO2 and brine/muscovite, respectively. Fϕ is the ratio of these two potentials. hD is the dimensionless distance. In this work, the data of the zeta potential of brine/muscovite [28–30] and brine/CO2 [31] are used as the parameters in Πele.


#### 2.2.3. Hydration Forces

In 2019, Van Lin et al. measured the hydration forces acting on mica surfaces and determined parameters in empirical formulations at different ions, salinity, and pH. The empirical model consists of two terms: monotonically exponential decaying curve and the decaying oscillation curve [32]. The disjoining pressure is determined by their magnitudes and the decay lengths [33], so Πhyd is obtained as follows:
(10)Πhydh=Km/λmexp−h/λm+Kosc/λosccos2πσh−φexp−h/λosc,where Km and Kosc are the coefficients of the monotonical and oscillated decaying of the hydration forces. λm and λosc are the decay lengths of the monotonical and oscillated decaying of the hydration forces. σ and φ are the structural hydration frequency and the phase shift.


### 2.3. The Augmented Young Laplace Equation

The equilibrium thicknessheq of the film is determined from the augmented Young Laplace equation. Provided that the CO2/brine/muscovite system with the brine film between CO2 and the muscovite are as shown in Figure 1, the augmented Young Laplace equation holds at the equilibrium state and is described as follows:
(11)Pc=2γBCR+Πh,where R is the curvature radius of the interface of brine/CO2, and Pc is the capillary pressure. 60 kPa is assumed as the base case of Pc. Assuming a typical droplet radius for the contact angle measurement, the Laplace pressure acting on the droplet was set as the value of Pc. The effect of Pc on θ is small enough to be neglected in this study though it must be included if the size of the droplet is of nanometer order because the Laplace pressure can be as high as MPa order. In the flat film region, 1/R=0 and equation (11) becomes equation (12):
(12)Pc=Πheq.Figure 1
Conceptual model of the interfacial region of the CO2/brine/mineral system; h is the film thickness, and heq is the equilibrium thickness of the water adsorption film. This thickness is determined from the relation between the capillary pressure and the disjoining pressure.The flat film has a thicknessheq in the equilibrium state, and the equilibrium contact angle θ can be calculated by equation (2). There can be multiple thicknesses which satisfy equation (12). In addition, the thin film at the thermodynamic equilibrium condition must be locally stable. Such a local stable state holds where ∂Πh/∂h<0, that is, Πh has a negative slope at the thickness [7]. Then, the trend of θ at all stable films is studied.


### 2.4. The Potential Energy of the Film

The system has a finite value ofθ when the integration part ∫0Πheqh′dΠ′ is negative. This integration is the potential energy required to form the film from infinite separation to the equilibrium thickness heq[7]. Based on equation (2), as shown in Figure S1(a), when the area of the blue part (Πh<0) is larger than that of the red region Πheq≥Πh≥0, cosθ is smaller than 1 and the system is in a partial wetting state. On the other hand, when the red region is larger than the blue region as shown in Figure S1(b), the system is in a complete wetting state. So, the negative disjoining pressure (attractive force) leads to an increase in the contact angle, and the positive disjoining pressure (repulsive force) leads to a decrease in the contact angle. By considering these models and mechanisms on the wetting state, the effects of the physical properties of CO2, brine, and minerals can be evaluated and discussed.


### 2.5. Calculation Condition

In this work, we compare three pressure values, namely, 0.1, 3.0, and 10.0 MPa, at constant temperature (313 K) to study the effect of increasing pressure. 0.1 MPa represents the ambient pressure condition, 3.0 MPa a high pressure but lower than the critical point (7.38 MPa), and 10.0 MPa a supercritical state of CO2. Also, 10.0 MPa and 313 K are typical pressure and temperature conditions for reservoir formations at 1 km depth. Physical properties at each pressure are listed in Table 1.Table 1
Parameters for calculation of the contact angle at 0.1 MPa, 3.0 MPa, and 10.0 MPa.
Parameter0.1 MPa3.0 MPa10.0 MPaHamaker constantA11 (J)1.0×10−191.0×10−191.0×10−19Hamaker constantA22 (J)5.52×10−266.63×10−237.33×10−21Hamaker constantA33 (J)3.38×10−203.38×10−203.40×10−20Hamaker constantA132 (J)−2.43×10−20−2.33×10−20−1.30×10−20Salinity (mol/kg)0.010.010.01pH5.03.373.24γBC (mN/m)68.050.032.0ϕBC (mV)-16.4-15.1-15.0ϕBM (mV)-12.72.43.5Capillary pressure (kPa)60.060.060.0Table 2
The number of references in the legend of Figure6.
NumberReferenceTemperatureSalinityType of measurement∗∗1Chiquet et al. (2007) [3]308 K0.01 MR20.1 M30.2 M40.5 M51 M60.01 MA7Broseta et al. (2012) [4]308 K0.08 MR∗8A9R10282 KA11R12Mills et al. (2011) [43]313 K35000 ppmS13A14R15Farokhpoor et al. (2013) [5]309 K0.8 MA∗∗ indicates the following: S = static angle; R = receding angle; R∗ = nonequilibrated receding angle; A = advancing angle.


## 2.1. Contact Angle Calculation by the Frumkin-Derjaguin Equation

Contact angleθ is determined by the balance of three interfacial tensions (IFT) or surface energy in the case of fluid/solid interfaces. It is formulated with Young’s equation (equation (1)), showing the mechanical equilibrium of IFT and surface energy:
(1)Cosθ=γCM−γBMγBC,where γBC, γCM, and γBM are IFT of brine/CO2, interfacial energy of CO2/mineral, and interfacial energy of brine/mineral, respectively. θ is zero when γCM−γBM+γBC≥0, while the system has a finite value of θ when γCM−γBM+γBC<0. The latter means the partial wetting state. Young’s equation is valid in the mechanical equilibrium condition. In order to formulate a contact angle in the thermodynamic equilibrium condition, however, it is necessary to consider the effect of water adsorption. γCM decreases because H2O adsorbs to lower the free energy of the system. By adsorption of H2O, the distance between CO2 and the mineral increases. The force acting between two interfaces (CO2/brine and brine/mineral) of the film balances the capillary pressure. This force acting on the film per unit area is a disjoining pressure and is related to the stability of the film [7]. Finally, a contact angle is calculated by equation (2), called the Frumkin-Derjaguin equation [7, 10, 11]:
(2)Cosθ=1+1γBC∫0Πheqh′dΠ′=1−1γBC∫∞heqΠhdh−heqΠheq,where h is the film thickness, heq is the film thickness in thermodynamic equilibrium, and Π is the disjoining pressure.


## 2.2. Formulation of Disjoining Pressure

Disjoining pressure is modeled considering the DLVO theory and structural forces [7]. The DLVO theory describes the balance between van der Waals forces and electrostatic forces. Hydration forces are non-DLVO forces and represent short-range forces between hydrophilic surfaces or hydrophobic surfaces, which are essential in the stability of colloid particles or a soap film [12]. Disjoining pressure Π is formulated by these three terms shown in equation (3). h means the thickness of the water film between the CO2 phase and the mineral phase.
(3)Πh=ΠvdWh+Πeleh+Πhydh.The integration ofΠh is defined as follows:
(4)Wh=−∫∞hΠhdh,Wh=WvdWh+Weleh+Whydh.


### 2.2.1. Van der Waals Forces

(5)ΠvdWh=−A6πh3.The coefficientA of the van der Waals interaction is the Hamaker constant. When A>0, this interaction acts as attractive forces. As shown in equation (6), the Hamaker constant of CO2 and H2O can be calculated from the Lifshitz theory using experimental data of the refractive index and the relative permittivity. Aii means the constant for material i is interacting across a vacuum.
(6)Aii=34kBTεi−1εi+12+3h′νe162ni2−12ni2+13/2,where kB is the Boltzmann constant, T is the temperature, εi is the relative permittivity of material i, h′ is the Planck constant, νe is the main electronic absorption frequency, ni is the refractive index of material i, and the material numbers of minerals, CO2, and H2O are 1, 2, and 3, respectively. The Hamaker constant of muscovite is determined from experimental data, as summarized in Table S1. Several existing studies [13–18] reported the value around 1.0×10−19 J. This value is used in this study for A11. Finally, the Hamaker constant of the water film sandwiched between the CO2 phase and the mineral phase (A132) is calculated from A11, A22, and A33 based on the mixing rule:
(7)A132=A12+A33−A13−A23=A11−A33A22−A33=A11−A33A22−A33.Values ofεi and ni at conditions for the calculation of equation (6) followed existing studies [19–23]. In this calculation, A11 is assumed to be constant with increasing pressure. The changes in the optical properties εi and ni of minerals are usually negligible within the pressure and temperature ranges in this study. For example, the optical properties of sapphire change less than 0.5% when the pressure increases from 0.0 Pa to 10.0 GPa [24].


### 2.2.2. Electrostatic Forces

The contribution from the electrostatic forces is calculated from equation (8) [25–27]. The constant potential (CP) model or the constant charge (CC) model is used to formulate the interaction of two dissimilar surfaces in electrolyte solutions. These models assume that the surface electrical potential or surface charge is constant when two surfaces approach. Each of them is calculated from the minus sign and the plus sign of equation (8), respectively. In reality, both potential and charge are likely to change as the interfaces approach each other. Between these two models, different contact angles can be obtained from one single pair of surface potentials ϕBC and ϕBM. Therefore, in this work, in order to evaluate the effect of the model, calculations are conducted by both CP and CC models:
(8)Πeleh=12ε0εκΦBM2±1+FΦ2κcschhD2+2κFΦcschhDcothhD,where
(9)κ=e2∑Cizi2ε0εkT,hD=κh,Fϕ=ϕBCϕBM.e is the elementary charge, Ci is the concentration of i (molecules/m3), and zi is the valence of ion i.ε0 is the permittivity of vacuum, ε is relative permittivity, and κ is reciprocal Debye length. ϕBC and ϕBM are surface electrical potentials of brine/CO2 and brine/muscovite, respectively. Fϕ is the ratio of these two potentials. hD is the dimensionless distance. In this work, the data of the zeta potential of brine/muscovite [28–30] and brine/CO2 [31] are used as the parameters in Πele.


### 2.2.3. Hydration Forces

In 2019, Van Lin et al. measured the hydration forces acting on mica surfaces and determined parameters in empirical formulations at different ions, salinity, and pH. The empirical model consists of two terms: monotonically exponential decaying curve and the decaying oscillation curve [32]. The disjoining pressure is determined by their magnitudes and the decay lengths [33], so Πhyd is obtained as follows:
(10)Πhydh=Km/λmexp−h/λm+Kosc/λosccos2πσh−φexp−h/λosc,where Km and Kosc are the coefficients of the monotonical and oscillated decaying of the hydration forces. λm and λosc are the decay lengths of the monotonical and oscillated decaying of the hydration forces. σ and φ are the structural hydration frequency and the phase shift.


## 2.2.1. Van der Waals Forces

(5)ΠvdWh=−A6πh3.The coefficientA of the van der Waals interaction is the Hamaker constant. When A>0, this interaction acts as attractive forces. As shown in equation (6), the Hamaker constant of CO2 and H2O can be calculated from the Lifshitz theory using experimental data of the refractive index and the relative permittivity. Aii means the constant for material i is interacting across a vacuum.
(6)Aii=34kBTεi−1εi+12+3h′νe162ni2−12ni2+13/2,where kB is the Boltzmann constant, T is the temperature, εi is the relative permittivity of material i, h′ is the Planck constant, νe is the main electronic absorption frequency, ni is the refractive index of material i, and the material numbers of minerals, CO2, and H2O are 1, 2, and 3, respectively. The Hamaker constant of muscovite is determined from experimental data, as summarized in Table S1. Several existing studies [13–18] reported the value around 1.0×10−19 J. This value is used in this study for A11. Finally, the Hamaker constant of the water film sandwiched between the CO2 phase and the mineral phase (A132) is calculated from A11, A22, and A33 based on the mixing rule:
(7)A132=A12+A33−A13−A23=A11−A33A22−A33=A11−A33A22−A33.Values ofεi and ni at conditions for the calculation of equation (6) followed existing studies [19–23]. In this calculation, A11 is assumed to be constant with increasing pressure. The changes in the optical properties εi and ni of minerals are usually negligible within the pressure and temperature ranges in this study. For example, the optical properties of sapphire change less than 0.5% when the pressure increases from 0.0 Pa to 10.0 GPa [24].


## 2.2.2. Electrostatic Forces

The contribution from the electrostatic forces is calculated from equation (8) [25–27]. The constant potential (CP) model or the constant charge (CC) model is used to formulate the interaction of two dissimilar surfaces in electrolyte solutions. These models assume that the surface electrical potential or surface charge is constant when two surfaces approach. Each of them is calculated from the minus sign and the plus sign of equation (8), respectively. In reality, both potential and charge are likely to change as the interfaces approach each other. Between these two models, different contact angles can be obtained from one single pair of surface potentials ϕBC and ϕBM. Therefore, in this work, in order to evaluate the effect of the model, calculations are conducted by both CP and CC models:
(8)Πeleh=12ε0εκΦBM2±1+FΦ2κcschhD2+2κFΦcschhDcothhD,where
(9)κ=e2∑Cizi2ε0εkT,hD=κh,Fϕ=ϕBCϕBM.e is the elementary charge, Ci is the concentration of i (molecules/m3), and zi is the valence of ion i.ε0 is the permittivity of vacuum, ε is relative permittivity, and κ is reciprocal Debye length. ϕBC and ϕBM are surface electrical potentials of brine/CO2 and brine/muscovite, respectively. Fϕ is the ratio of these two potentials. hD is the dimensionless distance. In this work, the data of the zeta potential of brine/muscovite [28–30] and brine/CO2 [31] are used as the parameters in Πele.


## 2.2.3. Hydration Forces

In 2019, Van Lin et al. measured the hydration forces acting on mica surfaces and determined parameters in empirical formulations at different ions, salinity, and pH. The empirical model consists of two terms: monotonically exponential decaying curve and the decaying oscillation curve [32]. The disjoining pressure is determined by their magnitudes and the decay lengths [33], so Πhyd is obtained as follows:
(10)Πhydh=Km/λmexp−h/λm+Kosc/λosccos2πσh−φexp−h/λosc,where Km and Kosc are the coefficients of the monotonical and oscillated decaying of the hydration forces. λm and λosc are the decay lengths of the monotonical and oscillated decaying of the hydration forces. σ and φ are the structural hydration frequency and the phase shift.


## 2.3. The Augmented Young Laplace Equation

The equilibrium thicknessheq of the film is determined from the augmented Young Laplace equation. Provided that the CO2/brine/muscovite system with the brine film between CO2 and the muscovite are as shown in Figure 1, the augmented Young Laplace equation holds at the equilibrium state and is described as follows:
(11)Pc=2γBCR+Πh,where R is the curvature radius of the interface of brine/CO2, and Pc is the capillary pressure. 60 kPa is assumed as the base case of Pc. Assuming a typical droplet radius for the contact angle measurement, the Laplace pressure acting on the droplet was set as the value of Pc. The effect of Pc on θ is small enough to be neglected in this study though it must be included if the size of the droplet is of nanometer order because the Laplace pressure can be as high as MPa order. In the flat film region, 1/R=0 and equation (11) becomes equation (12):
(12)Pc=Πheq.Figure 1
Conceptual model of the interfacial region of the CO2/brine/mineral system; h is the film thickness, and heq is the equilibrium thickness of the water adsorption film. This thickness is determined from the relation between the capillary pressure and the disjoining pressure.The flat film has a thicknessheq in the equilibrium state, and the equilibrium contact angle θ can be calculated by equation (2). There can be multiple thicknesses which satisfy equation (12). In addition, the thin film at the thermodynamic equilibrium condition must be locally stable. Such a local stable state holds where ∂Πh/∂h<0, that is, Πh has a negative slope at the thickness [7]. Then, the trend of θ at all stable films is studied.


## 2.4. The Potential Energy of the Film

The system has a finite value ofθ when the integration part ∫0Πheqh′dΠ′ is negative. This integration is the potential energy required to form the film from infinite separation to the equilibrium thickness heq[7]. Based on equation (2), as shown in Figure S1(a), when the area of the blue part (Πh<0) is larger than that of the red region Πheq≥Πh≥0, cosθ is smaller than 1 and the system is in a partial wetting state. On the other hand, when the red region is larger than the blue region as shown in Figure S1(b), the system is in a complete wetting state. So, the negative disjoining pressure (attractive force) leads to an increase in the contact angle, and the positive disjoining pressure (repulsive force) leads to a decrease in the contact angle. By considering these models and mechanisms on the wetting state, the effects of the physical properties of CO2, brine, and minerals can be evaluated and discussed.


## 2.5. Calculation Condition

In this work, we compare three pressure values, namely, 0.1, 3.0, and 10.0 MPa, at constant temperature (313 K) to study the effect of increasing pressure. 0.1 MPa represents the ambient pressure condition, 3.0 MPa a high pressure but lower than the critical point (7.38 MPa), and 10.0 MPa a supercritical state of CO2. Also, 10.0 MPa and 313 K are typical pressure and temperature conditions for reservoir formations at 1 km depth. Physical properties at each pressure are listed in Table 1.Table 1
Parameters for calculation of the contact angle at 0.1 MPa, 3.0 MPa, and 10.0 MPa.
Parameter0.1 MPa3.0 MPa10.0 MPaHamaker constantA11 (J)1.0×10−191.0×10−191.0×10−19Hamaker constantA22 (J)5.52×10−266.63×10−237.33×10−21Hamaker constantA33 (J)3.38×10−203.38×10−203.40×10−20Hamaker constantA132 (J)−2.43×10−20−2.33×10−20−1.30×10−20Salinity (mol/kg)0.010.010.01pH5.03.373.24γBC (mN/m)68.050.032.0ϕBC (mV)-16.4-15.1-15.0ϕBM (mV)-12.72.43.5Capillary pressure (kPa)60.060.060.0Table 2
The number of references in the legend of Figure6.
NumberReferenceTemperatureSalinityType of measurement∗∗1Chiquet et al. (2007) [3]308 K0.01 MR20.1 M30.2 M40.5 M51 M60.01 MA7Broseta et al. (2012) [4]308 K0.08 MR∗8A9R10282 KA11R12Mills et al. (2011) [43]313 K35000 ppmS13A14R15Farokhpoor et al. (2013) [5]309 K0.8 MA∗∗ indicates the following: S = static angle; R = receding angle; R∗ = nonequilibrated receding angle; A = advancing angle.


## 3. Results and Discussion

By focusing on each component of disjoining pressure (ΠvdW, Πele, Πhyd) in equation (3) using parameters of CO2, brine, and muscovite, the contact angles were calculated, and the mechanisms of its change are discussed below.


### 3.1. Van der Waals Forces

In Figure2, the pressure dependency of the disjoining pressure of the van der Waals forces at several values of the Hamaker constant was plotted. The absolute value of the forces becomes larger as the distance between the two surfaces becomes smaller. In the case of A132<0, the van der Waals forces are positive and act as repulsive forces. Based on equations (6) and (7), A132 at 0.1 MPa, 3.0 MPa, and 10.0 MPa are −2.43×10−20 J, −2.33×10−20 J, and −1.33×10−20 J, respectively. This indicates that van der Waals forces become less repulsive, and the system becomes less water wet, with increasing pressure. Therefore, the change in ΠvdW by increasing pressure is one of the causes of the increase in the contact angle of the CO2/brine/muscovite system.Figure 2
Dependence ofΠvdWh on the Hamaker constant A132. For the water film sandwiched between CO2 and muscovite, A132 is negative and repulsive forces act on the film. The decrease in the repulsive forces lead to the decrease in the integration part ∫0πheqh′dΠ′ (the red colored area in Figures S1 and S2). This means that increasing pressure leads the system to being less water wet (increase in the contact angle). A132 for each pressure is from Table 1.This trend ofA132 with increasing pressure is related to the fact that the density of CO2 increases more rapidly than that of H2O. Optical properties of molecular structures εi and ni, on which the Hamaker constant largely depends, increase linearly with the increasing densities of H2O and CO2 [19–23]. As seen in Figure S2, CO2 density increases considerably more than H2O density with increasing pressure, and this is seen in the trend of A22 and A33 (data of density is from Lemmon et al. [34]). A11, A22, and A33 are constant or increase with an increase in pressure. A132 is negative and decreases in magnitude A132 with an increase in pressure. Among the three materials, only CO2 drastically changes its density, and this is reflected in the trend of each of Hamaker constant.


### 3.2. Electrostatic Forces

Equation (8) indicates that Πele can be affected by several parameters: relative permittivity and salinity of brine and surface electrical potentials. A change of the relative permittivity in the pressure range of 0.1MPa~10.0MPa is small enough to be neglected, judging from its dependence on pressure [35], unlike CO2, which changes density drastically and changes the relative permittivity. Surface electrical potentials and charges are, on the other hand, primarily affected by pH change, and even the sign can change.In FiguresS4 and S5, Πele at several values of surface electrical potentials calculated by the CP and CC models are shown, respectively. Those at different pressures (0.1, 3.0, and 10.0 MPa) are shown in Figure 3. The shapes of the curves are dependent on the model choice, as summarized in Table S2. In order to evaluate the contact angle by this framework, its dependence on the model choice must be studied.Figure 3
Πele at each system pressure calculated from both the CP model (solid line) and the CC model (dashed line).With increasing pressure in the CO2/H2O two-phase system, the pH decreases from 6~7 to 2~3. pH is 3.37 and 3.24 at 3.0 MPa and 10.0 MPa, respectively [36]. By lowering pH from 5.0 to 3.5, ϕBC increases from -18.0 mV to -15.0 mV [37]. In this pH range, charge reversal happens for the H2O/muscovite surface [28–30]. ϕBM is -10.0 mV at pH 5.0, while it increases to around +5.0 mV at pH 3.5. This indicates that ϕBC and ϕBM have the same signs at low pressure (0.1 MPa), while they have opposite signs at high pressure (3.0 MPa and 10.0 MPa). They do not change much between 3.0 MPa and 10.0 MPa, so curves of these two pressure conditions are almost the same in Figure 3. In Figure 3, although Πele in the CP model acts as attractive forces while that in the CC model acts as repulsive forces, the trend by increasing pressure is the same; the integration of equation (2) decreases, and it leads to an increase in the contact angle. Therefore, lowering pH from 5.0 to 3.5 leads to being less water wet because the negative area of Πele increases, as seen in Figure 3. The change of Πele is one of the causes for increasing θ when the pressure increases from ambient pressure to the high-pressure range on the order of MPa.


### 3.3. Hydration Forces

Since it is not easy to measure hydration forces directly under high pressure, there is no data at high pressures of interest. Hydrating forces are short-range interactions that act at a few nanometers on the mineral surface and are strongly dependent on the adsorption structure. Changes in density and pH can be considered as influential factors as a result of pressure changes. However, since the density change of water is less than 0.4% (992.27 kg/m3 to 996.57 kg/m3) from 0.1 MPa to 10.0 MPa, the sensitive parameter is pH.In 2019, Van Lin et al. developed an empirical formulation based on their measurements of hydration forces of mica surfaces.Πhyd at several pHs (2.5, 3.5, 4.5, and 8.5) are shown in Figure 4. In order to see the effect of pressure, Πhydh at pH=4.5 is regarded as the case of 0.1 MPa, and Πhydh at pH=3.5 is for the case of 3.0 MPa and 10.0 MPa. By lowering pH, amplitudes of the oscillation Kosc decrease, and attractive interactions develop. In Figure S4, the integration ∫h∞Πhydhdh is plotted. The curve for pH=3.5 (red curve in Figure S4) is smaller than that for pH=4.5 (blue curve in Figure S4). This results in less wetting of the system.Figure 4
Hydration forcesΠhydh at different pHs (2.5, 3.5, 4.5, and 8.5) based on the hydration force curves [32].Note that the pH drops from 3.37 to 3.24 when the pressure changes from 3.0 MPa to 10.0 MPa. Comparing pH 3.5 and pH 2.5, the negative region ofΠhyd was greatly increased. Therefore, a slight decrease in pH in the higher pressure region (order of MPa) is considered to be significant on the increase in contact angle. The attractive force significantly increased.


### 3.4. Total Disjoining Pressure

Figure5 shows the total disjoining pressure Πtot and the integration ∫h∞Πtothdh at different pressures of the system: 0.1 MPa, 3.0 MPa, and 10.0 MPa. Physical properties at each case are listed in Table 1. The orange-colored dashed horizontal line in Figure 5 represents the value of Pc (60 kPa). Thicknesses at which the integration has a local minimum or maximum correspond to thicknesses where the disjoining pressure is equal to the capillary pressure (equation (12)). Among them, the blue circles in Figure 5 are stable films, which satisfy ∂Πh/∂h<0. The system can have contact angles at points heq1 (thinner) and heq2 (thicker). Each case calculated by both the CP (solid curve) and CC (dashed curve) models for Πele is drawn. Wtot on the model choice does not much affect the results of the equilibrium thickness and the stability of the film. The thickness of the thinner film is from 0.326 nm to 0.339 nm, and that of the thicker film is from 0.728 nm to 0.749 nm (see Table S3). These correspond to those of the structured water adsorption layer on muscovite, by X-ray CTR measurement [37–39] and molecular dynamics simulation [40, 41]. Differences of Wtotheq1 and Wtotheq2 between the CP and CC models are less than 0.74 mN/m and 0.30 mN/m, respectively. These are small enough to affect the results of the contact angle because values of γBC in equation (2) are from 68 mN/m to 32 mN/m in the pressure conditions.Figure 5
Total disjoining pressure and its integration at each pressure are shown. Curves calculated by both the CP and CC models are shown. Dashed and orange-colored horizontal lines in the upper figures showPc=60.0kPa. The local minimum of integration decreases with increasing pressure. This decreases cosθ and leads to being less water wet.Each term of Figure5 at each pressure is shown in Figure S5. At the pressure of 0.1 MPa, the thicker film has zero contact angle, i.e., it is completely water wet. With increasing pressure, the local minimum of the integration decreases. This leads to an increase in θ with increasing pressure both at thinner and thicker films. All values of heq and Wheq are summarized in Table S3 and Table S4.From 0.1 MPa to 3.0 MPa, the increase in the attractive forces ofΠele and Πhyd has led to the overall decrease in the integration part ∫h∞Πhydhdh and the local minimum. 93.0% (CP model) and 87.3% (CC model) of the decreases in Wtotheq1 are caused by the decrease in Whyd, and 84.2% and 77.4% of the decreases in Wtotheq2 are caused by the decrease in Whyd.From 3.0 MPa to 10.0 MPa,93.3~93.8% of the decreases in Wtotheq1 and Wtotheq2 are caused by the change in WvdW because the curves of Πele slightly change, and Πhyd is the same at these two pressures because pH at these pressures is almost the same. Although detailed quantification of the reduction of Πhyd from pH 3.37 to 3.24 was not done in this work, the data from the hydration curves of Van Lin et al. in 2019 show that attraction from pH 3.5 to pH 2.5 increases significantly. Therefore, it is considered that the change in Πhyd from pH 3.37 (3.0 MPa) to pH 3.24 (10.0 MPa) has a greater effect on the increase in contact angle than estimated here.


### 3.5. Effect of the Interfacial Tension of CO2/Brine

The interfacial tension of CO2/brine surface γBC is included in equation (2). γBC decreases with increasing pressure. As can be seen in equation (2), a decrease of γBC decreases 1/γBC∫0πheqh′dΠ′<0, which leads to a decrease in cosθ, that is, increases in θ. For example, when the pressure increases from ambient pressure to 3.0 MPa, γBC decreases from 68 mN/m to 50 mN/m (26.4% decrease). From 3.0 MPa to 10.0 MPa, it decreases from 50 mN/m to 32 mN/m (36.0% decrease) (the temperature is 312.9 K, and pure H2O is used) [42]. This decrease drastically affects θ.


### 3.6. Contact Angle

By calculating each component in equation (3), θ is obtained from equation (2), as plotted in Figure 6. θ at both thinner and thicker films increased with increasing pressure. This corresponds to the increasing trend seen in existing measurements. Key factors of this trend were (a) a decrease of repulsive van der Waals forces, (b) charge reversal for the two surfaces, (c) increase of attraction of the hydration forces, and (d) decrease in γBC. (b) and (c) are especially important for the change in the lower pressure range from 0.1 MPa to 3.0 MPa. (a) and (d) were influential in the whole range of the targeted pressure, but it drastically affected results within the higher pressure range from 3.0 MPa to 10.0 MPa. Since Πtot and Wtot calculated by the CP and CC models for Πele are not much different, the model choice does not much affect the values and the trend of the contact angle. Results obtained by the CC model are 1.16° to 1.45° smaller than those by the CP model because Πele remains positive (repulsive) as the film becomes thinner, as shown in Figure 3.Figure 6
Results of calculation (colored plots) and experimental data of the contact angle of the CO2/brine/muscovite system; plots of experimental data are modified from Iglauer et al. The numbers (1 to 15) of references in the legend are shown in Table 2.Sensitivity analysis was carried out about parameters of disjoining pressure.In Figure7, the effect of the Hamaker constant of muscovite A11 on the contact angle at the thinner film is plotted. Although the Hamaker constants of water and CO2 are accurately determined from their densities, that of muscovite has differences between reported values. The range of reported data of A11 is from 6.96×10−20 J [44] (-30.4% of ∆A11 in Figure 7) to 1.35×10−19 J [14] (+35.0% of ∆A11 in Figure 7). Changes in the contact angle values due to these differences are less than 10.5°, 8.7°, and 6.2° at each of the three pressures. Variations of these data affect the calculation results, especially in lower pressure ranges because A22−A33 in equation (7) is larger and A11 changes A132 more directly.Figure 7
The contact angle with changes of the Hamaker constantA11.In Figure8, by using the CP model, a 2D map of the contact angle at the thinner film was plotted as a function of ϕBM and the vertical axis as ϕBC. In this map, other parameters except for ϕBC and ϕBM are constant based on physical properties at 10.0 MPa. Maps at other pressure conditions are shown in Figures S11 and S12. As mentioned in the introduction of Πele, when the two surfaces charge oppositely, attractive forces act to decrease the potential energy of the film, which is the integration part of equation (2), and θ becomes higher. On the other hand, when these have the same sign of the surface charge, θ becomes smaller. Charge reversal of two surfaces of the brine film, from the same signs to the opposite signs, is a key mechanism of the contact angle alteration of the oil/brine/mineral systems [45]. In this study, the averaged value of three zeta potential values of brine/muscovite using data from Alonso et al. [28], Au et al. [29], and Zhou et al. [30] were used for ϕBM, and data from Kim and Kwak [31] was used for ϕBC. In these maps, contact angles calculated from each ϕBM are plotted. Differences in the values are less than 2.0°. Also, it can be estimated that the difference of ϕBC, which is less than 10 mV, causes the change in the contact angle to less than 2.0° at each ϕBM.Figure 8
The contact angle with changes in the surface electrical potentials. “□” shows the value calculated from the base case at Table1. “×”, “○”, and “+” indicate values calculated from each different reported value [28–30].In Figure9, dependencies of the contact angles on the coefficients of hydration forces were plotted. Variations of the magnitudes at pH 3.5 and 4.5 are probably within the range of values at pH from 2.5 to 8.5. Sensitivity analysis was carried out in these ranges using parameters by Van Lin et al. [32]. Both magnitudes can change from half to twice of those at pH 3.5 or 4.5, so the horizontal axis is from -50% to 200%. Results show that θ can be drastically changed by changing these magnitudes.Figure 9
(a) Sensitivity analysis of the magnitude of the monotonic term of the hydration forces. (b) Sensitivity analysis of the magnitude of the oscillation term of the hydration forces.
(a)(b)In addition to physical properties related to the disjoining pressure, the sensitivity of IFT of CO2/brine on the contact angle at the thinner film is studied here. Although many measurements have been performed for CO2/brine IFT, there are variations depending on the reported results. On the other hand, Georgiadis et al. [42] pointed out problems with conventional measurement methods (about 40% of underestimation may occur [42]) and they measured the IFT value by a more accurate method. This led us to use their data in this study. However, as can be seen from equation (2), IFT directly affects cosθ, and it can be a sensitive parameter. In Figure 10, the effects of changes in IFT are shown quantitatively. Sensitivity is higher in higher pressure. When the IFT error is less than 10% (6.8 mN/m, 5.0 mN/m, and 3.2 mN/m at 0.1 MPa, 3.0 MPa, and 10.0 MPa), the effect on the contact angle is less than 1.2°, 2.0°, and 3.1°, respectively. The contact angle may increase by about 9°, 15°, and 23° at each of three pressures when IFT is reduced by about 50%.Figure 10
Sensitivity analysis of IFT of CO2/brine.


## 3.1. Van der Waals Forces

In Figure2, the pressure dependency of the disjoining pressure of the van der Waals forces at several values of the Hamaker constant was plotted. The absolute value of the forces becomes larger as the distance between the two surfaces becomes smaller. In the case of A132<0, the van der Waals forces are positive and act as repulsive forces. Based on equations (6) and (7), A132 at 0.1 MPa, 3.0 MPa, and 10.0 MPa are −2.43×10−20 J, −2.33×10−20 J, and −1.33×10−20 J, respectively. This indicates that van der Waals forces become less repulsive, and the system becomes less water wet, with increasing pressure. Therefore, the change in ΠvdW by increasing pressure is one of the causes of the increase in the contact angle of the CO2/brine/muscovite system.Figure 2
Dependence ofΠvdWh on the Hamaker constant A132. For the water film sandwiched between CO2 and muscovite, A132 is negative and repulsive forces act on the film. The decrease in the repulsive forces lead to the decrease in the integration part ∫0πheqh′dΠ′ (the red colored area in Figures S1 and S2). This means that increasing pressure leads the system to being less water wet (increase in the contact angle). A132 for each pressure is from Table 1.This trend ofA132 with increasing pressure is related to the fact that the density of CO2 increases more rapidly than that of H2O. Optical properties of molecular structures εi and ni, on which the Hamaker constant largely depends, increase linearly with the increasing densities of H2O and CO2 [19–23]. As seen in Figure S2, CO2 density increases considerably more than H2O density with increasing pressure, and this is seen in the trend of A22 and A33 (data of density is from Lemmon et al. [34]). A11, A22, and A33 are constant or increase with an increase in pressure. A132 is negative and decreases in magnitude A132 with an increase in pressure. Among the three materials, only CO2 drastically changes its density, and this is reflected in the trend of each of Hamaker constant.


## 3.2. Electrostatic Forces

Equation (8) indicates that Πele can be affected by several parameters: relative permittivity and salinity of brine and surface electrical potentials. A change of the relative permittivity in the pressure range of 0.1MPa~10.0MPa is small enough to be neglected, judging from its dependence on pressure [35], unlike CO2, which changes density drastically and changes the relative permittivity. Surface electrical potentials and charges are, on the other hand, primarily affected by pH change, and even the sign can change.In FiguresS4 and S5, Πele at several values of surface electrical potentials calculated by the CP and CC models are shown, respectively. Those at different pressures (0.1, 3.0, and 10.0 MPa) are shown in Figure 3. The shapes of the curves are dependent on the model choice, as summarized in Table S2. In order to evaluate the contact angle by this framework, its dependence on the model choice must be studied.Figure 3
Πele at each system pressure calculated from both the CP model (solid line) and the CC model (dashed line).With increasing pressure in the CO2/H2O two-phase system, the pH decreases from 6~7 to 2~3. pH is 3.37 and 3.24 at 3.0 MPa and 10.0 MPa, respectively [36]. By lowering pH from 5.0 to 3.5, ϕBC increases from -18.0 mV to -15.0 mV [37]. In this pH range, charge reversal happens for the H2O/muscovite surface [28–30]. ϕBM is -10.0 mV at pH 5.0, while it increases to around +5.0 mV at pH 3.5. This indicates that ϕBC and ϕBM have the same signs at low pressure (0.1 MPa), while they have opposite signs at high pressure (3.0 MPa and 10.0 MPa). They do not change much between 3.0 MPa and 10.0 MPa, so curves of these two pressure conditions are almost the same in Figure 3. In Figure 3, although Πele in the CP model acts as attractive forces while that in the CC model acts as repulsive forces, the trend by increasing pressure is the same; the integration of equation (2) decreases, and it leads to an increase in the contact angle. Therefore, lowering pH from 5.0 to 3.5 leads to being less water wet because the negative area of Πele increases, as seen in Figure 3. The change of Πele is one of the causes for increasing θ when the pressure increases from ambient pressure to the high-pressure range on the order of MPa.


## 3.3. Hydration Forces

Since it is not easy to measure hydration forces directly under high pressure, there is no data at high pressures of interest. Hydrating forces are short-range interactions that act at a few nanometers on the mineral surface and are strongly dependent on the adsorption structure. Changes in density and pH can be considered as influential factors as a result of pressure changes. However, since the density change of water is less than 0.4% (992.27 kg/m3 to 996.57 kg/m3) from 0.1 MPa to 10.0 MPa, the sensitive parameter is pH.In 2019, Van Lin et al. developed an empirical formulation based on their measurements of hydration forces of mica surfaces.Πhyd at several pHs (2.5, 3.5, 4.5, and 8.5) are shown in Figure 4. In order to see the effect of pressure, Πhydh at pH=4.5 is regarded as the case of 0.1 MPa, and Πhydh at pH=3.5 is for the case of 3.0 MPa and 10.0 MPa. By lowering pH, amplitudes of the oscillation Kosc decrease, and attractive interactions develop. In Figure S4, the integration ∫h∞Πhydhdh is plotted. The curve for pH=3.5 (red curve in Figure S4) is smaller than that for pH=4.5 (blue curve in Figure S4). This results in less wetting of the system.Figure 4
Hydration forcesΠhydh at different pHs (2.5, 3.5, 4.5, and 8.5) based on the hydration force curves [32].Note that the pH drops from 3.37 to 3.24 when the pressure changes from 3.0 MPa to 10.0 MPa. Comparing pH 3.5 and pH 2.5, the negative region ofΠhyd was greatly increased. Therefore, a slight decrease in pH in the higher pressure region (order of MPa) is considered to be significant on the increase in contact angle. The attractive force significantly increased.


## 3.4. Total Disjoining Pressure

Figure5 shows the total disjoining pressure Πtot and the integration ∫h∞Πtothdh at different pressures of the system: 0.1 MPa, 3.0 MPa, and 10.0 MPa. Physical properties at each case are listed in Table 1. The orange-colored dashed horizontal line in Figure 5 represents the value of Pc (60 kPa). Thicknesses at which the integration has a local minimum or maximum correspond to thicknesses where the disjoining pressure is equal to the capillary pressure (equation (12)). Among them, the blue circles in Figure 5 are stable films, which satisfy ∂Πh/∂h<0. The system can have contact angles at points heq1 (thinner) and heq2 (thicker). Each case calculated by both the CP (solid curve) and CC (dashed curve) models for Πele is drawn. Wtot on the model choice does not much affect the results of the equilibrium thickness and the stability of the film. The thickness of the thinner film is from 0.326 nm to 0.339 nm, and that of the thicker film is from 0.728 nm to 0.749 nm (see Table S3). These correspond to those of the structured water adsorption layer on muscovite, by X-ray CTR measurement [37–39] and molecular dynamics simulation [40, 41]. Differences of Wtotheq1 and Wtotheq2 between the CP and CC models are less than 0.74 mN/m and 0.30 mN/m, respectively. These are small enough to affect the results of the contact angle because values of γBC in equation (2) are from 68 mN/m to 32 mN/m in the pressure conditions.Figure 5
Total disjoining pressure and its integration at each pressure are shown. Curves calculated by both the CP and CC models are shown. Dashed and orange-colored horizontal lines in the upper figures showPc=60.0kPa. The local minimum of integration decreases with increasing pressure. This decreases cosθ and leads to being less water wet.Each term of Figure5 at each pressure is shown in Figure S5. At the pressure of 0.1 MPa, the thicker film has zero contact angle, i.e., it is completely water wet. With increasing pressure, the local minimum of the integration decreases. This leads to an increase in θ with increasing pressure both at thinner and thicker films. All values of heq and Wheq are summarized in Table S3 and Table S4.From 0.1 MPa to 3.0 MPa, the increase in the attractive forces ofΠele and Πhyd has led to the overall decrease in the integration part ∫h∞Πhydhdh and the local minimum. 93.0% (CP model) and 87.3% (CC model) of the decreases in Wtotheq1 are caused by the decrease in Whyd, and 84.2% and 77.4% of the decreases in Wtotheq2 are caused by the decrease in Whyd.From 3.0 MPa to 10.0 MPa,93.3~93.8% of the decreases in Wtotheq1 and Wtotheq2 are caused by the change in WvdW because the curves of Πele slightly change, and Πhyd is the same at these two pressures because pH at these pressures is almost the same. Although detailed quantification of the reduction of Πhyd from pH 3.37 to 3.24 was not done in this work, the data from the hydration curves of Van Lin et al. in 2019 show that attraction from pH 3.5 to pH 2.5 increases significantly. Therefore, it is considered that the change in Πhyd from pH 3.37 (3.0 MPa) to pH 3.24 (10.0 MPa) has a greater effect on the increase in contact angle than estimated here.


## 3.5. Effect of the Interfacial Tension of CO2/Brine

The interfacial tension of CO2/brine surface γBC is included in equation (2). γBC decreases with increasing pressure. As can be seen in equation (2), a decrease of γBC decreases 1/γBC∫0πheqh′dΠ′<0, which leads to a decrease in cosθ, that is, increases in θ. For example, when the pressure increases from ambient pressure to 3.0 MPa, γBC decreases from 68 mN/m to 50 mN/m (26.4% decrease). From 3.0 MPa to 10.0 MPa, it decreases from 50 mN/m to 32 mN/m (36.0% decrease) (the temperature is 312.9 K, and pure H2O is used) [42]. This decrease drastically affects θ.


## 3.6. Contact Angle

By calculating each component in equation (3), θ is obtained from equation (2), as plotted in Figure 6. θ at both thinner and thicker films increased with increasing pressure. This corresponds to the increasing trend seen in existing measurements. Key factors of this trend were (a) a decrease of repulsive van der Waals forces, (b) charge reversal for the two surfaces, (c) increase of attraction of the hydration forces, and (d) decrease in γBC. (b) and (c) are especially important for the change in the lower pressure range from 0.1 MPa to 3.0 MPa. (a) and (d) were influential in the whole range of the targeted pressure, but it drastically affected results within the higher pressure range from 3.0 MPa to 10.0 MPa. Since Πtot and Wtot calculated by the CP and CC models for Πele are not much different, the model choice does not much affect the values and the trend of the contact angle. Results obtained by the CC model are 1.16° to 1.45° smaller than those by the CP model because Πele remains positive (repulsive) as the film becomes thinner, as shown in Figure 3.Figure 6
Results of calculation (colored plots) and experimental data of the contact angle of the CO2/brine/muscovite system; plots of experimental data are modified from Iglauer et al. The numbers (1 to 15) of references in the legend are shown in Table 2.Sensitivity analysis was carried out about parameters of disjoining pressure.In Figure7, the effect of the Hamaker constant of muscovite A11 on the contact angle at the thinner film is plotted. Although the Hamaker constants of water and CO2 are accurately determined from their densities, that of muscovite has differences between reported values. The range of reported data of A11 is from 6.96×10−20 J [44] (-30.4% of ∆A11 in Figure 7) to 1.35×10−19 J [14] (+35.0% of ∆A11 in Figure 7). Changes in the contact angle values due to these differences are less than 10.5°, 8.7°, and 6.2° at each of the three pressures. Variations of these data affect the calculation results, especially in lower pressure ranges because A22−A33 in equation (7) is larger and A11 changes A132 more directly.Figure 7
The contact angle with changes of the Hamaker constantA11.In Figure8, by using the CP model, a 2D map of the contact angle at the thinner film was plotted as a function of ϕBM and the vertical axis as ϕBC. In this map, other parameters except for ϕBC and ϕBM are constant based on physical properties at 10.0 MPa. Maps at other pressure conditions are shown in Figures S11 and S12. As mentioned in the introduction of Πele, when the two surfaces charge oppositely, attractive forces act to decrease the potential energy of the film, which is the integration part of equation (2), and θ becomes higher. On the other hand, when these have the same sign of the surface charge, θ becomes smaller. Charge reversal of two surfaces of the brine film, from the same signs to the opposite signs, is a key mechanism of the contact angle alteration of the oil/brine/mineral systems [45]. In this study, the averaged value of three zeta potential values of brine/muscovite using data from Alonso et al. [28], Au et al. [29], and Zhou et al. [30] were used for ϕBM, and data from Kim and Kwak [31] was used for ϕBC. In these maps, contact angles calculated from each ϕBM are plotted. Differences in the values are less than 2.0°. Also, it can be estimated that the difference of ϕBC, which is less than 10 mV, causes the change in the contact angle to less than 2.0° at each ϕBM.Figure 8
The contact angle with changes in the surface electrical potentials. “□” shows the value calculated from the base case at Table1. “×”, “○”, and “+” indicate values calculated from each different reported value [28–30].In Figure9, dependencies of the contact angles on the coefficients of hydration forces were plotted. Variations of the magnitudes at pH 3.5 and 4.5 are probably within the range of values at pH from 2.5 to 8.5. Sensitivity analysis was carried out in these ranges using parameters by Van Lin et al. [32]. Both magnitudes can change from half to twice of those at pH 3.5 or 4.5, so the horizontal axis is from -50% to 200%. Results show that θ can be drastically changed by changing these magnitudes.Figure 9
(a) Sensitivity analysis of the magnitude of the monotonic term of the hydration forces. (b) Sensitivity analysis of the magnitude of the oscillation term of the hydration forces.
(a)(b)In addition to physical properties related to the disjoining pressure, the sensitivity of IFT of CO2/brine on the contact angle at the thinner film is studied here. Although many measurements have been performed for CO2/brine IFT, there are variations depending on the reported results. On the other hand, Georgiadis et al. [42] pointed out problems with conventional measurement methods (about 40% of underestimation may occur [42]) and they measured the IFT value by a more accurate method. This led us to use their data in this study. However, as can be seen from equation (2), IFT directly affects cosθ, and it can be a sensitive parameter. In Figure 10, the effects of changes in IFT are shown quantitatively. Sensitivity is higher in higher pressure. When the IFT error is less than 10% (6.8 mN/m, 5.0 mN/m, and 3.2 mN/m at 0.1 MPa, 3.0 MPa, and 10.0 MPa), the effect on the contact angle is less than 1.2°, 2.0°, and 3.1°, respectively. The contact angle may increase by about 9°, 15°, and 23° at each of three pressures when IFT is reduced by about 50%.Figure 10
Sensitivity analysis of IFT of CO2/brine.


## 4. Conclusion and Future Perspective

In order to quantitatively investigate the mechanisms and contributing factors of the contact angle alteration of the CO2/brine/muscovite system caused by the change in pressure, the disjoining pressure curves and the contact angle were calculated both at three pressure cases, i.e., 0.1 MPa, 3.0 MPa, and 10.0 MPa.The results obtained were consistent with the trends of the data of the contact angle reported in previous studies. From 0.1 MPa to 3.0 MPa, about 80% to 90% of the decrease of the potential energy was caused by the change inΠhyd, which was due to the decrease in pH. From 3.0 MPa to 10.0 MPa, the pH does not change much, and the decrease in the potential energy was mostly caused by the change in ΠvdW, which is related to an increase in CO2 density. The IFT decreased by 26.4% from 0.1 MPa to 3.0 MPa, and it decreased by 36.0% from 3.0 MPa to 10.0 MPa. Therefore, it can be said that pH decrease is the key contributing factor in the lower pressure region, while an increase in CO2 density and IFT decrease are the ones in the higher pressure region. Sensitivity analysis also shows that the contact angle is sensitive to the interfacial tension of CO2/brine and the physical properties of hydration forces.Further measurements of physical properties related to CO2, brine, and other minerals are expected in the study of wettability in a broader range of conditions. Moreover, further investigation into interactions from an atomic viewpoint will help us to have a better understanding of sensitive parameters such as the coefficient of hydration forces..



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*Source: 6656460-2020-11-24.xml*