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

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.


Introduction
CO 2 Geo-Sequestration (CGS) and CO 2 -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 oilrecovery rate in CO 2 -EOR [2].
Contact angle θ is an indicator of wettability. Many measurements of CO 2 /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 CO 2 /brine/muscovite systems increases as pressure (of CO 2 or an experimental system) increases [3][4][5][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 CO 2 density are suggested by previous studies [3][4][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: CO 2 /brine, brine/mineral, and CO 2 /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][8][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 CO 2 /brine/muscovite systems by increasing pressure and investigated the contributing factors quantitatively.

Contact Angle Calculation by the Frumkin-Derjaguin Equation.
Contact angle θ 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: where γ BC , γ CM , and γ BM are IFT of brine/CO 2 , interfacial energy of CO 2 /mineral, and interfacial energy of brine/mineral, respectively. θ is zero when γ CM − ðγ BM + γ BC Þ ≥ 0, while the system has a finite value of θ when γ CM − ðγ BM + γ BC Þ < 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. γ CM decreases because H 2 O adsorbs to lower the free energy of the system. By adsorption of H 2 O, the distance between CO 2 and the mineral increases. The force acting between two interfaces (CO 2 /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]: where h is the film thickness, h eq is the film thickness in thermodynamic equilibrium, and Π is the disjoining pressure.

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 CO 2 phase and the mineral phase.
The integration of ΠðhÞ is defined as follows: The coefficient A 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 CO 2 and H 2 O can be calculated from the Lifshitz theory using experimental data of the refractive index and the relative permittivity. A ii means the constant for material i is interacting across a vacuum.
where k B is the Boltzmann constant, T is the temperature, ε i is the relative permittivity of material i, h ′ is the Planck constant, ν e is the main electronic absorption frequency, n i is the refractive index of material i, and the material numbers of minerals, CO 2 , and H 2 O 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][14][15][16][17][18] reported the value around 1:0 × 10 −19 J. This value is used in this study for A 11 . Finally, the Hamaker constant of the water film sandwiched between the CO 2 phase and the mineral phase (A 132 ) is calculated from A 11 , A 22 , and A 33 based on the mixing rule: Values of ε i and n i at conditions for the calculation of equation (6) followed existing studies [19][20][21][22][23]. In this calculation, A 11 is assumed to be constant with increasing pressure. The changes in the optical properties ε i and n i 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].

Electrostatic
Forces. The contribution from the electrostatic forces is calculated from equation (8) [25][26][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.

Geofluids
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 ϕ BC and ϕ BM . Therefore, in this work, in order to evaluate the effect of the model, calculations are conducted by both CP and CC models: where e is the elementary charge, C i is the concentration of i (molecules/m 3 ), and z i is the valence of ion i. ε 0 is the permittivity of vacuum, ε is relative permittivity, and κ is reciprocal Debye length. ϕ BC and ϕ BM are surface electrical potentials of brine/CO 2 and brine/muscovite, respectively. F ϕ is the ratio of these two potentials. h D is the dimensionless distance. In this work, the data of the zeta potential of brine/muscovite [28][29][30] and brine/CO 2 [31] are used as the parameters in Π ele .

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 Π hyd is obtained as follows: where K m and K osc are the coefficients of the monotonical and oscillated decaying of the hydration forces. λ m and λ osc 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.

The Augmented Young Laplace Equation.
The equilibrium thickness h eq of the film is determined from the augmented Young Laplace equation. Provided that the CO 2 /brine/muscovite system with the brine film between CO 2 and the muscovite are as shown in Figure 1, the augmented Young Laplace equation holds at the equilibrium state and is described as follows: where R is the curvature radius of the interface of brine/CO 2 , and P c is the capillary pressure. 60 kPa is assumed as the base case of P c . Assuming a typical droplet radius for the contact angle measurement, the Laplace pressure acting on the droplet was set as the value of P c . The effect of P c 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): The flat film has a thickness h eq 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 ∂ΠðhÞ/∂h < 0, that is, ΠðhÞ has a negative slope at the thickness [7]. Then, the trend of θ at all stable films is studied.

The Potential
Energy of the Film. The system has a finite value of θ when the integration part Ð Πðh eq Þ 0 h ′ dΠ ′ is negative. This integration is the potential energy required to form the film from infinite separation to the equilibrium thickness h eq [7]. Based on equation (2), as shown in Figure S1(a), when the area of the blue part (ΠðhÞ < 0) is larger than that of the red region ðΠðh eq Þ ≥ ΠðhÞ ≥ 0Þ, cos θ 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 CO 2 , brine, and minerals can be evaluated and discussed.  Figure 1: Conceptual model of the interfacial region of the CO 2 /brine/mineral system; h is the film thickness, and h eq is the equilibrium thickness of the water adsorption film. This thickness is determined from the relation between the capillary pressure and the disjoining pressure.
3 Geofluids a high pressure but lower than the critical point (7.38 MPa), and 10.0 MPa a supercritical state of CO 2 . 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.

Results and Discussion
By focusing on each component of disjoining pressure (Π vdW , Π ele , Π hyd ) in equation (3) using parameters of CO 2 , brine, and muscovite, the contact angles were calculated, and the mechanisms of its change are discussed below.
3.1. Van der Waals Forces. In Figure 2, 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 A 132 < 0, the van der Waals forces are positive and act as repulsive forces. Based on equations (6) and (7), A 132 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 Π vdW by increasing pressure is one of the causes of the increase in the contact angle of the CO 2 /brine/muscovite system. This trend of A 132 with increasing pressure is related to the fact that the density of CO 2 increases more rapidly than that of H 2 O. Optical properties of molecular structures ε i and n i , on which the Hamaker constant largely depends, increase linearly with the increasing densities of H 2 O and CO 2 [19][20][21][22][23]. As seen in Figure S2, CO 2 density increases considerably more than H 2 O density with increasing pressure, and this is seen in the trend of A 22 and A 33 (data of density is from Lemmon et al. [34]). A 11 , A 22 , and A 33 are constant or increase with an increase in pressure. A 132 is negative and decreases in magnitude jA 132 j with an increase in pressure. Among the three materials, only CO 2 drastically changes its density, and this is reflected in the trend of each of Hamaker constant. (8) indicates that Π ele 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 0:1 MPã 10:0 MPa is small enough to be neglected, judging from its dependence on pressure [35], unlike CO 2 , 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.

Electrostatic Forces. Equation
In Figures S4 and S5, Π ele at several values of surface electrical potentials calculated by the CP and CC models are shown, respectively. Those at different pressures (0.1,  For the water film sandwiched between CO 2 and muscovite, A 132 is negative and repulsive forces act on the film. The decrease in the repulsive forces lead to the decrease in the integration part Ð πðh eq Þ 0 h′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). A 132 for each pressure is from Table 1 Table S2. In order to evaluate the contact angle by this framework, its dependence on the model choice must be studied.
With increasing pressure in the CO 2 /H 2 O 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, ϕ BC increases from -18.0 mV to -15.0 mV [37]. In this pH range, charge reversal happens for the H 2 O/muscovite surface [28][29][30]. ϕ BM is -10.0 mV at pH 5.0, while it increases to around +5.0 mV at pH 3.5. This indicates that ϕ BC and ϕ BM 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 Π ele 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 Π ele increases, as seen in Figure 3. The change of Π ele 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.

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/m 3 to 996.57 kg/m 3 ) 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. Π hyd 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, Π hyd ðhÞ at pH = 4:5 is regarded as the case of 0.1 MPa, and Π hyd ðhÞ at pH = 3:5 is for the case of 3.0 MPa and 10.0 MPa. By lowering pH, amplitudes of the oscillation jK osc j decrease, and attractive interactions develop. In Figure S4, the integration Ð ∞ h Π hyd ðhÞdh 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. 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 of Π hyd 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. Figure 5 shows the total disjoining pressure Π tot and the integration Ð ∞ h Π tot ðhÞdh 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 P c (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 ∂ΠðhÞ /∂h < 0. The system can have contact angles at points h eq1 (thinner) and h eq2 (thicker). Each case calculated by both the CP (solid curve) and CC (dashed curve) models for Π ele is drawn. W tot 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

Geofluids
CTR measurement [37][38][39] and molecular dynamics simulation [40,41]. Differences of W tot ðh eq1 Þ and W tot ðh eq2 Þ 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 γ BC in equation (2) are from 68 mN/m to 32 mN/m in the pressure conditions. Each term of Figure 5 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 h eq and Wðh eq Þ are summarized in Table S3 and Table S4.
From 0.1 MPa to 3.0 MPa, the increase in the attractive forces of Π ele and Π hyd has led to the overall decrease in the integration part Ð ∞ h Π hyd ðhÞdh and the local minimum. 93.0% (CP model) and 87.3% (CC model) of the decreases in W tot ðh eq1 Þ are caused by the decrease in W hyd , and 84.2% and 77.4% of the decreases in W tot ðh eq2 Þ are caused by the decrease in W hyd . From 3.0 MPa to 10.0 MPa, 93:3~93:8% of the decreases in W tot ðh eq1 Þ and W tot ðh eq2 Þ are caused by the change in W vdW because the curves of Π ele slightly change, and Π hyd is the same at these two pressures because pH at these pressures is almost the same. Although detailed quantification of the reduction of Π hyd from pH 3.37 to 3.24 was not done in this work, the data from the hydration curves of Van Lin   Table 2. 6 Geofluids 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 Π hyd 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 CO 2 /Brine. The interfacial tension of CO 2 /brine surface γ BC is included in equation (2). γ BC decreases with increasing pressure. As can be seen in equation (2), a decrease of γ BC decreases ð1/γ BC Þ Ð πðh eq Þ 0 h′dΠ′ð<0Þ, which leads to a decrease in cos θ, that is, increases in θ. For example, when the pressure increases from ambient pressure to 3.0 MPa, γ BC 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 H 2 O 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  Figure 3.
Sensitivity analysis was carried out about parameters of disjoining pressure.
In Figure 7, the effect of the Hamaker constant of muscovite A 11 on the contact angle at the thinner film is plotted. Although the Hamaker constants of water and CO 2 are accurately determined from their densities, that of muscovite has differences between reported values. The range of reported data of A 11 is from 6:96 × 10 −20 J [44] (-30.4% of ΔA 11 in Figure 7) to 1:35 × 10 −19 J [14] (+35.0% of ΔA 11 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 ð ffiffiffiffiffiffiffi (7) is larger and A 11 changes A 132 more directly.
In Figure 8, by using the CP model, a 2D map of the contact angle at the thinner film was plotted as a function of ϕ BM and the vertical axis as ϕ BC . In this map, other parameters except for ϕ BC and ϕ BM 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 Π ele , 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 ϕ BM , and data from Kim and Kwak [31] was used for ϕ BC . In these maps, contact angles calculated from each ϕ BM are plotted. Differences in the values are less than 2:0°. Also, it can be estimated that the difference of ϕ BC , which is less than 10 mV, causes the change in the contact angle to less than 2:0°at each ϕ BM .  Table 1. " × ", "○", and "+" indicate values calculated from each different reported value [28][29][30].

Geofluids
In Figure 9, 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.
In addition to physical properties related to the disjoining pressure, the sensitivity of IFT of CO 2 /brine on the contact angle at the thinner film is studied here. Although many measurements have been performed for CO 2 /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 cos θ, 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%.

Conclusion and Future Perspective
In order to quantitatively investigate the mechanisms and contributing factors of the contact angle alteration of the CO 2 /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 in Π hyd , 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 Π vdW , which is related to an increase in CO 2 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 CO 2 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 Further measurements of physical properties related to CO 2 , 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..

Data Availability
Data for all the calculations are available through previously reported articles. These prior studies are cited at relevant places within the text as references.