Evolution and Interfacial Dynamics of Thin Electrolyte Films in Oil − Brine − Carbonate Rock Systems due to Chemical Equilibrium Disruptions

: This study presents the interfacial dynamics of viscoelastic thin electrolyte films between crude oil and rock surface, by integrating the effects of salt type and concentrations into the nonlinear evolution equation for viscoelastic thin liquid films. Dimensionless interfacial tension (IFT) is calculated for crude oil − NaCl, Na 2 SO 4 , MgCl 2 , MgSO 4 , CaCl 2 , and CaSO 4 interfaces. Subsequently, the interfacial dynamics of the electrolyte films (bulk phase) are evaluated at selected characteristic viscoelastic parameters and various exposure times. Results show that chloride salts of Na + , Mg 2+ , and Ca 2+ have lesser deteriorating effects on thin-film integrity compared with sulfate salts of the same cations while the presence of 1000 ppm MgCl 2 proves to constitute the least barrier to the stability of thin films. Contact angle is the most critical parameter affecting film dynamics, followed by crude oil − brine interfacial tension and the viscosity of thin electrolyte films. The difference between the ζ -potentials calculated at the crude oil − brine interface and at the brine − rock interface is a major factor in determining the response of thin electrolyte films to perturbations. A large difference between the two values of ζ -potential at the interfaces leads to better resistance to perturbations. Evaluation of the interfacial dynamics of viscoelastic thin electrolyte films is, therefore, a reliable method to determine wettability alteration due to smart water effects.


INTRODUCTION
Smart water flooding has received significant attention in the literature and it is very appealing to the oil and gas industry due to its lower capital intensity compared with other fullfledged enhanced oil-recovery (EOR) methods. 1 Several research studies have been conducted to investigate the effects of smart water in both sandstone and carbonate reservoirs. Most of the studies show that smart water injection has led to additional oil recovery. 2−7 In addition, improved oil recovery has been reported in the literature when smart water is coinjected with other EOR methods such as surfactants, polymers, and CO 2 . 8 Potential determining ions (Ca 2+ , Mg 2+ , SO 4 2− ) present in injection and formation water, crude oil polar components, and reservoir mineralogy have been identified to be major contributors to smart water effects in reservoir systems. 4 Despite the current level of understanding of smart water EOR, the main challenge remains in the definition of the dominant mechanism behind the improved oil recovery associated with smart water injection. 1,7−10 Meanwhile, arguments on dominant mechanisms by various researchers are driven by specific findings under particular experimental conditions. The uncertainty in defining the main mechanism behind smart waterflooding is mostly attributed to reservoir complex-ities when considered at the microscopic scale. 11 Hence, the oil and gas industry has conducted several field trials on smart waterflooding. Additional oil recovery from the trials shows that smart waterflooding requires more improvement to achieve its full potentials. Adequate knowledge of residual oil mobilization during smart waterflooding can unlock efficient and reliable design and deployment strategies required for greater oil recovery. Consequently, smart waterflooding is still considered to be an emerging EOR method, which requires extensive studies both at laboratory and field scales for effective design, deployment, and optimization. Crude oil mobilization from pore spaces is governed by thin-film dynamics, capillary forces, and intermolecular forces at the fluid−fluid and rock− fluid interfaces. The separation between these interfaces is marked by a potential profile caused by double-layer expansion as a result of the change in injection water chemistry. 8 There is, however, no existing direct experimental or mathematical approach that can be used to describe the dynamics of thin liquid films due to smart water effects in crude oil−brine−rock systems while considering the two mathematical interfaces.
Wettability alteration has mostly been described as the major contribution of smart water injection to increased oil recovery. Hence, the wettability of prescribed systems is deduced by estimating the contact angle at three-phase contact lines. The main effects of smart water, which lead to wettability alteration include brine−oil emulsification, wetting, and dewetting of the surface by oil, oil droplet drag, and snap-off suppression. These mechanisms are all affected by interfacial stability of the thin liquid film bound by oil−brine and brine− rock interfaces and the interfacial film stability is in turn controlled by the ionic concentration and interactions. Therefore, any method used to determine the smart water effect must capture the influence of rock mineralogy, pressure and temperature, salinity, pH, and the oil interfacial properties. The effect of any change in the mentioned factors on the wettability can be assessed by analyzing the stability of the thin water film between the rock surface and the bulk of the oil phase. Hence, evaluation of thin liquid film stability is the most reliable means by which smart water effects can be adequately captured.
The only approximate qualitative method available to relate thin-film dynamics to smart water effects is through the deduction of wettability changes by estimating the contact angle at three-phase contact lines using Derjaguin, Landau, Verwey, and Overbeek (DLVO) related techniques. While DLVO and related theories focus on the impact of interfaces on wettability alteration, the dynamics within the thin electrolyte films are much neglected. Meanwhile, recent findings have shown that additional oil recovery during smart waterflooding can be linked to the interfacial viscoelasticity of the thin electrolyte films. 12 Hence, formulations of a reliable mathematical model for describing smart water effects should include the integration of the interactions at the crude oil− brine and brine−rock interfaces, and the dynamics within thin electrolyte films in response to disruption in equilibrium of the reservoir system. The main purpose of this study is to investigate the interfacial behavior of the thin liquid film bound by the oil−brine and brine−rock interfaces to gain insight into the mechanism of smart water effects in carbonate reservoirs.
The stability of thin liquid films is an important aspect of wetting and dewetting of the rock surface by oil during crude oil mobilization from reservoirs. 13 Oil can be prevented from adhering to the rock surface if the thin liquid film is stable but unstable liquid film will lead to the rock surface becoming oilwet or mixed-wet. Thin liquid films lying over-reactive rock surfaces are constantly under disjoining pressure which tends to increase the film thickness when positive but can lead to the attraction of crude oil to the rock surface if negative. 14 The impact of the two mathematical interfaces, that is, oil−brine and brine−rock interfaces on the magnitude of disjoining pressure has been captured by various proposed expressions for calculating double-layer forces covered in Derjaguin, Landau, Verwey, and Overbeek (DVLO). 15−27 Preserving the stability of thin liquid films entails adequate understanding of the complexity of the interfacial microstructure as it relates to the interactions of surface active agents at the fluid−fluid interface, fluid−rock interface, and the bulk aqueous phase. The microstructures can lead to complex rheology of interfaces and thereby influence wetting and dewetting dynamics of such thin films. 11,28 One major interfacial property which strengthens thin-film stability is viscoelasticity and Sheng 6 concluded that salinity has significant effects on interfacial elasticity and viscous and elastic moduli. The importance of specific ions such as sodium (Na + ), magnesium (Mg 2+ ), calcium (Ca 2+ ), and sulfates (SO 4 2− ), the viscoelasticity of the interfacial film was studied by Tang and Morrow. 7 The authors reported that stronger interfacial films due to increased viscous and elastic properties were observed with SO 4 2− ions while Ca 2+ had a deteriorating effect on the films. A similar observation was made by McGuire et al., 2 who concluded that viscoelasticity of the interfacial film is linked with improved snap-off suppression.
Zhang and Morrow 3 reported the roles of asphaltenes and organic acids on viscoelastic properties of interfacial films between crude oil and brine. The authors suggested the need for the integration of viscoelasticity with other parameters (wettability, fluid distributions, and mobility control), which might contribute to residual oil mobilization during smart waterflooding, Zhang et al. 4 reported increased viscoelasticity with decreased ionic strength of the aqueous phase. Al-Shalabi and Sepehrnoori 29 identified the role of sulfate ions in increasing the viscoelastic properties of interfacial films. The authors conducted coreflooding and interfacial rheology experiments with sulfate-rich smart water. Ding and Rahman 8 reported the impact of changes in the connectivity of the nonwetting phase on relative permeability and ultimate oil recovery. The importance of nonwetting phase connectivity and coalescence of oil ganglion has also been substantiated by RezaeiDoust et al. 9 Double-layer expansion is a proposed mechanism behind smart water effects, which integrates the different aspects of interfaces in oil/brine/rock systems. 10 The electric surfaces vary with ionic strength, pH, and ionic composition, and cannot be explained by simple adsorption models. 30 Thus, surface complexation models (SCMs) are applied in modeling the chemical interactions that accompany smart water injection into crude oil reservoirs and the electrical potential that develops between a charged surface and aqueous solutions. 31−54 SCM takes into consideration both adsorption onto surfaces and the electric double-layer (EDL) which is lacking in simple adsorption models. 55,56 In this work, the viscoelastic thin-film evolution base model originally proposed by Rauscher et al. 57 and numerically solved by Barra et al. 58 is modified to accommodate the gradients of interfacial tension (IFT) that may occur in fluids with and without surface active agents or potential determining ions. 59 Integrating interfacial tension gradients with the original evolution equation for viscoelastic thin liquid films allows for the mathematical evaluation of the interfacial dynamics and the lubrication effects of thin electrolyte films bound by oil−brine and brine−rock interfaces in smart water-altered carbonate reservoirs.
The rest of the paper is organized as follows: The geometry of the problem and inclusion of the fluid−fluid interfacial effect into the nonlinear evolution equation for viscoelastic thin liquid films is discussed in Section 2. In Section 3, the estimation of dimensionless interfacial tension for the fluid− fluid interface is carried out. In Section 4, we present the simulation parameters used in this work. In Section 5, we perform the numerical simulations of the dynamic behavior of the system under different conditions. The correlation of the ζpotential at the interfaces with interfacial dynamics of thin electrolyte films is presented in Section 6, and the conclusion drawn from the results of this study is presented in Section 7. Figure 1 defines the thin electrolyte film evaluated in this study. It consists of a system of viscoelastic thin electrolyte film subjected to perturbation by disjoining pressure. Disjoining pressure comprises three main forces, which are van der Waals force, structural force, and electric double-layer force. The geometry illustrates the schematic representation of the nondimensional potential profile between two charged plates combined with fluid interfaces and boundary conditions. There exist surface potentials at the two mathematical (oil−brine and brine−rock) interfaces and the separation between the interfaces is marked with potential profiles, which are a function of the ionic interactions and adsorption of surface reactive components in crude oil (acidic and basic contents), brine (cations and anions), and the carbonate rock (calcite and carbonates). Hence, the geometry presented here is representative of the thin electrolyte film sandwiched by oil and rock. The stability of the film is under disjoining pressure and it is controlled by exposure time, salt type, and concentrations.

GEOMETRY OF THE PROBLEM
The ionic interactions at the interfaces lead to the ζpotential ψ 0 at the brine−rock interface and ψ h at the crude oil−brine interface. The two interfaces are separated by dimensionless thickness ξ = 0 and ξ = κh, where, κ [m −1 ] is the reciprocal of Derby length and h [m] is the distance between them. The charges at both interfaces are represented by σ. The longitudinal direction is denoted by x, the transverse direction by y, and the respective velocity components by u and v. The liquid film is assumed to be thin enough, and van der Waals forces are effective and strong enough that a continuum theory of the liquid is applicable. The thin electrolyte film is subject to an external disjoining pressure, w, and a tangential stress, φ.
At equilibrium, the sum of the surface forces in the described geometry should balance out i.e equals to zero. The balance is disturbed by ionic interactions that occur when the chemistry of the system is altered e.g., injection of smart water. The physicochemical interactions caused by the variation in the ionic composition of the system can lead to a shift in the wetting condition of the rock surface. A change in the wettability of any particular rock surface is determined by contact angle measurements. Factors that affect the contact angle and therefore, wettability include pressure and temperature, 60−64 rock mineralogy, 30,65,66 pH, 67,68 salinity, 60,64,69−73 and the surface reactive components mostly reported as total acid number (TAN) and total base number (TBN). 68 Changes in these factors can be investigated by analyzing the stability of the thin liquid film. 14,74 The augmented Young−Laplace equation is used to assess the stability of liquid films bound by surfaces that deviate from ideal solid surfaces, represented by the following equation where (2) Equation 2 shows that the stability of thin liquid films depends on the competition between the repulsive and attractive forces originating from disjoining pressure. Disjoining pressure is zero if it is equal to the capillary pressure, repulsive if it is positive, and attractive if it is negative. Estimation of disjoining pressure is used to predict the wettability of surfaces. The link between disjoining pressure and wettability is expressed as a measure of contact angle, 78 which can be predicted using the augmented Young−Laplace equation given as Figure 1. Schematics of the geometry of the research problem with the described thin electrolyte film bound above by crude oil−brine and below by brine−rock interfaces. The interfaces have potential, ψ 0 and ψ h and charges, and σ 0 and σ h for the brine−rock and the oil−brine interfaces, respectively. The prescribed forces (van der Waals, w and a tangential stress, φ) acting on the oil−brine interface are also shown.
Energy & Fuels pubs.acs.org/EF Article where αβ is the oil/water interface and h(P c ) [m] is the film thickness at capillary pressure, P c . Equation 3 illustrates that changes in wettability of the oil− brine−rock system is altered by factors such as oil−brine interfacial tension, change in equilibrium thin liquid film thickness, and variations in disjoining pressure across the thin liquid film. DLVO theory has been applied as a tool for evaluating various processes such as adsorption at interfaces 15−18 and colloidal instability 19 by considering intermolecular forces as the basis for the mechanisms responsible for smart water effects during enhanced oil recovery. 8,20−26 Contact angle estimation based on DLVO theory and the augmented Young−Laplace equation cannot, however, exactly match the experimental data even though DLVO theory can be applied to conduct the quantitative analysis of smart water effects on wettability change in oil/brine/rock systems. 79 In this work, the focus is, therefore, shifted to the changes in the oil−brine interfacial behavior and the dynamics of the thin electrolyte film, instead of using wettability alteration through contact angle prediction to analyze the smart water effect. Hence, experimentally measured equilibrium contact angles, θ e , is included directly in a disjoining pressure, Π T , expression which has been applied to thin liquid films of this nature 58,80−82 where n 1 and n 2 are constants such that n 1 > n 2 > 1. Several values of (n 1 , n 2 ) have been studied in the literature and (3, 2), which have been widely used, 58,80−82 are chosen for this work. σ and h * are the interfacial tension and the short length scale introduced by the van der Waals potential, respectively. In this form, the contribution of the electric double-layer force to total disjoining pressure is captured in the measured equilibrium contact angle, the interfacial tension, equilibrium thin-film thickness, and resulting thin-film thickness.
The dynamics of the thin films (shown as electrolyte solution in eq 1) bound by the crude oil−brine and brine− rock interfaces is, therefore, evaluated by applying the modified nonlinear evolution equation for viscoelastic thin films presented and numerically solved in our earlier study. 83 The dimensionless nonlinear evolution equation for viscoelastic thin films 57 is given as where, for compactness, Q, and R have been used such that where λ 1 and λ 2 are the relaxation and retardation characteristic times, respectively. W is the dimensionless van der Waals induced by disjoining pressure, h is the thin-film thickness, p is the capillary pressure, and b is the slip coefficient. The effect of the fluid−fluid interface is, however, trivialized in eq 6. Hence, we define an expression for interfacial tension within the long wave approximation of the Navier−Stokes equation, with Jeffreys constitutive model for viscoelastic stresses, to allow the study of interfacial dynamics due to the influence of physical and chemical properties of crude oil/ brine/rock systems.
The spatial variation of surfactant concentration, C, along the interfaces, which gives rise to interfacial shear stress is considered and the interfacial tension is assumed to decrease linearly with surfactant concentration, 84 is the dimensionless interfacial tension for the constant part of the interfacial tension, σ 0 , at the equilibrium concentration, C 0 , and M s is the solution version of the Marangoni number, proportional to where we remind the reader that σ is the dimensional interfacial tension, and the dimensionless surfactant concentration is expressed as C = C/C 0 . Hence, the dimensionless capillary pressure, p, can be expressed as Hence, the parameters to be estimated before eq 6 can be applied are defined by eq 9. Contrary to simplistic assumptions by previous investigators, model formulation in this work reveals that both the capillary and van der Waals components of the pressure term are affected by the properties of the thin film including the fluid− fluid interactions. The final nonlinear evolution equation, therefore, becomes

DIMENSIONLESS INTERFACIAL TENSION CALCULATIONS
The system under consideration consists of six selected salt types from Lashkarbolooki et al. 85 with unperturbed thickness h 0 = 1. The density ρ, the kinematic viscosity ν, and the constant part of the interfacial tension σ 0 are collected from the literature. The dimensionless interfacial tension for the constant part of the interfacial tension is, therefore, calculated using eq 10. The Marangoni number is calculated for each electrolyte using eq 11 by estimating the equilibrium concentration, C 0 from the reported concentration in Lashkarbolooki et al. 85 The gradient of interfacial tension with concentration, C is estimated by taking the slope of the plot of change in the reported interfacial tension with concentration. The dimensionless interfacial tension due to brine concentration is, therefore, calculated for each salt type.
The response of a viscoelastic liquid to deformation when considering Jeffreys model is characterized by the relaxation time, λ 1 , and the retardation time, λ 2 , which are related by where ν s and ν p are, respectively, the viscosity of the Newtonian solvent and the polymeric solute, such that ν = ν s + ν p . Noting that the ratio ν r = ν s /ν s + ν p ≤ 1, we have λ 1 ≥ λ 2 . 57,86,87 It is also observed that within the Jeffreys model, the Maxwell viscoelastic model is recovered when λ 2 = 0, and a Newtonian fluid when λ 1 = λ 2 . 58 Defining the dimensionless interfacial tension within the nonlinear evolution equation requires that the individual components that make up the expression be estimated as mentioned earlier. The following subsections describe the calculations of each parameter that constitute the dimensionless interfacial tension (see eq 9) due to brine concentration for each salt type and concentration.
3.1. Constant Part of the Interfacial Tension, Σ 0 . The system under consideration consists of a thin electrolyte film with unperturbed thickness, h 0 , bound above by the crude oil− brine interface and below by the brine−rock interface. The density ρ, the kinematic viscosity ν, and the constant part of the interfacial tension, σ 0 , are collected from the literature. The dimensionless interfacial tension for the constant part of the interfacial tension is, therefore, calculated for the selected salts from Lashkarbolooki et al. 85 using eq 10.
3.2. Marangoni Number, M s . The Marangoni number is calculated for each electrolyte solution using eq 11 by estimating the equilibrium concentration, C 0 , from the reported brine concentrations in Lashkarbolooki et al. 85 The gradient of interfacial tension with concentration, ((∂σ)/(∂C)) is calculated by estimating the slope of the plot of change in the reported interfacial tension with concentration.

Dimensionless Concentration, C.
The dimensionless concentration for the selected brine solutions is calculated by dividing the reported concentrations (1000, 5000, 15,000, 30,000, 45,000 ppm) in Lashkarbolooki et al. 85 by the equilibrium concentrations of the adsorbed cations at the crude oil−brine interface using PHREEQC (a chemical speciation software). The chemical evolution modeling to estimate ζ-potential and the amount of adsorbed cations at the crude oil-brine and brine-rock interfaces is presented in the Supporting Information.
where ν s and ν p are the viscosity of the Newtonian solvent and the polymeric solute respectively, such that = + s p (16) Noting that the ratio So that λ 1 ≥ λ 2 . 57,86,87

SIMULATION PARAMETERS
The parameters for estimating the constant part of the dimensionless interfacial tension are shown in Table 1.
Lashkarbolooki et al. 85 8,89,90 The density of the thin film at equilibrium, ρ, is assumed to be the density of the deionized water since the contributions of the crude oil to the total density are only at the interface and can be said to be negligible. Variation of the interfacial tension with different electrolyte solution concentrations and compared with the experimental data reported in Lashkarbolooki et al. 85 Hence, the variation of interfacial tension, (∂σ/∂C), for each salt type is estimated by finding the slope of the logarithmic trendline of the plots using Microsoft Excel.
The gradient of interfacial tension with salt concentration shows that the changes in interfacial tension are slower when the brine solutions are predominantly chloride salts compared to the changes observed when sulfate salts are used. The difference in the interfacial tension variation for Na + salts (NaCl and Na 2 SO 4 ) is smaller when compared with Mg 2+ salts (MgCl 2 and MgSO 4 ) and that of Ca 2+ salts (CaCl 2 and CaSO 4 ). There is a downward trend of interfacial tension as indicated by the negative gradient numbers, which shows a reduction in the interfacial tension with salt concentrations. It is, however, difficult to make any generalization on the gradient of interfacial tension for CaSO 4 since the experiment was conducted for only two salt concentration values (1000 and 1500 ppm). Tables 2−4 show the estimated dimensionless salt concentrations, Marangoni number, and dimensionless interfacial tension for the selected salt types and concentrations.

DYNAMICS OF VISCOELASTIC THIN ELECTROLYTE FILMS
In this section, the numerical results for dewetting thin electrolyte films in response to the impact of disjoining pressure as constituted by van der Waals interactions are presented. The initial flat fluid interface of thickness h 0 = 1 is perturbed with k = k m and δ = 0.01. The calculated domain size is 44.45 and an equilibrium film thickness h * = 0.05. The set of parameters used for all simulations in this work including the dimensionless interfacial tension and measured equilibrium contact angles are shown in Tables 2−4. Other parameters remain as presented previously. 5.1. Validation. The numerical investigations are validated by comparing the growth rate for the early times with the linear stability analysis (LSA) of eq 6. Figure 2 shows the comparison of the computed growth rates for the wavenumber of the maximum growth rate with the one given by the dispersion relation ω(k), for a film with λ 1 = 5 and λ 2 = 0.05, when b= 0. For these numerical simulations, the domain size is chosen according to the wavelength that corresponds to the wavenumber of the maximum growth rate. Similar comparisons between the computed growth rate and LSA were made for all the simulations. 5.2. Base Case. The dynamics of the thin electrolyte films at three selected times are discussed, which describe the    Figure  3 shows three phases of the interfacial dynamics of the thin viscoelastic electrolyte film composed of deionized water (i.e., without any salt types), which serves as the base case. The initial phase corresponds to the short-time viscous response of the fluid before the film separates in two retracting rims (Figure 3a). In the intermediate phase, the fastest dynamics occurs and the response of the liquid is elastic, holes and retracting edges form in this regime (Figure 3b). During the last regime, the rims increase in height, until the interface reaches its final configuration, attaining an equilibrium contact angle with the solid surface (Figure 3c). During this third stage, the fluid shows a long-time Newtonian response again. 5.3. Effects of NaCl and Na 2 SO 4 . The response of the described viscoelastic thin electrolyte film to the prescribed perturbation caused by the van der Waals induced disjoining pressure using the reported contact angle is investigated at various concentrations of NaCl and Na 2 SO 4 . The spontaneous dewetting of the films is studied at the selected three phases described. Figure 4 shows the dynamics of the films at various concentrations of NaCl at the three exposure time values. At the initial regime when t = 1.45 × 10 6 ( Figure 4a) and for all concentrations, separation of rims has started but not fully developed. The film dynamics is affected by the concentration of Na + within the thin film. The increase in the Na + concentration causes further bridging between the rock surface and the crude oil until it reaches an optimum level beyond which it deteriorates the stability of the film at the injection salinity of 45,000 ppm. The separation becomes faster and fully developed at the intermediate regime when t = 1.59 × 10 6 (Figure 4b). There is also the formation of a retracting hole at this stage. Different growth rates are observed at different concentrations of the electrolyte with the film at 45,000 ppm of NaCl reaching the highest growth while the least growth is observed at 5000 ppm of NaCl. Therefore, the amount of Na + needed to support optimum double-layer expansion where the effect of disjoining pressure on the film is minimum is achieved at 5000 ppm. In the last phase of the film configuration ( Figure   4c), all films irrespective of the electrolyte concentration reached the maximum growth and ruptured.
The van der Waals forces dominate the responses of the films to perturbation at the early stage of the film configuration since the film growth show dependence on the salinity of NaCl. This observation is in agreement with several experimental studies. 91 At this stage, the disjoining pressure is positive, which leads to higher attraction of the films to the surface as the concentration of NaCl increses but there are no observable significant contributions of the dimensionless interfacial tension. This trend continues until the intermediate regime when all the films develop further and some of them rupture. There are, however, some changes in the configuration of the films, which could be attributed to the effects of dimensionless interfacial tension. The film heights correspond to the reduction of dimensionless interfacial tension with the highest at a salinity of 45,000 ppm (Σ = 0.2182) and the lowest at a salinity of 1000 ppm (Σ = 0.2236). The dynamics at the intermediate regime correspond to the effects of various concentrations of NaCl on wettability changes and eventual additional oil recovery, which have been demonstrated in reported experimental studies. 91−95 In the last regime, there is no noticeable dominant factor that is responsible for the film behavior since all the films reach their maximum growth and attained approximately equal height and rupture. Figure 5 shows the evolution and configurations of the viscoelastic thin electrolyte films formed at various concentrations of Na 2 SO 4 at the three selected phases. Figure 5a shows that the films have fully developed and the rims already separated at the early time regime. The only observable differences in the configurations of the films according to salinity at this stage are the heights of the rims formed and the final growth of individual films. The rims quickly disappear and none can be noticed at the intermediate time regime but the difference in final growth reached by the films remains unchanged from the earlier stage (Figure 5b). There is no observable difference between the film configuration at the intermediate phase and the final regime at t = 3.45 × 10 6 ( Figure 5c).
The films formed between Na 2 SO 4 and crude oil at various concentrations result in a higher contact angle and dimensionless interfacial tension. The dynamics of the films are faster than the ones for NaCl and reach the maximum height at the early regime. The only observable factor that suggests the contributions of individual determinants is the height of the hole formed during the separation of the rims. The film morphology in Figure 6a shows that the hole heights are dependent on the dimensionless interfacial tension. Even though the films proceed at approximately the same rate, the maximum height attained slightly vary, which indicates the influence of the dimensionless interfacial tension. These observations are in agreement with experimental results where the presence of SO 4 2− with brine solution could not yield any significant additional oil recovery. 9 5.4. Effects of MgCl 2 and CaCl 2 . The dynamics of the dewetting films developed when MgCl 2 is used at the five selected concentrations are shown in Figure 6. All the films except the one at 1000 ppm MgCl 2 have fully developed and the rims separated at the early phase of the film configuration (Figure 6a). There is no difference in the film growth by the time the dynamics gets to the intermediate phase of the film configuration but all the films except the one at 1000 ppm have ruptured, as shown in Figure 6b. At the last time regime It is interesting to note that the strongest film is developed at the highest dimensionless interfacial tension. Hence, the dominance of the contact angle is demonstrated in the responses of crude oil-MgCl 2 film to the prescribed perturbation regardless of the values of dimensionless interfacial tension. There is, however, an inverse relationship between the dimensionless interfacial tension and the measured contact angle with salinity. Taheriotaghsara et al. 79 explained the increasing contact angle and the decreasing interfacial tension with MgCl 2 concentration by suggesting that the reduction in interfacial tension leads to improved spreading, which enables the oil to occupy a larger area on the rock surface, resulting in less water-wetness. Similar observations have been made somewhere else. 68,96 It follows from here that an optimum interfacial tension could be sought to preserve the integrity of thin liquid films. Figure 7 shows the evolution and dynamics of two distinct dewetting films developed for various concentrations of CaCl 2 electrolyte solutions. At the early stage of the film configuration (Figure 7a), all the films have already fully developed and rims fully separated with formation of a hole each. The films at the end of the early time regime show a similar growth rate. There are no observable differences in the growth rate and maximum film height at the intermediate regime (Figure 7b), except for the fact that the rims have disappeared. These observations are similar to the ones for MgCl 2 electrolyte films in configurations but the film growth in MgCl 2 is higher and the film at 1000 ppm salt concentration is not fully developed even at the intermediate time regime.

Effects of MgSO 4 and CaSO 4 .
The responses of the thin films to perturbations due to the effects of sulfate salts of Mg 2+ and Ca 2+ are shown and discussed in this section. The evolution and dynamics of the dewetting films with MgSO 4 as shown in Figure 8a proceed very fast at the initial time regime just as described for MgCl 2 but with a more developed film at 1000 ppm salt concentration. There is formation of a hole in the film at 1000 ppm showing that the film is greatly impacted by the prescribed force in this case. At the middle stage of the film dynamics (shown in Figure 8b), the hole has disappeared   38 measured the contact angle on oil-wet calcite and concluded that modified seawater containing Mg 2+ and SO 4 2− could lead to wettability alteration to more waterwet conditions. Figure 9 shows the dynamics of two distinct dewetting films at 1000 and 1500 ppm of CaSO 4 electrolyte solution at two of the three selected time regimes (the final stage of the film configuration is not shown since there is no observable difference between it and the intermediate stage). At the early phase of the film configuration shown in Figure 9a, the film with lower salinity is already fully developed and ruptured while the other film with higher salinity is merely developed with separated rims and formation of a hole. By the intermediate regime (Figure 9b), both films have fully developed and ruptured with the film of lower salinity having a higher film height.

CORRELATION OF THE ζ-POTENTIAL AT THE INTERFACES WITH INTERFACIAL DYNAMICS OF THE THIN FILMS
The impact of salt type and concentrations on ζ-potentials at both the crude oil−brine and brine−rock interfaces, and concentrations of cations in the formation water are discussed in this section. Figure 10 shows the effects of chloride and sulfate salts of Na + on the calculated ζ-potential at crude oil− brine interface and brine−rock interface. First, there is a relationship between the estimated ζ-potential at the brine− rock interface and the contact angle which shows that more negative or lower ζ-potential at the brine−rock interface results in a lower contact angle (Table 2). Second, the ζ-potential at both the crude oil−brine interface and brine−rock interface become more negative with Na 2 SO 4 salt compared to NaCl salt. Conversely, there is an inverse relationship between the estimated ζ-potential at the crude oil−brine interface ( Figure  10) and the calculated dimensionless interfacial (Table 2). To correlate the ζ-potential at both interfaces, the difference between the estimated ζ-potential values at both interfaces is compared with the dynamics of the thin electrolyte films, shown in Figures 4 and 5. There is a corresponding increase in the strength of thin electrolyte films with the differences in ζpotential values at the interfaces. Thin films within the same salt type respond to perturbations according to the differences in ζ-potential values between the crude oil−brine interface and brine−rock interface. A higher difference in the ζ-potential leads to delayed film development and late rupture. The observed dissimilarity between the responses of the films of different salt types to perturbations can be explained by the force of attraction between the crude oil−brine interface and brine−rock interface caused by the presence of Cl − and SO 4 2− in the bulk phase. The result of the dynamics simulation shows that SO 4 2− ions increase forces of adhesion more than the Cl ions. Figure 11 shows the comparison of the estimated ζpotentials at the crude oil−brine and brine−rock interfaces for chloride and sulfate salts of Mg 2+ ions. Again, the presence of sulfate ions increases the negativity of ζ-potential. With reference to Table 3, while there is a direct relationship between the estimated ζ-potential of the MgCl 2 brine−rock interface and the contact angle, however, there is no relationship between ζ-potential and contact angle at the MgSO 4 brine−rock interface. Meanwhile, there is a direct relationship between the ζ-potential at the crude oil−brine interface and dimensionless interfacial tension for both salt types (i.e., MgCl 2 and MgSO 4 ) in which dimensionless interfacial tension decreases with increasing ζ-potential.
To correlate the ζ-potential at both interfaces, the difference between the estimated ζ-potential values at both interfaces is compared with the dynamics of the thin electrolyte films shown in Figures 6 and 8. For MgCl 2 , there is a corresponding increase in the strength of thin electrolyte films with the differences in ζ-potential values at the interfaces. Thin films within the same salt type respond to perturbations according to the differences in ζ-potential values between the crude oil− brine interface and the brine−rock interface. A higher difference in the ζ-potential leads to delayed film development and late rupture. Energy & Fuels pubs.acs.org/EF Article Figure 12 shows the effects of chloride and sulfate salts of Ca 2+ on the calculated ζ-potential at the crude oil−brine interface and brine−rock interface. The estimated ζ-potential at the interfaces becomes more negative upon the injection of CaSO 4 compared to when CaCl 2 was injected. There is no observable correlation between the thin-film dynamics and the estimated ζ-potential at the interfaces.

CONCLUSIONS
The nonlinear evolution for viscoelastic thin electrolyte films developed in this study involves the definition of the modified expression for interfacial tension within the long wave approximation of the Navier−Stokes equation, with the Jeffreys constitutive model for viscoelastic stresses. Integration of the dimensionless interfacial tension into the evolution equation for viscoelastic thin electrolyte films allows the study of interfacial dynamics due to the influence of physical and chemical properties of crude oil/brine/rock systems. The constant part of the dimensionless interfacial tension constitutes the physical properties of the thin electrolyte films while the product of the Marangoni number and the cation concentration forms the chemical component of the dimensionless interfacial tension. Hence, only the Marangoni number aspect of dimensionless interfacial tension is altered by changes in injection water chemistry.  Energy & Fuels pubs.acs.org/EF Article Dimensionless interfacial tension is calculated for NaCl, Na 2 SO 4 , MgCl 2 , MgSO 4 , CaCl 2 , and CaSO 4 . The effects of these electrolytes and their concentrations on the film dynamics are evaluated using the modified thin-film evolution equation developed in this study at three time regimes. The destabilizing effects of adding Ca 2+ on the dynamics of the viscoelastic thin electrolyte films are stronger than that of Mg 2+ and Na + , irrespective of the salt type. Viscoelastic thin electrolyte films with MgCl 2 exhibit the slowest dynamics. Effects of the salt type and concentrations on the values of the estimated ζ-potentials at the interfaces are investigated. The ζpotential profiles reveal a correlation between charges at the mathematical interfaces and the interfacial dynamics of the thin electrolyte films. The larger the difference between the ζpotential at the crude oil−brine and brine−rock interfaces, the stronger the viscoelastic thin electrolyte films and the longer it takes for the films to rupture. ■ ASSOCIATED CONTENT
Chemical evolution modeling, surface complexation, cation exchange and adsorption, advection-transport calculations, chemical composition of the evolved thin electrolyte films, Figures S1−S6 (PDF)  Energy & Fuels pubs.acs.org/EF Article Figure 10. Calculated ζ-potential for chloride and sulfate salts of sodium ion (Na + ) at the crude oil−brine and brine−rock interfaces, as a function of salinity. Figure 11. Calculated ζ-potential for chloride and sulfate salts of magnesium ions (Mg 2+ ) at the crude oil−brine and brine−rock interfaces, as a function of salinity. Energy & Fuels pubs.acs.org/EF Article