Silica Nanoparticle

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Wettability Alteration Modeling for Oil-Wet Calcite/Silica Nanoparticle System Using Surface Forces Analysis: Contribution of DLVO versus Non-DLVO Interactions Abolfazl Dehghan Monfared,*,†,‡,§ Mohammad Hossein Ghazanfari,† Mohammad Kazemeini,† Mohammad Jamialahmadi,‡ and Abbas Helalizadeh‡ †

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran 11155-9564, Iran Department of Petroleum Engineering, Petroleum University of Technology, Ahwaz 6199171183, Iran § Department of Petroleum Engineering, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr 75169-13817, Iran

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‡

S Supporting Information *

ABSTRACT: In this work, application of silica nanoparticles for wettability alteration of initially oil-wet calcite was investigated through analysis of surface forces and DLVO theory. Doing so, the wettability and zeta potential of calcite surfaces were measured through the sessile drop method and an inhouse experimental setup, respectively. Primary evaluation indicated that incorporating DLVO terms in the Frumkin−Derjaguin model was not sufficient to describe the wettability in an oil-wet calcite/nanofluid system. Sensitivity analysis showed that calculating the double-layer interaction using constant potential-constant potential boundaries along with structural hydrophobic forces (non-DLVO interaction) incorporation improved the modeling performance. Considering hydrophobic interactions through linear correlation between hydrophobicity and wettability change for both single-exponential and harmonic equations provided some confidence on the modeling approach. Moreover, structural forces were suggested to be introduced as a combination of hydrophobic/hydrophilic interactions corresponding to stearic acid-coated/silica nanoparticle-covered sites, respectively; which in turn demonstrated a successful prediction of measured wettability data.

1. INTRODUCTION

was limited literature focused on the application of SNP for wettability alteration in carbonate rocks.13 In our recent investigation, a mechanistic study describing the underlying mechanism for altering the wettability of initially oil-wet calcite to a water wet state using SNP was presented.13 Among different quantitative wettability evaluation methods discussed in the literature, contact angle was referred to as the best one when pure fluids and artificial surfaces (the utilized situation in this study) were applied. Contact angle measurement gives a macroscopic-scale evaluation criterion. Classic Young’s equation interconnects this macroscopic quantity to fluid−fluid and fluid−solids surface energies. In other words, Young’s equation states that wettability in a three-phase system (i.e., oil/brine/rock) depends on the surface forces existing between the present phases. Therefore, investigating the wettability alteration behavior on the basis of surface force analysis prospects can provide some valuable insights into better understanding the microscopic aspects involved in this process. In addition to

Wettability, as the main basic concept in the surface sciences, controls the performance of a vast range of phenomena in current technological processes. From a petroleum engineering point of view, the impact of wettability on hydrocarbon recovery from oil and gas reservoirs is undeniable. Investigating the change in the state of wettability during introduction of different fluids through porous media could give some information about the types and extents of fluid/species− rock interactions.1−3 Wettability alteration was recognized as an effective method for improving oil recovery from carbonate reservoirs (which contain more than one-half of the worldwide proved oil reserves). To achieve this end, several techniques/materials including surfactant flooding,4,5 alkaline-surfactant,6 modified salinity water injection,7 and utilizing the wetting reversal potential of some divalent ions8,9 have been introduced in the literature. More recently, the impact of nanoparticles (NP) on changing the wetting state of solid surfaces has been also addressed.10 In this regard, silica nanoparticles (SNP) were found more attractive for reservoir rocks wettability alteration.11,12 However, compared to sandstones minerals, there © XXXX American Chemical Society

Received: May 2, 2018 Revised: October 4, 2018 Accepted: October 9, 2018

A

DOI: 10.1021/acs.iecr.8b01918 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

The disjoining pressure, which is the result of different forces acting at the molecular scale, is usually described by DLVO theory (after Derjaguin and Landau, Verwey, and Overbeek). However, DLVO theory was also utilized for evaluating different processes such as colloidal stability,21 adsorption,22,23 other interaction between materials in aquatic environment,24,25 and so on. However, much evidence26−28 demonstrated that DLVO interactions were not sufficient to account for some experimental data, and other surface forces (namely, non-DLVO interaction) were required to be considered. Thus, the disjoining pressure isotherms could be written in the following general form

Young’s equation, there exist some other mathematical expressions that govern the wetting state of surfaces such as Wenzel and Cassie−Baxter equations.14 Regarding small-scale description of wettability at a three-phase contact line, a pair of interfaces separated by a thin liquid film, covered the solid surface, is encountered. The wetting state of the solid surface determines the stability of this thin wetting film.15,16 At the equilibrium state, augmented Young−Laplace equation gives Pc = Π + 2Hmσ

(1)

where Pc is capillary pressure, Π is disjoining pressure, Hm is mean curvature of meniscus, and σ is interfacial tension (IFT). Frumkin17 and Derjaguin18 developed the proposed theoretical model of Bangham and Razouk19 to achieve the following relation for equilibrium contact angle calculation 1 cos θe = 1 + σ

∫0

Π(h0)

hd(Π(h))

Π total = ΠDLVO + Π non‐DLVO = Π vdW + ΠEDL + Π non‐DLVO

(3)

where ΠvdW and ΠEDL are van der Waals and electrical doublelayer disjoining pressure, respectively. Explanation of terms and details of disjoining pressure isotherm calculation from surface forces is discussed in the following section. Equation 2 was addressed by some researchers to describe the wettability in different situations; Churaev29 explained the phenomena of prewetting and wetting transition using this equation along with the theory of long-range surface forces in a macroscopic manner. He also proved the concept of line tension, thermodynamic and mechanical equilibrium, and establishment of dynamic contact angles. Churaev and Sobolev30 applied the FD approach to predict the contact angles in electrolyte solution−quartz systems. They evaluated the disjoining pressure isotherms on the basis of different types of molecular forces. Hirasaki15,31 was one of the pioneers who developed a basic framework according to the FD models to evaluate the wettability in the petroleum industry. He described the wettability of reservoir rock in the presence of water and oil considering the surface force components as van der Waals, electrostatic, and structural. Hirasaki15 also expressed the criteria for the stability of the wetting film in different situations. Takahashi and Kovscek32 evaluated the wettability of siliceous shale using the concept of surface force and thin film stability as well as fine migration. The estimated contact angles in the pH range from 3 to 12 were compared with the results of their previously performed core imbibition tests using the Amott index technique. They found that the pHdependent wettability alteration behavior showed the same trends for both cases.32 Sadeqi-Moqadam et al.33 explored the role of the electrical behavior of oil, water, and rock on the contact angle prediction using the FD model. To calculate the disjoining pressure isotherms, they considered different situations encountered in the electrical double-layer calculation as well as the effect of electrolyte on the van der Waals interactions. They also revised the adhesion boundary for the experimental work reported by Buckley et al.34 This manuscript aims at presenting a surface force-based conceptual framework to understand the wettability alteration behavior of initially oil-wet calcite to a water-wet condition using SNP. In this way, the key factors are contact angle measurements, electrokinetic properties, FD model, and selecting the proper surface force components contributing to the total disjoining pressure. The zeta potentials of oil-wet and SNP-treated calcite were measured by the streaming potential method using an in-house experimental setup. Using the measured values of contact angle and evaluation of

(2)

where h is separation distance or film thickness and Π(h0) is the disjoining pressure at the equilibrium thickness h0 or capillary pressure. In fact, in this model the surface forces are introduced in terms of disjoining pressure isotherms (Π(h)). The derivation of eq 2 from eq 1 can be found elsewhere.20 The Frumkin−Derjaguin (FD) equation is an explanation of the relation between the wettability, the surface forces, and the film stability. Figure 1 illustrates the three different possible

Figure 1. Schematic of different types of disjoining pressure isotherms.

behaviors of the disjoining pressure isotherm. In the case of curve I, the disjoining pressure is always positive and a complete wetting state (θe = 0) as well as a stable liquid film is predicted. For curve II, the disjoining pressure is negative in a wide range of separation. In this state, if calculation of the second term in the right-hand side (RHS) of eq 2 gives −2 or a lesser value, a contact angle of 180° is achieved and the liquid indeed does not wet the surface; thus, the wetting film is ruptured. However, if the summation of terms in RHS of eq 2 falls in the interval from −1 to 1, a finite contact angle therefore exists. The surface tends to be oil-wet in this scenario. Finally, curve III describes the situation in which the disjoining pressure indicates an “S-shaped” feature. Again, if the RHS in eq 2 yields a value between −1 and 1, a partial wetting state (θe in the range of 0−180°) is expected. Thus, eq 2 is a way of calculating the wettability of a solid surface (in terms of contact angle) from the disjoining pressure isotherms (or equivalently surface forces). B


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3. MATERIALS AND METHODS 3.1. Materials. 3.1.1. Nanoparticles. An ultrapure (99.999%) bare surface (unmodified) SNP was purchased from TECNAN (Navarrean Nanoproducts Technology, Spain) in the powder form. This high-quality SNP had a white color and characterized by a spherical morphology with the nominal average size of 10−15 nm. The specific surface area and density were 180−270 m2/g and 2.2 g/cm3, respectively. A TEM image of SNP is depicted in Figure 2.

different terms contributing to disjoining pressure isotherms, suitable models that described the wettability alteration in oilwet calcite/SNP solution systems were proposed.

2. DISJOINING PRESSURE COMPONENTS 2.1. Van der Waals Interaction. The disjoining pressure in the liquid film resulting from the van der Waals forces is often attractive. For the case of two interacting parallel plates the retarded ΠvdW is related to the separation distance (h) as35 Π vdW (h) = −

(

h

) )

A 15.96 λ + 2 lw

(

h

12πh3 1 + 5.32 λ

2

lw

(4)

where A is the Hamaker constant and λlw is the London wavelength. The details of the Hamaker constant approximation can be found in the Supporting Information. 2.2. Electrical Double-Layer Interaction. The electrical double-layer term of the disjoining pressure isotherm can be obtained by solving the so-called Poisson−Boltzman (PB) equation for appropriate boundary conditions. For simplicity, the PB equation (as a nonlinear differential equation) is linearized using the Debye−Hü ckel approximation36 as follows37 d2ψ = κ 2ψ dx 2

Figure 2. TEM image of SNP. Reprinted with permission from ref 13. , Copyright 2016 American Chemical Society.

(5)

where ψ is the electrical surface potential and κ is the inverse of the Debye length. The solutions of the linearized PB equation for three different pairs of boundary conditions can be expressed as follows.38 For constant potential-constant potential surfaces ΠEDL‐PP(h) =

2 2 ε0εrκ 2 2ψ1ψ2 cosh(κh) − ψ1 − ψ2 2 sinh2(κh)

3.1.2. Electrolyte. Sodium chloride (NaCl) in deionized water solution was applied as electrolyte. The NaCl salt with a purity of 99.5 was supplied by Merk Co. 3.1.3. Oil Phase. To provide a synthetic controllable oil phase, stearic acid (SA) was dissolved in n-heptane. The purity of SA and n-heptane was >99% and 99.9%, respectively; both from Merk Co. products. 3.1.4. Carbonate Rock Sample. A moderately high-purity calcite rock sample (approximately 99%) was supplied from Aligoodarz Mine (southwest of Iran).22 Figure S1 (in the Supporting Information) shows the accommodation between the X-ray diffraction (XRD) pattern of the utilized carbonate rock sample and calcite pattern. 3.2. Methods. 3.2.1. Preparation of Nanofluid Suspension. To prepare SNP dispersion, nanoparticles were added to a suitable amount of deionized water. It was designed to prepare a stock solution of 2500 mg/L and was then diluted to the desired nanofluid concentrations. In doing so the suspension of SNP in water was stirred using a magnetic stirrer for about 15 min. This process was followed by sonication to break the SNP agglomerates and provide homogeneous and uniform nanofluid dispersion. Having performed stability analysis, the sonication time was selected to be around 40 min. 3.2.2. Calcite Surface Modification. On the basis of experimental purposes, the provided calcite samples were utilized in two forms: crushed and thin substrates. The former was used to prepare a sand pack (porous media), and the latter were applied in contact angle measurement tests. For both states, it was required to render the calcite surface to an oil-wet state. In doing so they were wetted with deionized water and aged in sample oil. The samples (crushed or substrates) were then pulled off from the solution and washed with n-heptane and deionized water to remove the residue of synthetic oil from the surfaces. At this stage strongly oil-wet calcite samples

(6)

For constant charge-constant charge surfaces ΠEDL‐CC(h) =

2 2 ε0εrκ 2 2ψ1ψ2 cosh(κh) + ψ1 + ψ2 2 sinh2(κh)

(7)

For constant potential-constant charge surfaces ΠEDL‐PC(h) =

2 2 ε0εrκ 2 2ψ1ψ2 sinh(κh) + (ψ1 − ψ2 ) 2 cosh2(κh)

(8)

where ε0 is the vacuum permittivity and εr is the relative permittivity of the medium. Although linearization of the PB equation offers significant simplicity in deriving and applying the solutions, it can impose some degree of error in the final results. Gregory37 compared the above-mentioned approximate expressions with the corresponding exact solutions obtained from the nonlinear PB equation. In the case of constant charge, eq 7 was regarded to be a poor approximation at a close separation distance. To improve the solution, Gregory applied the “compression approximation” method.37 However, for the oppositely charged surface, eq 7 could give a good agreement with exact computation. For the constant potential case, he found that eq 6 interestingly was very close to the exact solution. Finally, it was concluded that utilizing the linear superposition approximation led to intermediate results.37 C


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4. RESULTS AND DISCUSSIONS 4.1. Zeta Potential and Contact Angle Measurements. To measure the zeta potential of calcite sands in both conditions of untreated (initially oil-wet) and treatment with SNP suspension at different concentration levels, coupling coefficients were estimated on the basis of streaming potential versus pressure difference relations. Ignoring the surface conductance of rock, the Helmholtz−Smoluchowski equation was applied to estimate the zeta potential. 39,40 The concentration of electrolyte and average equilibrium pH of injected solution were 0.005 M and 8.5 ± 0.3, respectively. The calculated values of the zeta potential for initially oil-wet calcite aging with nanofluids of different concentrations are shown in Figure 3 (left vertical axis).

were achieved due to the adsorption of stearates onto the rock surfaces. 3.2.3. Porous Media. The utilized porous media was a sand pack comprised of a Plexiglas cylinder (length of 18.5 cm and inner i.d. of 3 cm) packed with crushed calcite (the calcite pieces was ground to reduce their size in the range of 74−100 μm). The average absolute permeability and porosity of this calcite sand pack were measured to be around 2.766 D and 38%, respectively. The sand pack was initially saturated with deionized water, and an additional 10 pore volume (PV) of water was injected to clean the crushed calcite. 3.2.4. SNP Induced Wettability Alteration. To change the wettability of initially oil-wet calcite using SNP, the rock samples were aged in desired nanoparticle suspensions. The substrates were soaked in the beakers containing SNP nanofluids in the concentration range of 250−2000 mg/L. To evaluate the wettability, the substrates were taken out from the container and the corresponding contact angles were then measured in an oil/water/calcite system. To alter the wetting state of calcite porous media, the sand pack (comprised from initially oil wet crushed calcite) was flooded with around 10 PV of SNP suspension at the concentration designed for each experiment (i.e., five tests in 250, 500, 1000, 1500, and 2000 mg/L). The system was then aged for 24−48 h. Following this procedure, the nanofluid was displaced by water and the treated porous media was applied to estimate the zeta potential in a streaming potential apparatus. 3.2.5. Zeta Potential Measurement. To measure the zeta potential, an in-house experimental setup, capable of determining the streaming potential and pressure difference across the sand pack simultaneously, was designed and constructed. The streaming potential was detected using a pair of nonpolarized Ag/AgCl electrodes in which lowpermeable ceramics were contrived in their tips. The pressure difference and voltage across the porous media were measured by a differential pressure (DP) transmitter and a digital multimeter, respectively. The tolerances of multimeter and DP were 0.1 mV and 0.1 psi, respectively. The coupling coefficient was then determined through recording the potential and pressure difference in a range of injection flow rate. Having determined the coupling coefficient, the value of the zeta potential at different conditions of aging with SNP nanofluids was calculated by the Helmholtz−Smoluchowski equation.39,40 3.2.6. Contact Angle Measurements. The calcite rock wettability state was evaluated through contact angle measurement. To do so, the sessile drop technique was applied to measure the static equilibrium contact angle. Following the aging of calcite substrates in sample oil, the resulted oil-wet samples were aged in the five predesigned nanofluid concentrations (i.e., 250, 500, 1000, 1500, and 2500 mg/L). To measure the contact angle at the initial oil-wet condition and after treatment in different SNP suspensions, substrates were immersed in a cell (filled with water) at a horizontal position. From a needle contrived at the bottom of the container, oil was injected to introduce a droplet just beneath the substrate. The contact angle was then estimated by analyzing the images of oil drop captured using a highresolution camera. The size of drop might affect the value of measured contact angle. To achieve reproducible contact angles, a suitable volume of oil was injected to introduce droplets with base diameters of about 5−7 mm.41,42

Figure 3. Zeta potential and wettability profile of oil-wet calcite treated with silica nanofluids at different concentration levels.

On the basis of the measurements performed in our previous work,22 the zeta potential of the untreated (bare) calcite surface was around −16 mV. Compared to this value, the zeta potential of −19.6 mV estimated for SA treated calcite sand (in this work) proved that the surface charge of rock has been changed during the aging process. This reduction in zeta potential value demonstrated the presence of stearate layers on the calcite surface. The obtained value of the zeta potential for oil-wet calcite (SA modified surface) was in close agreement with the value reported by Kasha et al.43 (measured by a Brookhaven ZetaPALS zeta potential analyzer). The change in substrates wettability induced by aging in nanofluids is shown in Figure 3 (right vertical axis). From Figure 3 one could deduce that the profiles of wettability alteration and changes in zeta potential values followed similar trends as the concentration of SNP in aging suspensions were changed. We have previously proposed and verified the underlying mechanism for the wettability alteration of oil-wet calcite by SNP as the partial release of carboxylate groups from the surface and their replacement with NP.13 Figure 3 reveals that the zeta potential decreased from −19.6 to around −30.8 mV when the nanofluid concentration increased from 0 to 2000 mg/L. To ratiocinate this reduction, consider the zeta potential value of −35 mV (at the current electrolyte concentration and pH) for pure SNP (based on our previous measurements).22 This value was more negative than that of SA-treated calcite. Therefore, replacement of stearate with SNP on calcite was responsible for changes the average surface charge to a more negative value. This process was enhanced as the SNP concentration increased. Thus, the reduction of the zeta potential (toward more negative values) was attributed to the proposed release and replacement phenomenon which in D


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Industrial & Engineering Chemistry Research turn provided another objective support for the proposed mechanism. 4.2. Disjoining Pressure and Contact Angle Prediction. As discussed before, the disjoining pressure isotherm is constructed from surface force analysis. Herein below, the roles of different surface forces in wettability alteration are scrutinized through a sensitivity analysis on different related parameters/conditions. 4.2.1. Role of DLVO Forces. To calculate the van der Waals interaction term of disjoining pressure, described by eq 4, the Hamaker constant was required to be estimated. The Hamaker constant of an oil drop (applied for contact angle measurements) was determined based on the physical properties of kerosene. The dielectric constant, refractive index, and absorption frequency of kerosene are 1.8, 1.44, and 3 × 1015, respectively.44 On the basis of eq S2 (Supporting Information), the Hamaker constant for the oil phase (kerosene) was approximated to be 5.66 × 10−20 J, which was close to the value of 5.17 × 10−20 J reported by Argüelles-Vivas and Babadagli.45 In the same manner, the Hamaker constant of calcite was calculated to be 9.47 × 10−20 J. The required physical properties of calcite were extracted from the literature.46 The obtained values of the Hamaker constants were based on considering vacuum as the interacting media. Thus, the Hamaker constant for kerosene−calcite in water was estimated to be 2.71 × 10−21 J using eq S3. In the case of the double-layer interaction term the main issue was the selection of the proper surface boundary conditions. Generally, if charge regulation occurs as the surfaces approach each other, the surfaces are said to be at constant potential whereas constant charge condition is considered for charge regulatory prohibition case.14,26,44 However, for two dissimilar approaching charged surfaces, neither constant charge nor constant potential condition prevails and both of them are variable.38 The water− hydrocarbon interface carries a negative charge attributed to the adsorption of the hydroxyl group from water to the hydrocarbon surface.47 To describe the oil/water interfaces, application of constant charge27 and constant potential32 boundary conditions was reported. Thus, we decided to determine the double-layer repulsion for both cases and chose the more suitable one according to the experimental contact angle values. On the other hand, the charge state of many mineral oxides in the nature was supposed to be constant potential.48 Although the calcite surface in oil-wet state was covered by a stearate layer, as SA molecules were able to have charge regulation from their polar head attached to the rock surface, the calcite/water interface could be assumed as constant potential. The surface potential was usually approximated by the zeta potential.49 The calcite/water zeta potential for different aging conditions was utilized by the values obtained from streaming potential measurements (Figure 3). The zeta potential of the oil drop (kerosene) in the studied pH (8.5) was estimated to be −90 mV.50 Figure 4a shows the wettability prediction for application of four different possible pairs of boundary conditions in doublelayer interaction evaluation. The corresponding disjoining pressure isotherms considering the initial state of wettability was constructed in Figure S2 of the Supporting Information. The equilibrium thickness was usually determined by finding the root of the total disjoining pressure isotherm. However, Churaev30 mentioned that in the case of hydrophobic surfaces

Figure 4. (a) Prediction of wettability profile using DLVO forces for application of different possible pairs of boundary conditions in calculating the electrical double-layer interaction. (b) Predicted contact angles considering DLVO forces versus experimental data for different SNP concentrations (constant potential assumption on both interfaces).

the equilibrium film thickness was very small (less than 0.5 nm). At poor wetting conditions, for low-energy surfaces a film thickness of the order of molecular sizes was achieved.51 Therefore, an equilibrium thickness of 0.28 nm (approximately the molecular size of water) was used for calculation in the current study. According to Figure 4a, it could be deduced that utilizing a constant potential for both aforesaid interfaces led to better results. However, as shown in Figure 4b, there was still a discernible difference between the calculated contact angle from the FD model (using DLVO) and experimental data. Thus, application of pure DLVO forces for construction of the disjoining pressure isotherm in the FD model failed to forecast the contact angle data. However, the small window in Figure 4b demonstrated that the change in calculated contact angle with SNP concentrations followed a similar trend as the measured data. To corroborate the effect of capillary pressure on the FD model results, disjoining pressures for different values of capillaries ranging from 0 to 10 bar were evaluated. Results showed that a value of capillary pressure as large as 10 bar caused the calculated values of contact angle was changed only E


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in the range of 10 6 −5 × 10 8 Pa and 0.2−1 nm, respectively.30,51,52 The constant forces values in the order of 109 Pa were also used.56 The positive sign of structural force constant for hydrophilic surfaces indicates a repulsive interaction. Churaev and Derjaguin52 applied a value of 1 nm for the decay length. The reported magnitudes of structural force parameters for hydrophobic surfaces were also close to those of hydrophilic surfaces.30 However, the sign of As was negative to account for the attractive nature of hydrophobic forces. Compared to short-range structural forces, some researchers reported a larger range hydrophobic interaction with a decay length as high as tens of nanometers.57 Due to this fact, the use of a double-exponential equation to account for both short- and high-range structural forces seemed to be reasonable57,58

by less than 1°! Therefore, the large error in modeled values could not be due to the capillary pressure effect. As the last concern, the effect of PB equation linearization on the solutions utilized to approximate the double-layer interaction should also be considered. As mentioned before, for the case of constant potential on both surfaces, Gregory37 compared the solution (eq 6) derived from the linear PB equation and the exact solution and found a good agreement between the obtained results. Therefore, the discrepancy between the experimental wettability data and those derived from the DLVO-based modeling process could not be attributed to the error associated with the linearization of original differential equation used to account for double-layer interaction. Overall, the DLVO theory was not sufficient to predict the wettability alteration of oil-wet calcite using silica nanofluids, and it could only mimic the trend of wetting state variation. Therefore, the non-DLVO interaction must be considered to improve the prediction ability of contact angel model. 4.2.2. Contribution of Non-DLVO Interaction. Considerable effort was made to explore the appropriate non-DLVO term that improves the wettability prediction. If two interacting interfaces are located in the water as the third medium, a layer of water molecules forms on both surfaces. When interfaces approach each other, structural force emerges as a result of water layers overlap.52 Derjaguin and Zorin53 were the pioneers who developed the structural term of disjoining pressure isotherm by investigating the absorption of polar liquid vapor molecules onto the glass surface. The theoretical and experimental data proved that the structural forces decreased with the increase in liquid film thickness. The general governing equation for structural disjoining pressure could be written as52 ij h yz Πs(h) = A s expjjj− zzz j λo z k {

ij h yz ij h yz Πs(h) = A s1 expjjj− zzz + A s2 expjjj− zzz j λ z j λ z k 1{ k 2{

(10)

where indices 1 and 2 correspond to short and high range, respectively, and λ1 < λ2 whereas |As1| > |As2|. Some measurements also explored short-range oscillatory repulsive hydration (structural) force.59−61 However, Israelachvili mentioned that in a number of conditions the oscillatory structural interaction was disturbed and transformed into a monotonic curve.62 Thus, the hydrophobic forces (in water) could be usually described by single- or double-exponential equations.57,58 As the hydrophobic forces are attractive, a formulation similar to van der Waals interaction has also been proposed to describe the hydrophobic structural disjoining pressure (Πhpb)63 Πhpb(h) = −

KH 6πh3

(11)

in which KH is a parameter that plays the role of Hamaker constant. However, the value of this parameter is 1−2 orders of magnitude larger than typical Hamaker constants. Application of a single parameter in this harmonic form equation makes it more convenient to use. Analysis of the results showed that the incorporation of hydrophobic forces in the disjoining pressure isotherm improved the prediction of the contact angle by the FD equation. In doing so we encountered three choices: singleexponential, double-exponential, and van der Waals like (or harmonic) formulation. The double-exponential expression was an extended form of the single one considering the effect of long-range interaction. Rabinovich and Derjaguin64 measured the long-range structural forces between hydrophobic surfaces and from curve fitting to experimental data found the values on the order of 104 for As2, while the magnitude of As1 was reported to be in the range of 107−108.51 To investigate the effect of long-range hydrophobic forces on contact angle prediction using the FD model, a sample prediction of contact angle was done by applying the typical mentioned values of the parameters (λ1 = 1, λ2 = 15, As1 = −5 × 107, and As2 = −5 × 104) as explained below. Suppose that the disjoining pressure was purely hydrophobic considering eq 10 and the above parameter values resulted in a contact angle of 80.6°. If the second term in the RHS of the double-exponential equation, eq 10, was ignored, the FD model prediction was changed to 79.7°. Therefore, the effect of long-range hydrophobic disjoining pressure on the final results

(9)

where As is a constant and λo is the structural forces decay length. These empirical parameters are determined experimentally. The origin of structural force between to interfaces approaching each other in water; as intervening medium, returns to the way that water molecules order themselves near the interfaces. As a hydrophobic surface has no ionic/polar groups and is not able to form a hydrogen bond, it has no tendency to bond with water.54 Water molecules in the bulk liquid form about 3−3.5 hydrogen bonds, while in the vicinity of an inert solute they could have a coordination number of 4.38 On the approach of a pair of hydrophobic surfaces placed in water, the molecules confined between them (with a horizontal alignment55) migrate from the gap to the bulk liquid to reach a lower free energy and unlimited chance to form hydrogen bonds. This in turn leads to the occurrence of attractive force between two hydrophobic interfaces.54 In contrast, the affinity of water to adsorb onto the hydrophilic surfaces disturbs the ordering of molecules presented near the surface (achieve a vertical alignment55). Because of the bond between water molecules and such surfaces, for the surfaces to come close to each other, the layers of molecules imposing a barrier must be expelled.54 Therefore, in this situation, a repulsive structural (hydrophilic) interaction is encountered. The experimentally based reported values of structural force constant, As, and decay length, λo, for hydrophilic surfaces were F


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constants: As and KH. If the dependency of force constants on the contact angle values was explored, it would be possible to predict the surface wettability at different stages of nanofluid aging. To construct this functionality the published literature data should be addressed. Zhang et al.66 measured the hydrophobic forces between silica surfaces in surfactant CnTAC1 solutions of different hydrocarbon chain during which contact angles between 47°and 64° were achieved. Here, their reported adhesion force for different wettability states was plotted, as shown in Figure 5, and a linear relationship was

was negligible, and application of single-exponential equation was adequate. To incorporate the hydrophobic structural term in the FD model the disjoining pressure isotherm can be now written as follows Π(h) = Π vdW (h) + ΠEDL(h) + Πhpb(h)

(12)

Combining this equation with eq 2 one can evaluate the impact of the hydrophobic interaction on disjoining pressure and in consequence on surface wettability. The computation of ΠvdW(h) and ΠEDL(h) were discussed in section 4.2.1. To calculate the hydrophobic disjoining pressure, we started with the initial state of calcite wettability and found the unknown structural force parameters considering the contact angle in the FD equation as a known value (156.0°). In the first step, Πhpb(h) was approximated by a singleexponential model. The value of the decay length was supposed to be 1 nm.30,51 The structural force constant was then calculated to be −10.8 × 107 Pa, which was in the aforementioned range. Thus, given a logical value for the hydrophobic force, the contact angle in the initial state of wettability could be predicted. The disjoining pressure isotherm was constructed according to eq 12, in which the non-DLVO term was introduced through a hydrophobic single-exponential equation, and plotted against the best-case DLVO-based disjoining pressure in the Supporting Information (Figure S3). Compared with pure DLVO isotherms, incorporation of a hydrophobic term in the disjoining pressure led to total stronger attractive forces with a relatively longer interaction range. The product of As × λo determined the adhesion works between the water and the hydrophobic surface. The obtained value of −108 mJ/m2 was close to that of water/hydrocarbon (i.e., −100 mJ/m2)38 from which a strong oil-wet surface was deduced (as expected). Applying eq 11 to evaluate the structural interaction eventuated to KH = 2.412 × 10−19 J, which was about 2 orders of magnitude larger than the Hamaker constant for kerosene/oil-wet calcite system. The calculated KH was also in the range of literature reported values.65 The next step of calculation was to determine the contact angle values in a different state of aging with SNP suspensions. However, application of the force constants derived from the initial wetting state failed to predict the wettability for other conditions. Therefore, to predict the contact angle in the recent case a value rather than the initial wettability constant was then supposed to be considered. Here, the main issue was the way of incorporating the opportune amount as modeling parameters. Regarding Figure 4, as the contact angle decreased, the forecasting capability of DLVO was improved. Churaev and Sobolev30,51 professed that in the application of DLVO theory, originally developed for moderately lyophobic colloids, at an intermediate degree of hydrophilicity, i.e., between 15− 20° and 40−50°, the dominant role was played by van der Waals and electrostatic interactions. For contact angles below 15−20° and above 40−50°, the hydrophilic and hydrophobic structural forces should be included in the DLVO disjoining pressure isotherm, respectively.30,51 Thus, as the contact angle values decreased from high values (e.g., 156.0°) toward 40− 50°, the contribution of hydrophobic forces in disjoining pressure decreased and the prediction of wettability by DLVO was ameliorated (see also Figure 4). The decrease in hydrophobic interaction was equivalent to reduction in force

Figure 5. Linear relationship between hydrophobic adhesion forces and contact angle for Zhang et al. data (Data are from ref 66).

then found. Another set of data was reported by Churaev and Sobolev51 in which the mica surfaces were treated with CTAB to provide hydrophobicity in the range of 65−113°. According to their data, the behavior of adhesion work (Asλo), obtained from curve fitting to the single-exponential model, versus contact angle was explored in Figure 6. An approximately

Figure 6. Trend of change in hydrophobic force with contact angle for Churaev and Sobolev data (Data are from ref 51).

linear relation was again observed. The two data points lying outside of the linear trend can be due to the small difference in the contact angles (94° and 95°) that might not distinguishably reflect the change in force with variation in wettability. It is worth noting that the analysis of long-range hydrophobic forces (reported by Zhang et al.57,66) proved that the corresponding decay length followed a linear trend with change in contact angle. However, an exponential increase in G


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the calcite surface was therefore decreased. Equivalently, variation of the hydrophobic forces explained above could be interconnected with (and also verified) the proposed mechanism. In the above-mentioned procedure, to evaluate the role of hydrophobic forces, an average value for surface hydrophobicity was considered and no discussion about the presence of different sites was made. However, the suggested wettability alteration mechanism demonstrated the simultaneous presence of stearates and SNP at different stages of the aging process. Therefore, as another way to understand the structural interaction, the interacting forces for a surface composed of both hydrophobic sites (adsorbed stearates) and hydrophilic sites (adsorbed SNP) could be also studied. Cassie67 proposed a relation to describe the wettability of surfaces comprised from combination of different sites which for a two-site case was reduced to

force constant was observed. As mentioned before, the effect of long-range forces on the results could be ignored. Therefore, it would be appropriate to write a linear function to find the correlation that existed between the parameter of hydrophobic force term and contact angle. To construct a linear function, two points were required. The initial state of wettability, 156.0° and its corresponding values of force parameters, was considered as the first point. The second point was selected on the basis of aforementioned discussion about the applicability range for pure DLVO interaction. To do so it was supposed that the contribution of hydrophobic force vanished at the contact angle value of 30°, i.e., the middle of the interval from 15−20° to 40−50° in which the disjoining pressure was suggested to be calculated by considering the pure DLVO interaction. Therefore, applying KH = 2.412 × 10−19 at 156.0° and KH = 0 for 30.0° resulted in straight line KH(θ ) = ( −1.355383 cos θ + 1.173796) × 10−19

cos θ = f1 cos θ1 + f2 cos θ2

(13)

(15)

where f1 and f 2 are the fraction of sites for which the contact angles are θ1 and θ2, respectively. As the SNP was strongly water-wet, the contact angle value of zero was used for SNP-adsorbed sites. For stearate sites, we supposed that the calcite surface in the initial oil-wet condition was fully covered by SA and the value of 156° was then considered. Thus, for the oil-wet calcite treated with SNP nanofluid, the Cassie equation was expressed as

To verify the proposed linear equation, the values of KH were calculated from the FD model incorporating the experimental contact angles and were then compared with the predictions of the proposed model. Figure 7 (right vertical axis) shows a good agreement between the experimentally based calculated values of hydrophobic force constants and those predicted by applying eq 13.

cos θ = FSA cos(156°) + (1 − FSA )cos(0°)

(16)

where FSA is the fraction of sites covered by stearates. According to this equation, for each experimental contact angle, a value of FSA (or fraction of hydrophobic sites) could be calculated. On the other hand, attempts were made to develop a theoretical basis to find this fraction by applying surface forces analysis (as another objective of this study). In this way, the structural forces were introduced in the FD model as a combination of hydrophobic/hydrophilic interactions. The hydrophobic disjoining pressure evaluation was treated as before. However, to account for the hydrophilic force the following relation was utilized (after Hirasaki)15 ij h yz ΠHPL(h) = AHPL expjjj− zzz j λs z k {

Figure 7. Match between experimentally-based calculated values of hydrophobic force constants/adhesion work and their corresponding proposed linear model applied in the prediction of wettability alteration process using SNP nanofluids.

where AHPL= 1.5 × 10 and λs = 0.05 nm. Therefore, the disjoining pressure isotherm could be obtained by Π(h) = Π vdW (h) + ΠEDL(h) + FSA ΠHPB(h)

To evaluate the structural hydrophobic disjoining pressure using the single-exponential function, values of adhesion work (Wa = −As × λo) at 156.0° and 30.0° were considered that gave Wa(θ ) = −60.7 cos θ + 52.56777

(17)

10

+ (1 − FSA )ΠHPL(h)

(18)

The indices HPB and HPL indicate the hydrophobic and hydrophilic sites, respectively. Introducing eq 18 into the FD model allowed one to theoretically evaluate the fraction of sites covered by stearates for different values of contact angle. The simulated values of FSA, for incorporation of hydrophobic forces in the form of single-exponential equation as well as harmonic model (i.e., eq 11), were compared with the values obtained from eq 15 in Figure 8. It was obviously inferred from this figure that the proposed model could properly reproduce the experimentally derived values for fraction of SA-covered sites. The methodology applied in this study is illustrated in a workflow shown in Figure 9. Although the analysis and modeling process was performed at atmospheric conditions

(14)

In a similar way, the proposed linear model for variation of adhesion work with change in contact angle was also verified by the experimentally derived values. Again, the result implied a good match between the data points and the model predictions, as illustrated in Figure 7 (left vertical axis). Reduction in the contribution of hydrophobic forces in the disjoining pressure isotherm calculation could be also argued on the basis of our previously suggested mechanism for wettability alteration of oil-wet calcite using SNP suspensions.13 In this regard, when an oil-wet calcite surface was aged in SNP suspensions, the hydrophobic stearates were replaced by hydrophilic SNP and the number of hydrophobic sites on H


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SNP nanofluid/oil-wet calcite), the same flowchart (Figure 9) can be utilized, but one should take care about the non-DLVO term(s) of disjoining pressure isotherms. Strictly speaking, having scrutinized the different phenomena occurring at the interfaces the appropriate structural and/or other non-DLVO interaction(s) along with their way of application must be explored. In other words, to apply the current modeling approach for wettability prediction in other systems, the inclusion of van der Waals and electrical double-layer interactions is necessary but may not be sufficient. However, in application of double-layer forces the suitable boundary conditions should be explored. The situation for incorporation of non-DLVO term(s) can be different from this study. The intrinsic properties of interacting interfaces as well as the nature of intervening media dictate the proper selection of contributing non-DLVO forces.

Figure 8. Prediction of wettability on the basis of the fraction of sites covered with SA.

5. CONCLUSIONS In this work, wettability alteration of initially oil-wet calcite by silica nanoparticles suspensions was studied by applying surface force analysis and DLVO theory. In this regard, the values of measured contact angles were attempted to be calculated by the Frumkin−Derjaguin model in which DLVO theory was applied to construct disjoining pressure isotherms. Results indicated that applying different boundary conditions in solving the Poisson−Boltzman to calculate double-layer interaction as well as changing capillary pressure (even as high as 10 bar) could not account for the large deviation from the observed wettability data. Among different non-DLVO surface forces, the structural hydrophobic interaction was found to improve the modeling results significantly. This interaction was considered by two approaches. In the first approach, the so-called singleexponential and harmonic equations were considered, in which the unknown hydrophobic constant parameters were estimated from the experimental data. Analysis revealed that the contribution of the hydrophobic term in the disjoining pressure isotherm was decreased as the degree of hydrophilicity increased. A linear trend was then proposed for such a variation and validated by the values obtained from experimental measurements. As a second approach, for the first time, the role of structural disjoining pressure was explored through introduction of a hydrophobic/hydrophilic surface sites concept. The contribution of non-DLVO interaction as a combination of hydrophobic and hydrophilic terms, attributed to the stearic acid and silica nanoparticles covered sites, respectively, again showed a significant improvement in the final prediction. A good match was then observed between the fraction of sites covered by stearic acid calculated from the Frumkin−Derjaguin model and experimentally derived values based on the Cassie equation. Overall, at the initial stage of wettability (i.e., strongly oil-wet calcite surface), the main contribution of surface forces comes from hydrophobic non-DLVO interaction. However, the effect of non-DLVO disjoining pressure term(s) in wettability alteration modeling decreased as the concentration of nanoparticles in the aging nanofluid increased.

Figure 9. Workflow of wettability alteration modeling for oil-wet calcite/SNP nanofluid system through surfaces analysis.

(ambient pressure and temperature), it was supposed to be a basic framework that described the modeling procedure for application in other situations. In this way, the measurements and calculation of initial input parameters; including the Hamaker constant, zeta potential, and contact angle data, should be performed at that desired conditions. At this stage the pressure and/or temperature dependency of these parameters may be required to be considered. Zeta potential values were demonstrated to be affected by pressure and temperature variations.68 The pressure/temperature dependency of the contact angle was also mentioned in some situations.69 However, Hamaker constant values were usually reported along with their corresponding temperatures.38 For the cases which differ from that explained in this work (i.e.,

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b01918. I


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X-ray diffraction pattern of calcite rock; Hamaker constant calculation; disjoining pressure isotherms for initial oil-wet state; incorporation of hydrophobic interaction in disjoining pressure isotherms. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +98 77 3122 2612. ORCID

Abolfazl Dehghan Monfared: 0000-0003-1026-8839 Notes

The authors declare no competing financial interest.

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