Dynamic Asphaltene-Stearic Acid Competition at the OilâWater Interface

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Dynamic Asphaltene-Stearic Acid Competition at the Oil-Water Interface Bastian Sauerer, Mikhail Stukan, Jan Buiting, Wael Abdallah, and Simon Ivar Andersen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00684 • Publication Date (Web): 17 Apr 2018 Downloaded from http://pubs.acs.org on April 18, 2018

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Dynamic Asphaltene-Stearic Acid Competition at the Oil-Water Interface Bastian Sauerer , Mikhail Stukan , Jan Buiting , Wael Abdallah , Simon Andersen †

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Schlumberger Dhahran Carbonate Research Center, Dhahran Techno Valley – KFUPM, P.O. Box 39011, Dammam / Doha Camp 31942, Saudi Arabia †

‡

Retired, formerly Saudi ARAMCO, Reservoir Characterization Department, Dhahran 31311, Saudi Arabia

Schlumberger DBR Technology Center, 9450 – 17th Avenue, Edmonton, AB T6N 1M9, Canada

§

ABSTRACT Interfacial tension (IFT) is one of the major parameters which govern the fluid flow in oil production and recovery. This paper investigates the interfacial activity of different natural surfactants found in crude oil. The main objective was to better understand the competition between carboxylic acids and asphaltenes on toluene/water interfaces. Dynamic IFT was measured for water-in-oil pendant drops contrary to most studies using oil-in-water drops. Stearic acid (SA) was used as model compound for surface-active carboxylic acids in crude. The influence of concentration of these species on dynamic IFT between model oil and deionized water was examined. The acid concentrations were of realistic values (total acid number 0.1 to 2 mg KOH/g oil) while asphaltene concentrations were low and set between 10 and 100 ppm. In mixtures, the initial surface pressure was entirely determined by the SA content while asphaltenes showed a slow initial diffusion to the interface followed by increased adsorption at longer times. The final surface pressure was higher for asphaltenes compared to SA, but for binaries, the final surface pressure was always lower than the sum of the individuals. At high SA concentration, surface pressures of mixtures were dominated entirely by the SA, although, Langmuir isotherm analysis shows that asphaltenes bind to the interface 200-250 times stronger than SA. The surface area/molecule for both SA and asphaltenes were found to be larger than the values reported in recent literature. Various approaches to dynamic surface adsorption were tested, showing that apparent diffusivity of asphaltenes is very low in agreement with other works. Hence, the adsorption is apparently under barrier control. A possible hypothesis is that at the initial phase of the experiment and at lower concentration of asphaltenes, the interface is occupied by stearic acid molecules forming a dense layer of hydrocarbon chains that may repel the asphaltenes.

KEYWORDS Interfacial tension, Asphaltene, Stearic Acid, Diffusion, Gibbs-Langmuir, Adsorption, Interface.

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INTRODUCTION Fluid transport in porous media, which determines the rate of oil recovery from hydrocarbon reservoirs, is governed by the interplay of viscous and capillary forces.1 The latter is predominately controlled by the surface-active constituents of the crude oil, which accumulate at oil-brine and oil-rock interfaces.2 Molecular rearrangements taking place near the phase boundaries affect the interfacial tension (IFT) and surface wettability,3,4 two critical parameters that are the base to determine reservoir fluids relative permeability, which is the main input to reservoir simulators used for proper estimation of residual oil saturation and recoverable oil volume. Furthermore, some of the surface-active species existing in crude oil are known to stabilize water-in-oil emulsions,5 which causes further problems in recovery operations.6 Despite the extensive investigations on the processes occurring at the oil/water interface, which have been conducted over the last five decades,6-19 the mechanistic background for interfacial phenomena, especially the time resolved decay of interfacial tension for crude oil-water mixtures is not yet understood in detail.6,18,20,21 One of the reasons for this is the complexity of crude oil compositions. Interfacial tension variation is due to a combination of polar (Acid-Base) and non-polar (Lifshitz-van der Waals) forces.22 If only pure non-polar components are present, we do not expect time dependence in the interfacial tension measurement. If polar components are present, however, time dependence of interfacial tension values is expected and should lead to lower IFT values over time. The magnitude of this reduction is not known a priori and needs to be quantified. Several polar components like asphaltenes, resins, carboxylic acids, and other nitrogen/sulfur/oxygen containing compounds are common in crude oil.23 One or more of these compound classes are expected to be the reason for the lowering of the IFT values as was shown by Seifert.17 The asphaltene fraction has attracted special attention and is the most studied of the petroleum fractions, due to the ability of this class of molecules to stabilize water-in-oil emulsions.5,12,15,16,24-26 Kilpatrick and co-workers have shown that resins, which could be organic acids, may penetrate asphaltene interfacial layers, changing the structure and mechanical properties of these layers.26 In emulsion interfacial layers, an abundance of components, inferred to be acids through neutralization experiments, has been found.27 Recently, we have shown by gas chromatography mass spectrometry (GC-MS) that a large range of homologous carboxylic acids indeed deposit in abundance at the crude oil-water interface.20 Examination of Langmuir films of asphaltenes and carboxylic acids indicates a specific interaction between the acid and the asphaltenes, leading to an apparent softening of the interfacial film.21 Carboxylic acids are well known surface-active species in nature. They adsorb at the oil-water interface and can form regular organized film structures. Such fatty acids have, due to their abundance in nature and especially in biological material, been examined in great details in the surface sciences. One of these


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species, stearic acid (C17H35COOH), is highly insoluble in water due to the chain length but can form very well organized expanded films at the oil-water interfaces. Ionization of the head group will contribute to this structuring and to deviations from what is known as the condensed state where the film almost approaches a solid state at high concentrations. From the analysis of surface pressure, one may obtain important information about the structure of interface. The adsorption at the water-oil interface has been reported to be dependent on the organic solvent.28 This is related to the chemical potential difference between bulk and interface and also relates to the packing at the interface. Different solvents will lead to different states of swelling of the organic hydrophobic part of the film monolayer.28 Asphaltenes, being a generic, solubility defined fraction of crude oil, have been known to stabilize emulsions and also to lower IFT of solutions in organic solvents such as toluene.29 This fraction is extremely complex, and only average properties are known. No true model compound has been designed that can emulate asphaltene behavior and this dictates the use of original samples in any scientific investigation. In the present case, we used asphaltenes obtained from an oil of moderate asphaltene content. The concentration of asphaltenes (below 0.010 wt% in toluene) in this study was limited by the need for optical transparency of the measured solution, as we examined water-in-oil pendant drops. Compared to crude oils with asphaltene contents as high as and beyond 20 wt%, the investigated concentrations were very low, but this allowed for a study of less saturated surfaces with limited skin formation. Time dependence of IFT in multicomponent systems will depend on the diffusion of species to the interface, the rate of adsorption and desorption to and from the interface, and therefore also an equilibrium constant, which is the ratio of the two rate constants. The equilibrium constant (KL) also reflects the energy of adsorption or strength of adhesion to the interface. Some molecules tend to form soft interfacial films, while others may form rigid, mechanically strong interfacial films. In crude oil, asphaltenes are known to form rigid, membrane-like films under laboratory conditions. Whether interfacial films exist in the oil reservoir is not known. Due to the complexity of the crude oil, there might be competition between various types of surface-active compounds, resulting from differences in equilibrium adsorption energies but also due to interactions between crude oil species in the bulk and in the vicinity of the surface. This so called subsurface region plays an important role in the diffusion and adhesion to the interface. The rate of diffusion from the bulk to the interface of a given substance in a multicomponent mixture is related to the diffusion coefficients of individual species and the adsorption mechanism (including


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strength of adherence). Hence, over time this observed rate can change if one species diffuses faster than the other but upon arrival at the interface exhibits less energy of adsorption. Therefore, valuable information is found in the analysis of the dynamic IFT both at initial conditions as well as on the slower long term development as the equilibrium state is approached. Also, as the process involved is adsorption based, the change in IFT can give information of the individual adsorption isotherms providing further information of both the individual adsorbents as well as the mutual competition and interaction. To elucidate the mechanistic impact of these natural immanent surfactants, residing in the crude oil, on the dynamic IFT, we study the time resolved interfacial tension of model oils spanning a total acid number (TAN) from about 0.1 to 2 mg KOH/g oil. The study focuses on measurements of solutions of stearic acid (SA) and asphaltenes in toluene. Stearic acid is an excellent average model compound for the variety of carboxylic acids which is found at the oil-water interface after equilibration.20 Furthermore, we investigate the influence of asphaltenes isolated from Saudi Arabian crude oil on interfacial tension. Finally, the competitive nature of carboxylic acids and asphaltenes at the interface is studied by analyzing the interfacial tension kinetics of defined mixtures of stearic acid and the asphaltenes. Thus, we gather deeper knowledge of the interplay of these compounds at the interface and their overall effect on interfacial tension. As surface and interfacial behavior of stearic acid is abundantly reported in the literature, we can also use changes to the stearic acid film properties as a probe of the nature of the interfacial activity of asphaltenes. There is abundant literature, showing that stearic acid films may block or repel other molecules from the air-water interface. This is due to strong interactions between the hydrocarbon chains. At the oil-water interface this is normally assumed to be reduced due to the swelling of the film which apparently reduces the van der Waals forces between chains. Dutta and co-workers investigated the interaction of simple non-substituted polyaromatics and stearic acid at the air-water interface and showed that anthracene would be squeezed out of the interfacial film formed by stearic acid. 22,30 The apparent surface area occupied at the interface is an important parameter in understanding the conformation and structure of an interfacial monolayer film. Dutta et al. reported the apparent molecular area at the air-water interface for pure polyaromatics as: chrysene 0.32 nm2; perylene 0.32 nm2; anthracene 0.21 nm2; 9,10-diphenylanthracene 0.26 nm2. These are all reported positioned in an angle relative to the interfacial plane and they crystalize at the interface at high coverage.22,30 In the mixed films, repulsion between stearic acid and the aromatic solute was observed, leading to non-ideal film behavior,


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expressed by changes in average molecular surface areas. In the condensed state at the air-water interface, the surface area per molecule of fatty acid is approximately 0.20 nm2, which in the oil-water case will increase as the head group is ionized, e.g. in deionized water, and the brush of carbon chains is swollen by solvent. The limiting area of benzene derivatives is about 0.24 nm2. Rondelez et al.23 reported in another study that benzene-hexa-alkanoates showed apparent parallel adsorption of the benzene ring assisted by the 6 carboxylic acids at the chains anchoring the molecule to the surface. The areas were reported to be between 1.10 and 3.00 nm2. In recent works on asphaltenes at the oil-water interface a surface area per molecule of 0.30 nm2 has been reported, and the authors claim that this is a result of the large central polyaromatic portion being placed parallel to the water-solvent interface.31-32 There is a clear discrepancy between reported values of simple molecules of well-known orientation and molecular structure and the claim of parallel adsorption. We assume that such a value as 0.30 nm2, although similar to apparent surface areas of polyaromatic at air-water interfaces, for a large molecule such as the asphaltene indicates that a significant portion of the material is not present at the interface especially when also allowing for solvent-solute interaction in the film. Intuitively one may also assume that the activity of the asphaltene constituents may vary broadly. Recently, Andersen et al.33 have confirmed that only specific types of asphaltenes are found at the interfaces, which means some types of asphaltenes are less surface-active and therefore also easily excluded. Similar to the reported crystallization of polyaromatic molecules, spread at the air-water interface, asphaltenes also form solid islands at the interface at high coverage.34 Therefore, the presence of the solvent is necessary in order to make meaningful studies as this enables asphaltenes to potentially swell and also re-dissolve into the solvent phase. While most studies on hydrocarbon-water IFT by the pendant drop method apply the oil-in-water approach, we have decided to use droplets of water in the model oil. This non-conventional approach was selected both for practical purposes (e.g. easier cleaning procedures) and the quasi constant bulk concentration this offers. The study comprises a range of concentrations of each of the two types of surface-active material and combinations of these. Stearic acid concentrations were taken to represent the most abundant range of total acid numbers reported for crude oils, as indicated above. The use of water-in-oil and the optical analysis of IFT dictates the upper limitation for the asphaltene concentration due to reduced transparency of the solutions. Therefore, the systems investigated, in many ways resemble a light oil with variations mainly in the acid content. This allows us to emphasize the competitive actions


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of the carboxylic acids and the asphaltenes in the solution and, as mentioned above, to avoid interference from skin formation. In this work, we report findings showing that, while carboxylic acids will initially dominate an interface due to very fast adsorption, asphaltenes diffuse slower (at the investigated concentrations) and have much higher energy of adsorption and therefore bind to the surface much stronger than carboxylic acids. However, competitive effects are very dominant when excess acid is present, and it seems that stearic acid can block the access to the adsorption sites of the interface, leading to negligible adsorption of asphaltenes. This is not explained by a simple Gibbs-Langmuir approach, according to which stearic acids should slowly be replaced by the stronger binding asphaltenes.

MATERIALS AND METHODS

Chemicals Anhydrous toluene was purchased from Sigma Aldrich in 99.8% purity. Deionized water was used from a Milli Q Integral 5 water purification system with 0.055 µS/cm and was degassed before use. Stearic Acid was purchased from Loba Chemie in 98% purity. Asphaltenes were isolated from Saudi Arabian crude oil (density of 0.859 g/cc, a viscosity of 7.11 cP at 30ᵒC and average molecular weight of 243 g/mol) by precipitation in n-heptane, followed by vacuum filtration and excessive washing with n-heptane. Asphaltenes were subsequently recovered by dissolution and drying. Extra pure n-heptane was purchased from Scharlau in 99% purity and used as received. Stock solutions in toluene of stearic acid and asphaltenes were prepared by weight. The solutions of lower concentration were created by adequate dilution by weight. Asphaltene solutions were 0.001 to 0.01 wt% (10 to 100 ppm) and stearic acid solutions were between 0.05 and 1.00 wt % (500 – 10,000 ppm). The low asphaltene concentrations were dictated by the optical transparency of the sample as the IFT data was recorded by pendant drops of water in bulk oil.

Interfacial Tension Measurements Dynamic IFT was measured on a Rame-Hart tensiometer using the pendant drop method. A glass cuvette was filled with the bulk phase (solution of surface-active components in toluene) and placed in an environmental chamber where the sample was heated to 30°C to maintain a stable temperature. Drops of water were created using an auto dispenser, connecting a water reservoir with a stainless steel needle that can be submerged in the sample through a cover. The needle was grounded to eliminate distortion of the drop shape by static charge.35 The chamber was illuminated from the back with a fiber optic lamp.


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From the front, a video camera captured the image which was then digitized. The interfacial tension values were calculated from the drop shape using the Young-Laplace equation. In all calculations, tabulated density values were used for water (995.65 kg/m3 at 30°C) and toluene (857.57 kg/m3 at 30°C), assuming negligible effects of the low solute concentrations on the density of the solvent phase. All data presented is the averaged result of three or more repeated measurements over 90 minutes each. For each concentration considered, results provided are averaged values of several measurements for sequential drops. The reproducibility of the measurements in all three types of systems (water-stearic acid in toluene, water-asphaltenes in toluene, water-asphaltenes and stearic acid in toluene) warrants a standard deviation of the IFT values, within 0.4 mN/m. The example of IFT plots for sequential drops used for the averaging are provided in the Supporting Information (Figure S1). A reference baseline for the IFT of the toluene-water system was initially established based on 10 individual measurements of water-in-toluene. As seen in Figure 1, the IFT decreased slightly with time which can be ascribed to the presence of small amounts of impurities in the system that adsorbed and accumulated at the oil-water interface. Time resolved dynamic IFT was studied for concentrations of stearic acid in the range that corresponds to the weight percentages of acids typically found in crude oils, as proven by neutralization experiments: 0.05, 0.10, 0.25, 0.50 and 1.00 wt% of stearic acid in toluene. Examples of measured curves are given in Figure S2 in the Supporting Information.


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Figure 1: Interfacial tension as a function of time for: water in neat toluene, 1.00 wt% stearic acid in toluene and 0.01 wt% aphaltenes in toluene. Literature value of toluene-water IFT is 36 mN/m.36

RESULTS AND DISCUSSION In order to get a better understanding of the interplay between carboxylic acids and asphaltenes, which have been identified as the major surface-active components in crude oil, it was aimed to study first the individual contributions of these surface-active species on the interfacial tension of toluene-model oilwater systems, followed by investigations of mixtures of these. In the following, we first discuss the various observations followed by a rigorous analysis of both adsorption and diffusion. It is important to note that as asphaltene content was kept at levels of up to 0.01 wt%, stearic acid content was up to 1.00 wt%. Assuming a molecular weight of asphaltenes in the range of 1000 g/mol, the molar ratio between SA and asphaltenes may be as high as approximately 1750, meaning a great abundance of stearic acid. The low asphaltene concentration used herein allowed us to observe the actual competition between asphaltenes and stearic acids. As we have observed and describe below, the long-term effect of asphaltenes on the interfacial properties is more dominant at lower molar ratios.


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After establishment of the background measurement for pure solvent, drops of water were measured in solutions of stearic acid in toluene. Equilibrium was not reached in any of the experiments within the 90 minutes experimental interval as seen in Figure 1. To compare the influence of different surface-active species on IFT, we present the data in formalism of surface pressure rather than using the interfacial tension plots. The time dependent surface pressure P is defined as the difference between the solution IFT value g at time t and go of water in the neat toluene measured at the same time t after drop creation:

P(t) = g0(t) − g(t)

(1)

The plots of this parameter as a function of time for stearic acid and asphaltene solutions of different concentrations are provided in Figure 2 and Figure 3, respectively. The analysis is further enabled by semi logarithmic plots of surface pressure versus log (time). This allows for a closer examination of the initial part of the development of IFT. For the stearic acid, we observed an initial rapid change over very short time during drop formation, followed by a re-equilibration of the subsurface layer and the bulk, and then a slow adsorption-desorption process towards equilibrium. Asphaltenes, on the other hand, exhibit a steady and slow adsorption process.


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Figure 2: Surface pressure versus time for water in stearic acid solutions of different concentration in toluene.

Figure 3: Surface pressure versus time for water in asphaltene solutions of different concentration in toluene. Notice the obvious concentration dependences of the induction time at which asphaltenes start to adsorb to the interface.

As the logarithmic representation in Figure 2 shows, the initial surface pressure value increases systematically with increasing SA concentration beyond 0.1 wt%. This indicates that an ultra-fast adsorption is taking place as the droplet is being formed in the solution, already attaining a substantial surface coverage. The development of the geometric shape of the droplets indicated that the volume-toarea becomes constant within 2-3 seconds for all measurements investigated. Hence, the process observed, consists of the initial fast adsorption followed by a slower development of the interfacial film. This indicates a depletion of the subsurface region as the interface is created, which is then followed by the diffusion of stearic acid into this region before further adsorption takes place. In Figure 3, we observe a significant difference in development of the surface pressure with time as the asphaltene concentration changes from 0.001 to 0.01 wt%. The observed trends agree with the representation of similar data by Rane et al.20 To enhance the analysis of the initial surface pressure


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development, the data is also plotted on a semi-log scale. The initial wiggling of the data is basically due to initial instability in the toluene data subtracted. The graduate development with bulk concentration is now easily observed and seems to be due to differences in the rate of diffusion and adsorption to the interface. A clear relation between the concentration and the induction time at which surface pressure starts to increase is seen. The induction time is about 200 s for the lowest concentration and 10 s for the highest concentration. It is remarkable that the initial surface pressure values are very small in comparison to those for stearic acid solutions. This can be explained by the fact that the large asphaltene molecules need much more time to diffuse to the interface than the small stearic acid molecules. This also indicates that asphaltenes do not readily bind to the interface during the dynamic droplet formation. Comparison of the contributions of respectively asphaltenes and stearic acid shows that the long-term effects are relatively stronger (per concentration unit) for asphaltenes compared to stearic acid. Therefore, stearic acid dominates the interface rapidly whereas asphaltenes show a slow rate of diffusion and adsorption. Below this will be seen to matter in the extreme cases for mixtures of the two solutes. In petroleum both asphaltenes and carboxylic acids coexist and as observed above, both possess surface affinity. Therefore, we finally consider the actual conditions of the co-existence of these components and the impact on the surface behavior of mixed solutions of surface-active materials containing both asphaltenes and stearic acid. The goal is to understand how different surface-active materials influence IFT dynamics when they interact with each other or compete, i.e. if the effect of different components is additive, competitive or singular. Several combinations of component concentrations were analyzed. In total, nine different solutions were investigated. The solutions considered represent all binary combinations between solutions having concentrations of 0.001, 0.005 and 0.010 wt% asphaltenes in toluene and solutions having concentrations of 0.05, 0.25 and 0.50 wt% stearic acid in toluene. Although the upper limit of the surface pressure values observed in stearic acid solutions are higher than those in case of asphaltene solutions, the actual values are comparable and, thus, neither of the components should be expected to be dominant a priori. This is especially important as there is a notable difference in the analyzed range of molar concentrations of stearic acid and asphaltenes which is a result of the optical constraints of the investigation of water-in-oil droplets. While the molecular weight of SA is 284 g/mol, the asphaltenes are a distribution of molecules both in terms of size and structure. For the sake of argument, we define the molecular weight of the asphaltenes as 1000 g/mol. This means the molar concentration of stearic acid spans from 1.5 to 30 mol/m3, while that of asphaltenes span from 0.009 to


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0.09 mol/m3. Hence, stearic acid is always present in excess. The adsorption of stearic acid will create well-organized, simple monolayer films with little cohesive interaction along the interface. The asphaltenes, on the other hand, may interact both along the interface as well as with asphaltene molecules in the vicinity of the interface. In the mixed case both preferential adsorption (positive Gibbs Excess) as well as interactions between stearic acid and asphaltene at both interface and subsurface as well as in bulk (hydrogen bonding) could affect the interfacial tension. The analysis of the initial surface pressure in Figure 4 shows that this is entirely determined by the stearic acid and independent of asphaltene concentration at short times and then, beyond 10 seconds induction time, the asphaltenes start to have an influence dependent on the asphaltene concentration. As we approach 0.5 wt% SA, the surface is completely dominated by the acid through fast adsorption and asphaltenes have limited influence on the development of the IFT. This should be seen in the light of the very large difference in adsorption equilibrium constant (see below) which in theory would favor asphaltene adsorption. This is surprising, as studies of systems of binaries of different concentration and adsorption strength normally will show that over time an exchange process takes place where the surfactant of lowest adsorption energy is replaced by the other, independent of concentration.37 There is only a weak indication of this in Figure 4, where asphaltenes provide a limited effect of less than 1 mN/m in case of high (0.5 wt%) concentration of SA. In Supporting Information, Figure S3-5 composite SA/asphaltene isotherms are given for comparison. The values reached at 5400 seconds are also given for the various combinations showing how asphaltenes have little impact at high stearic acid contents (Figure S6 in Supporting Information).


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Figure 4. Surface pressure versus time for water in solutions of fixed stearic acid contents of 0.05 wt% and 0.50 wt% respectively with varying content of the asphaltenes.

For the system with low SA concentration (0.05 wt%), the effect of the asphaltenes is actually substantial despite a low molar concentration of the asphaltenes relative to that of the stearic acid. Therefore, per molecule the interfacial affinity is substantially larger for asphaltenes than for the stearic acid. It is worth mentioning that initial surface pressure values are close to those for single component stearic acid solutions (see Figure 2 and Figure S7). This is due to the fact that in the binary mixtures, large asphaltene molecules need much more time to diffuse to the interface and thus, the initial dynamics of surface pressure is governed by the much smaller, highly mobile stearic acid molecules.38 In binary mixtures of surface-active material, the adsorption to the interface may be affected by interaction between solutes e.g. hydrogen bonding between asphaltenes and carboxylic acid, and different affinity for the surface like demulsifier action.39,40 In ideal mixed films the surface film composition is proportional to the bulk phase composition. Any deviation (excess adsorption) is an indication of non-ideal contribution governed by difference in surface and solvent affinity.41,42 It is therefore important to examine the partial contribution of each component to the interfacial film.


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For each binary mixture, the surface pressure (PBMx%+y%) was compared with surface pressures for respective components (PAsphx% and PSAy%) and the hypothetical additive surface pressure value (PSx%+y%), which correspond to the case when each component of the mixture contributes to the surface pressure independent of the second component and proportional to the bulk concentration. Mathematically, additive surface pressure is defined as: PSx%+y%(t) = PAsphx%(t) + PSAy%(t)

(2)

where PAsphx%(t) is the surface pressure of x weight percent solution of asphaltenes in toluene at time t and PSAy%(t) is the surface pressure of y weight percent solution of stearic acid in toluene at time t. To better analyze the contributions to the surface pressure coming from the individual surface-active components as well as to investigate presence of possible synergistic effects, the corresponding parameters were considered in several normalized forms: respective surface pressures for individual components were normalized on corresponding surface pressure for binary mixtures and the binary mixture surface pressures were normalized on corresponding additive surface pressures. These normalized plots are provided in Figure 5 below, as well as in Figures S7 and S8 in the Supporting Information. In the beginning of all experiments the surface pressure of binary mixtures is very close to the surface pressure of the corresponding stearic acid solution (See Supporting Information Figures S7 and S8). The influence of asphaltenes on the binary mixture surface pressure values becomes noticeable only at the later stages of the measurements. In all experiments but one (0.0010 wt% asphaltene + 0.50 wt% stearic acid, and even there the deviation is insignificant and within the experimental error), collaborative effect of stearic acid and asphaltenes in the form of binary mixture was bigger than the effect coming from any of the single components (except in the very initial moment of the experiments t1000 s). Singularity is observed only at the initial stage of the experiments and for the systems where stearic acid contribution is clearly predominant. Competitiveness tends to be higher for the cases where both components are present at high concentration. This conclusion is confirmed by analysis of the cumulative effect in form of a two-dimensional map. In Figure 6 the ratio PBM/PS at t = 90 min is provided. This ratio characterizes the cumulative effect achieved by simultaneously having stearic acid and asphaltenes in the solution. As one can see, the actual surface pressure is closer to the hypothetical additive one for those cases where one of the components (stearic acid) clearly dominates or where both components provide similar contributions of moderate value. As the sum of two contributions goes up (right-top region of the map) the cumulative effect goes down. There are different possible explanations of these observations. One is that the high concentrations of the solutes leads to surface saturation. The interpretation from a monolayer stand point may not be correct at the high concentrations although we do observe an increase in the surface pressure of neat stearic acid solutions when going from 0.5 to 1 wt%, indicating that more material is adsorbed. Asphaltene skin formation was not visually observable and probably was not a major contributing factor in these experiments due to the low asphaltene concentration. In conclusion, for moderate and low stearic acid content the effect of the presence of asphaltenes is remarkable even when the molar ratio (SA/Asph) is as high as 170 e.g. for the 0.25 wt% Stearic Acid +


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0.005 wt% Asphaltenes. This indicates that the effects observed must be related to the structure of the stearic acid film which is rapidly formed when the water droplet is created. The slow diffusive asphaltenes (see below) therefore cannot compete and at the higher SA concentration examined, the SA film is apparently packed sufficiently enough that a repulsive interaction between the hydrocarbon chains and the asphaltenes may take place. In this, we emphasize that this interaction is exactly what causes asphaltenes to precipitate when an alkane is added to a crude oil. Dutta et al.22,30 also observed that coronene would start to associate and stack into crystals in the stearic acid film at the air-water interface. If using this as an analog, we may expect that asphaltenes, when located in the interfacial film with carboxylic acids present, could start to associate. Due to the very low asphaltene content investigated, it is hard to generalize our findings. One can expect that if the asphaltene content is high, this may overcome the induction period and a favorable competition between asphaltenes and carboxylic acids may be possible as the droplet is formed. This is supported by the significant change in the asphaltene induction time as the concentration is increased. This is a matter of further investigations.

Figure 5: Dynamic surface pressure for water in different binary mixture solutions of asphaltenes (Asph) and stearic acid (SA) in toluene normalized on corresponding sum of individual impacts.


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Langmuir

Figure 6: Water in different binary mixture solutions of asphaltenes (Asph) plus stearic acid (SA) in toluene. Ratio PBM/PS at t = 90 min with 90% confidence intervals.

Gibbs-Langmuir Analysis of Adsorption The reported data have been analyzed in phenomenological terms aiming at understanding the competition between stearic acid and asphaltenes which seems to be important for petroleum systems, especially for crude oil with high total acid number. As reported recently, chemical analysis of interfaces from real crude oils show that homologous series of carboxylic acids are indeed present along with asphaltenes which are not representative of the entire asphaltene fraction.20,33 In the following, a classical analysis of the data is performed to elucidate the differences in the adsorption observed by providing magnitudes of equilibrium constants and surface concentrations given as surface area/molecule. This also enables us to compare the observed systems with other systems in the literature. The dynamic development of the interfacial tension is dependent on both the affinity for the adsorption at the interface of a given species and the diffusion rate of the given species from the bulk to the subsurface from which the adsorption takes place. For multicomponent solutions, there will be a competitive adsorption determined by the individual species. Finally, in multicomponent mixtures both the interaction of species in the bulk phase and at the interface leading to molecular rearrangement can


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affect the final equilibrium IFT. This may also lead to initial adsorption of one type of molecules which later is expelled from the interface by more surface-active species.37,43 For complex mixtures where multiple interactions and mechanisms prevail we obviously need to simplify. Hence, in the following we will also assume the stearic acid-asphaltene system to behave as a binary surfactant solution and that there is no partitioning between oil and water phases. To summarize and as described above, the two solutes, asphaltenes and stearic acid, independently show some very different features. The asphaltenes have a slow progressing surface pressure development in the concentration range examined, showing an induction period followed by a steep increase and then finally an approach to equilibrium. Within the first seconds of droplet formation, the stearic acid however exhibits an initial, almost instantaneous, abrupt increase of surface pressure which is proportional to the bulk concentration. This is followed by a steady increase in surface pressure towards an equilibrium value which is not reached within the experimental 90 minutes time frame. This equilibrium value is also a function of the bulk concentration. In the present experimental approach, using the water-in-oil pendant drop, the initial bulk concentration C0 is identical to the equilibrium concentration Ceq due to the large volume ratio of oil phase to water phase. A plot of geq vs C0 should therefore approach the adsorption isotherm. The observed dynamics indicate that as the droplet is formed in the stearic acid solution, the subsurface region between bulk and the interface is being depleted immediately. This then slows down the transfer of molecules from bulk to interface as the subsurface needs to be restocked. The time dependence and the slow diffusion also indicate that the surface layer serves as a kinetic barrier. The asphaltene time dependence shows resemblance with protein adsorption from low concentration solutions for which several regions of different mechanisms are well documented. The same trend is observed with an initial induction period of slow adsorption followed by a much faster region and then finally a somewhat slower approach towards equilibrium.44,45 When examining the composite systems, it is clear the much higher stearic acid concentration dominates and the dynamic IFT development for low SA content is approximately a superposition of the two isotherms of the individual species. At the highest SA concentration, the effect of the addition of asphaltenes at any concentration investigated has a very small effect on the IFT, which is completely dominated by the fatty acid. By regression of the contributions of individual isotherms to the composition isotherms, this may reveal if the adsorption is independent and consists of a superposition of the individuals. This is similar to the analysis above, using ratios of measured and calculated surface pressures. This type of analysis reveals that, in the concentration range investigated, the contribution of


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Langmuir

the acid is close to unity (SA is not affected by presence of asphaltenes), while the asphaltene contribution is always less and in between 0 and 2/3 of the expected contribution, if no interaction was present. Hence asphaltenes are strongly to moderately affected by presence of SA. The 2/3 contribution of the asphaltenes is for the system containing 0.05 wt% SA and 0.01 wt% Asph. This also indicates that asphaltenes are more surface-active in terms of molar activity given the relative low concentration of apshaltenes compared to SA. This is manifested by the relative net increase in surface pressure relative to concentration which is significantly higher for the asphaltenes. The surface pressure versus concentration relations at different time intervals were fitted for respectively SA and Asph with a Gibbs-Langmuir adsorption isotherm according to: Π = γ% − γ = RTΓ* ln(1 + K 1 c)

(3)

When the concentration c is expressed in mol/m3, Γ* is the maximum adsorption or surface concentration in mol/m2 and KL in m3/mol is the adsorption equilibrium constant which relates to the rate of adsorption and desorption from the interface as well as the energy of adsorption. The application of this equation to dynamic data is frequent in the literature and has been proven to provide reasonable data for further understanding of interfacial phenomena despite the monolayer assumption.41,44,45,46,47 The fitting performed at different times might also be used to indicate when a quasi-equilibrium condition is reached. For the stearic acid, the maximum adsorption was found to be in the expected 10-6 mol/m2 range reported in other studies.41,46 This corresponds to approximately 1 nm2/molecule which is higher than the values reported for compressed interfaces of alkanoic acid at the air-water interface which is 0.2-0.3 nm2/molecule also known as the excluded area which equals 1/G¥,46,47 where G¥ is maximum adsorption or surface concentration at finite compression. It is generally expected that the Langmuir approach yields an area about 1/3rd larger than the real value of the excluded area. In our case, the value is much larger and it could indicate an expanded interfacial film where the expansion is a result of both, the interaction of the partially ionized head group and the swelling of the hydrocarbon chain by the solvent. KL,SA is in the range of 4 to 6 m3/mol which is also in reasonable agreement with published data on similar structured molecules.47 Both values of area and adsorption constant were observed to slowly develop over the time of the experiment and reached constant values after about 2000 seconds, despite the observation that IFT continues to change without reaching equilibrium in the time frame of the experiment (Figure 7).


Langmuir

7 (nm2/molecule) or (m3/mol)

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nm2/molecule

6

KL

5 4 3 2 1 0 0

1000

2000

3000 Time (s)

4000

5000

6000

Figure 7: Time dependence of Gibbs-Langmuir fit, development of interfacial surface area/molecule and adsorption constant of stearic acid in toluene - deionized water interfaces.

The application of Gibbs-Langmuir to asphaltenes has to be based on the assumption that all asphaltene molecules have the same relative surface activity. This is obviously a significant approximation as we may assume that there is quite a large variation in this. However, we do not currently have any possible way to quantify this surface activity distribution and hence revert to assuming uniform composition or average behavior. On the other hand, this will still emulate crude oil behavior. The fit to the asphaltene data was reasonable and allowed for a comparison at the “molecular level” considering an average molecular weight of 1000 g/mol for asphaltenes. Although this assumption has an effect on the calculations, the overall tendencies are not affected substantially. The fitting procedure was performed at three different time steps as well as the regressed equilibrium interfacial tension geq as derived below from the WardTordai approach48 (Figure 8).


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500 sec 5400 sec G-L 2000 sec EQ model

2000 sec G-L 500 sec Equlibrium W-T approach G-L 5400 sec

14 Surface pressure (mN/m)

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Langmuir

12 10 8 6 4 2 0 0

0.02

0.04 0.06 Asphaltene concentration (mol/m3)

0.08

0.1

Figure 8: Gibbs-Langmuir fit of surface pressure versus asphaltene concentration of dynamic data and the estimated equilibrium surface pressure using the Ward-Tordai (W-T) approach. EQ model is GibbsLangmuir fit to Equilibrium data (see below).

For the asphaltenes, the surface area value was 2.5 nm2/molecule at 5400 second whereas KL,Asph was 1128 m3/mol. We observed a steady increase in KL with time, starting with very low initial values around 1 in agreement with the initial induction period where the surface pressure hardly changes (Figure 9). The high KL for asphaltenes compared to the one for stearic acid indicates that when asphaltenes adsorb, they adsorb much stronger than the stearic acid or may be trapped in the subsurface layer. Contrary to the stearic acid data, the surface area per molecule of asphaltenes increases with time from about 1 to 2.5 nm2/molecule. (See Figure S9) This could indicate that there is an exchange of material where some species are expelled or it could indicate a reorientation of molecules at the interface. Probably this is due to an initially ad-hoc adsorption of material across the asphaltene range of molecules. With time there is an exchange of the molecular types, as weakly adsorbed species are replaced by the stronger adsorbed species which eventually could start to interact parallel to the interface, resulting in a gelled surface film with stronger mechanical properties as reported by Pauchard and coworkers.15,27,49 The magnitude of the surface concentration or molecular surface area is in agreement with the works by Bauget et al.50 (3 nm2/molecule) and Pradilla et al.40 (1.6 nm2/molecule) which is reasonable given the size of the molecule compared to simple molecules. The value reported by Pauchard and co-workers of 0.3 nm2/molecule is not in accord with the molecule architecture,49 and especially not in accord with the


Langmuir

claim that asphaltenes are adsorbed flat-on, as this value is very close to that of simple surfactant molecules forming compact films by packing perpendicular to the interface or simple aromatics at interfaces. Hence, this observation unfortunately throws some doubt on the analysis and conclusions regarding a molecular “aromatic core flat-on adsorption” of asphaltenes at the water-oil interface.16,3132,49

1200 1000 KL (m3/mol)

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800 600 400 200 0 0

1000

2000

3000 Time (s)

4000

5000

6000

Figure 9: Increase in adsorption constants for asphaltenes with time in dynamic interfacial adsorption at the toluene-water interface.

The ability of the Langmuir approach to predict the behavior of even complex systems could, as also pointed out by Pradilla et al.,40 indicate that the interfacial tension is dominated by the first layer of adsorbed molecules, while the further multilayer adsorption, leading to the skin formation, plays a minor role on IFT. One could observe this as though initially an apparent equilibrium droplet shape is established and then, on the outside of this, the solid film is formed with little effect on the shape. This would be in accord with the observations. Slow diffusion could be due to competing interactions between asphaltenes types in the bulk, the asphaltenes concentrating in the subsurface and finally the adsorbed layer. The fit of Gibb-Langmuir equation to the extrapolated equilibrium data from the Ward-Tordai analysis presented below, shows even more expansion of the film and very high unphysical values of KL in the vicinity of 500 000 m3/mol, which compared to other systems seems to be far too high. When fixing the molecular surface area to the same values as obtained for 5400 seconds, the regression yields a KL,Asph value of about 12 000 m3/mol. This specific result merely shows how sensitive this type of analysis is and also indicates that care should be taken in using these values in a more elaborate interpretation of the surface behavior.


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Langmuir

The much higher KL value for asphaltenes at long time intervals implies that these molecular types would dominate and should be able to alter the mixed interface with time as there is a high selectivity towards asphaltene adsorption (KL,Asph/KL,SA >>1). Hence, one would expect stearic acid to be replaced by asphaltenes with time. Also, this should, despite the much lower concentrations of asphaltenes, still lead to equilibrium conditions where the surface concentrations of asphaltenes and stearic acid should behave according to the following relation: 45678 495

=

:;,5678 =5678 :;,95

(4)

=95

However, as observed, when sufficient stearic acid is present, the asphaltenes are outperformed and do not contribute noticeably to the interfacial adsorption within the observed time frame. It should be noted that KL,Asph represents a multitude of components which may have very different individual KL values and some may even not show any marked surface affinity. Hydrogen bonding between stearic acids and asphaltenes could indeed block anchoring functionalities on the asphaltene molecules making them less prone to approach the interface when stearic acid is present in excess. From the values of the equilibrium constants assuming Langmuir adsorption the surface coverage q is estimated as:51

q=

K LC 1 + K LC

(5)

The surface coverage was found to be about 86 %, and beyond 99 % for respectively 0.05 and 1.00 wt% stearic acid solutions. At the high acid concentrations, almost complete apparent coverage was attained within 50 seconds after the formation of the water droplet and remaining changes in IFT are assumed to be due to interface rearrangement and packing. For the asphaltenes the coverage determined from relation (5) is also in the range of 90 to 98 % at 5400 seconds and dependent on the concentration. Again, these numbers are sensitive to the fitting procedure. For binary surface-active mixtures, the Gibbs relation takes the form: Π = −𝑅𝑇(Γ@A 𝑑𝑙𝑛𝐶@A + ΓAFGH 𝑑𝑙𝑛𝐶AFGH )

(6)

For a binary surfactant mixture, a common assumption is that molecules have a similar surface adsorption (Gm = GSA = GAsph) which then simplifies the analysis to: Π = 𝑅𝑇ΓI ln (1 + 𝐾@A 𝐶@A + 𝐾AFGH 𝐶AFGH )


(7)

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Pradilla et al.40 showed that equation (7) could in principle fit IFT of mixtures of asphaltenes and a surfactant. Equation (7) indicates that individual contributions to the equilibrium surface tension will be governed by the balance between the products of the bulk concentrations and the equilibrium constants. The equilibrium constants derived by the individual isotherms are respectively 4 and 1128 m3/mol for stearic acid and asphaltenes and the molar concentration range is up to 30 mol/m3 for the stearic acid and only about 0.09 mol/m3 for the asphaltenes assuming MAsph = 1000 g/mol. For the 0.50 wt% SA and 0.01 wt% Asph mixture, the magnitudes of Ki ci are respectively 60 and 100. This would mean that asphaltenes should indeed show similar contributions to the surface tension even at these very low asphaltene concentrations. However, as observed in the experiments, as soon as 0.50 wt% SA is reached, the contribution from the asphaltenes is limited within the concentration range examined. This is further surprising as the actual difference in partial molar areas as shown by Fainerman and Miller38 could affect the adsorption-desorption process assuming c1 >> c2 and similar products of Kici >> 1 as:

K4L K4M

= −

NM

(8)

NL

Where wi is the partial molar area of component i. As seen from Gibbs-Langmuir analysis the molar areas of stearic acid (component 1) and asphaltenes (component 2) are in the range of respectively 0.3 (assuming excluded area in compressed films) and about 2.5 nm2/molecule. Hence, a small change in the adsorption of asphaltenes could lead to a 10-fold larger desorption of stearic acid. Using the values observed from the Langmuir analysis of the experiments presented above, the ratio in equation (8) is 1.5 to 2.5 which means this will have little effect and the assumptions taken to derive equation (8) should be approximately valid. In that case, the interfacial adsorption should be governed by the products Kici and be relatively proportional to the individual concentrations. This obviously fails for the analysis of systems with high concentrations of stearic acid pointing at another overruling mechanism. Further a pairwise analysis of isotherms for one of the components, while keeping the other fixed, indicates that the KL,

Asph

drops almost 2 orders of magnitude, even at the lowest stearic acid

concentration, and obviously approaches zero at 0.50 wt% stearic acid, where the asphaltenes have little impact. On the other hand, KL,SA only changes within the experimental error of the data regressed. This could indeed indicate that there could be a competing mechanism in the bulk phase, as one normally


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Langmuir

would expect for binary surfactant mixtures, as it is expected that the most surface-active component, expressed by the high K value, dominates over time, even when present in modest concentrations.50 The bulk phase reaction could, as mentioned, be through hydrogen bonding between the carboxylic acid group and the surface-active functional groups on the asphaltene molecule. This is in accord with the findings of Seifert, who reported that phenols would diminish the surface activity of petroleum carboxylic acids.17 Merino-Garcia et al.52 measured strong interactions between nonylphenol and asphaltenes by titration calorimetry, which easily could be envisioned to also happen in carboxylic acid-asphaltene solutions. Table 1. Rosen and Hua analysis of bulk and surface composition molar fractions of asphaltenes out of “total surface-active species”: Casph/(Casph+CSA). MWasph = 1000 g/mol. wt% Stearic molar Acid Solution wt% 0.05 1.51 0.25 7.54 0.50 15.07

Asphaltenes Solution 0.005 0.0430

0.001 0.008 6

0.010 0.0860

*Bulk Mole Fraction Active Components 0.006 0.028 0.054 0.001 0.006 0.011 0.001 0.003 0.006 *Monolayer Mole Fraction Active Components 0.05 1.51 0.300 0.488 0.515 0.25 7.54 0.145 0.276 0.375 0.5 15.07 0.125 0.21 0.264 *Asphaltene molar fraction in bulk or monolayer

Based on the approach of Hua and Rosen, the surface film composition was estimated at pseudoequilibrium conditions.53 This approach requires the determination of the concentration (Ci0) of the individual solutes in the binary that yields the same interfacial tension as the mixture of interest. To estimate this, the Gibbs relation was applied and linear correlations between ln Ci and g (at pseudo equilibrium) were established for solutions of either SA or Asphaltenes. This was used to establish (Ci0) for both SA and Asphaltenes at the interfacial tension of each of the mixtures. Rosen devised the following relation:

( X 1 ) 2 ln(C1 / C10 X 1 ) =1 (1 - X 1 ) ln C 2 /(C 20 (1 - X 1)

[

]

(9)

Where X1 is the molfraction of species 1 in the binary monolayer and Ci and Ci0 are respectively the molar concentration of the bulk solution and the established concentration at which gmix = gi. The molecular weight of asphaltenes was assumed to be 1000 g/mol. After establishing the Gibbs correlations and establishing Ci0 for all mixtures one can solve equation 9 iteratively for X1.


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∆P

As the contribution from ∆Q is much higher for asphaltenes than for stearic acid (Figure S10), one would assume asphaltenes to dominate. Using this approach, we observe that there is a significantly higher surface molar fraction of asphaltenes compared to bulk (Table 1). However, as the stearic acid concentration increases, the contribution from asphaltenes decreases significantly. The method on the other hand appears not to entirely reflect the direct experimental observation, that at very high SA concentrations the asphaltenes provide a marginal contribution to the surface pressure. This means SA could entirely exclude asphaltenes from the interface. Estimation of the surface interaction parameter defined by Rosen and Hua was not unambiguous and for asphaltenes it seemed to go from a synergistic interaction to an antagonistic interaction as the SA concentration increased. Given that we do not have an exact estimate of the concentration of surface-active asphaltenes, this may affect the conclusions drawn. The detailed analysis is given in the Supporting Information in connection with Figure S10. The above analysis indicates that using a general approach, such as Langmuir, should be treated with caution for mixed systems despite that the model may show apparent acceptable fit to experimental data. The effects observed in the pseudo-binary adsorption experiments indicate that the analysis of heptane asphaltenes, as a pseudo-component, is not adequate and we may speculate that this is because only a fraction of the asphaltenes adsorbs in competition with stearic acid. This is in agreement with findings of Yang et al.51 That would make sense as it would mean that KAsphcAsph could be much smaller than KSAcSA if not compensated by an equivalent increase in equilibrium constants. This could explain why stearic acid would dominate at concentration at or above 0.5 wt% as also observed. It cannot be excluded that there could, as indicated above, be a competing bulk phase reaction which renders the asphaltenes less surfaceactive.

Diffusion There are two effects in dynamic interfacial tension measurements of complex molecules that need to be stressed as part of the further analysis: 1) that equilibrium rarely is reached within reasonable time frames and 2) that the equilibrium interfacial tension is a function of the bulk equilibrium concentration which in the present experimental set-up is equal to the initial bulk concentration. Further the molecular state of the species undergoing diffusion and adsorption will affect the rate as well. This can be the diffusion of associated molecules (dimers of the carboxylic acids or nano-aggregates of asphaltenes) and the dissociation of these in the subsurface before adsorption. Association close to the


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Langmuir

interface could also affect the behavior – and especially a slow association leading to the well-known asphaltene skin formation at the oil-water interface. Dynamic interfacial tension has been modelled in various ways, either at the initial development (short term) or the long-term development, reaching the equilibrium interfacial tension. The analysis is based on regression of equations and data, and interpretation of the obtained data. This may reveal the controlling mechanisms behind the adsorption.47 The analysis of the diffusivity D is important in the understanding of the process. If D is found to be much smaller than the values estimated or measured for bulk phase diffusion, this indicates that adsorption barriers exist additional to the diffusion. D can be approximated, as shown by Wilke and Chang, from the molecular volume V (cc/mol) of the diffusing molecule,54 the kinematic viscosity h (m2/s) of the solvent, the solvent molecular weight M (g/mol) and the temperature T (K) as:

𝐷 =

ST√V WX Y.[

(10)

b is a constant which with the given units is 7.4x10-12 with the diffusion coefficient D in m2/s. For unrestricted diffusion, we would assume the value to be approximately 5x10-10 and 1.1x10-9 m2/s for respectively asphaltenes and stearic acid in toluene. Dimerization of the stearic acid affecting only the apparent molecular weight will lead to a reduction in D to 7x10-10 m2/s. The common guideline for this analysis is to compare deviations from typical bulk phase diffusion coefficients which are in the range of 5x10-10 m2/s. The analysis, however, requires some definition of “short” and “long” term in the analysis. In the present case, short term will be within the first 100 seconds, given the pendant drop methodology used, while long term will be beyond 3000 seconds. These limits stem simply by inspection of the data and how the data conforms to the equations selected. For kinetically or diffusion limited/controlled adsorption this is related to the diffusion of compounds from the bulk to the proximity of the interface (subsurface) followed by the transfer and “attachment” to the interface. Based on the Ward and Tordai approach, the diffusion coefficient (D) for the initial (short term) adsorption can be estimated from:48

P = 2 RTC

Dt

(11)

p


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Where t is the time, R is the gas constant, T is the absolute temperature, C is the bulk concentration. Accordingly, D is obtained from the slope of a plot of surface pressure P2 vs t. This can be then compared with known or estimated bulk phase diffusion. Also, one may compare the various bulk concentrations by plotting P/C vs

t . Examples of the analysis is given in the Supporting Information Figures S11 and

S12 which also gives the extrapolated initial IFT for stearic acid solutions. As observed, the two solutes examined show very different initial adsorption behavior. Stearic acid diffuses to the interface within the time of drop development, leading to an apparent instantaneous increase in surface pressure which is dependent on bulk concentration. If we, assuming that droplet formation is instantaneous, use the first reported IFT at 8 ms, the initial value diffusion coefficients derived for the lower concentrations are in the range between 10-10 and 10-9 m2/s, indicating diffusion is dominant. However, from that point and onwards the stearic acid diffusion coefficient, as derived from the surface pressure time relation, decreases almost by 4 orders of magnitude, indicating a barrier control (see below). Asphaltenes however obviously seems to be have a more complex control mechanism. Estimations according to the Tordai-Ward equation (Eq. 10) indicate that the initial diffusion coefficients of asphaltenes, taken at the time frame between 10 and 50 seconds, are in the range of 1x10-13 to 8x10-13 m2/s. This is about 1000 times lower than diffusion coefficients of many compounds with similar molecular features in organic solution.47 The effect of the assumed molecular weight of asphaltenes on D is relatively small between MWs of 500 and 10000 g/mol. See details in Figure S13 The adsorption behavior of asphaltenes again is seen to be very similar to other natural macromolecules such as proteins. Part of this can be ascribed to the “unfolding” of asphaltenes as the change in interactions go from asphaltene-asphaltene to asphaltene-water, as the water-toluene interface is formed and appears. As seen reported in the Supporting Information in Figure S14, the D value is slightly dependent on concentration and appears to make an abrupt change between 0.001 and 0.0025 wt%. It is not clear at this point if the change in diffusion coefficient with concentration is due to a change in conformation or aggregation state. Although it is tempting to ascribe this to a change in nano-aggregation state, the data is insufficient to support such a conclusion. The long-term diffusion controlled adsorption when equilibrium conditions are reached is expressed by Ward and Tordai as:


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𝛾 − 𝛾]^ = −

_T4` M =

b

acde = 𝐴𝑡 hi/k

(12)

Where Gm is the equilibrium surface area (as in Equation 10), 𝛾]^ is the equilibrium IFT and D is the diffusion coefficient. This relation can be re-written as 𝛾(𝑡) = 𝛾]^ + 𝐴𝑡 hi/k

(13)

which allows the extrapolation of data to equilibrium, if not reached (which is the case for all the systems considered), and provides a simple analysis of the adsorption process. This analysis was performed for all data as indicated in Figure 10. Table 2 reports both the estimated equilibrium interfacial tension and the parameter A as well as the final recorded IFT at 5400 seconds. As seen, the data fall in a very narrow range with the boundaries being the stearic acid results at low and high level. An analysis of the least square fit residuals (Yexp-Ycalc) shows a non-random deviation which indicates a systematic but small deviation between calculated and experimental data, and therefore the application is only an approximation. Notice the significant difference between the equilibrium data and the final measured value of IFT. In theory, the change in A with concentration for the solutions of SA or Asphaltenes should develop linearly with 1/c if Gm and D were constants. For both systems, a plot of A*c vs c shows a linear dependence for SA while a slight downwards curvature is observed for asphaltenes as the concentration increase (Figure 11). The magnitudes of the slopes of linear regressions are 310 and 243 for SA and Asph, respectively (assuming M Asph =1000 g/mol). This indicates that the term 𝛤Ik /√𝐷 develops in a similar fashion for the two very different molecules. However, this indicates that the mechanism behind the process is not diffusion controlled and, as mentioned, D values estimated from the data are orders of magnitude smaller than expected and heavily concentration dependent. For the asphaltenes, an increase in the subsurface viscosity, if the subsurface concentration increases beyond C0, could be one reason for this barrier. Yet another could be a local increased molecular association and skin formation.


Langmuir

0.001 Asph/0.05 SA 0.005 Asph/0.25 SA 0.001 Asph/0.5 SA SA 0.05

5

0.005 Asph/0.05 SA 0.001 Asph/0.25 SA 0.005 Asph/0.5 SA SA 0.50

0.01 Asph/0.05 SA 0.01 Asph/0.25 SA 0.01 Asph/0.50 SA

4.5

gt-ge (mN/m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

3.5 3 2.5

0.013

0.014

0.015

0.016

1/SQRT(t)

0.017

0.018

(1/s0.5)

Figure 10: Ward-Tordai analysis of all mixture data. Bordered by low (0.05 wt%) and high (0.50 wt%) stearic acid relations. Series legend is concentration of ASPH/SA in wt%.

Table 2: Results of fitting the Ward-Tordai equation for dynamic interfacial tension beyond 3000 seconds. Stearic Acid wt% Asph wt%

g5400s

mN/m 0.000 0.001 0.005 0.010

35.5 31.8 28.7 27.8

0.00 A

geq

g5400s

mN/m s0.5 mN/m mN/m 41 279 263 231

35.0 27.9 25.2 24.6

29.7 28.5 26.5 24.3

0.05 A

geq

g5400s

0.25 A

geq

g5400s

mN/m s0.5 mN/m mN/m mN/m s0.5 mN/m mN/m 166 234 255 254

27.5 25.3 22.9 20.9

26.0 25.1 24.4 22.9


241 243 256 251

22.7 21.8 20.9 19.5

23.3 23.4 23.0 22.3

0.50 A mN/m s0.5 316 261 269 271

geq

mN/m 18.9 19.9 19.3 18.9

10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0

25

y = 311 x

A*c (mN s0.5 mol/m4)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

A*c (mN s0.5 mol/m4)

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20 15 y = 244 x

10 5 0

0

10 20 30 40 Stearic acid concentration (mol/m3)

0

0.05 0.1 Asphaltene concentration (mol/m3)

Figure 11: The development of the slope of 𝛾(𝑡) = 𝛾]^ + 𝐴𝑡 hi/k as a function of concentration for (A) stearic acid and (B) asphaltenes.

The long term diffusion analysis at times beyond 3000 seconds (Figure S15) reveals the diffusion coefficient of the asphaltenes in toluene to be in the range of 0.5 to 3.5 * 10-14, and it is also a function of concentration. The longer term D is therefore seen to be orders of magnitude lower that the short-term diffusivity values and diminish substantially with concentration. Bauget et al.50 also reported very low diffusion coefficients for asphaltenes in the range of 10-17 m2/s, which was interpreted as a failure of the application of the analysis. This change must be due to a significant barrier towards adsorption, making simple diffusion too simple to account for the formation of the interfacial film. However, it is still in line with the very slow process observed where equilibrium is not reached within hours. There has been a tendency to interpret abrupt changes in properties of asphaltene solutions as an indication of the existence of some critical concentration behavior related to association. However, in the present case we cannot rule out that the observation between 0.001 and 0.0025 wt% simply indicates that the fundamental assumptions of the applied model are not valid for the system examined. It may also indicate that the adsorption of asphaltenes is irreversible and hence a physical barrier is already formed at these very low concentrations. In other words, the interfacial measurement is not related to a bulk phase phenomenon but to subsurface or film phenomena. However, for polymeric surfactant systems, significant decreases in D are observed beyond aggregation related changes, such as the critical micelle concentration.54 Mostly adsorption takes place under restricted or barrier conditions and, as indicated from the above analysis of the diffusion controlled approximation, the processes analyzed herein happens under barrier


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restriction. That means the rate of adsorption between subsurface layer and the surface is much slower than the rate of diffusion between bulk and subsurface. The energy barrier or transfer limited adsorption can as well be attributed to changes at the surface such as re-orientation or changes in the association and interaction amongst solutes. This type of analysis is often expressed by an exponential decay function derived from the various adsorption mechanisms. Below a few of these are given:39,55 𝛾 = 𝛾]^ + (𝛾% − 𝛾]^ )𝑒 he/n

(14)

𝛾 = 𝛾]^ + 𝛾% 𝑒 hoe/n

(15)

𝛾 = 𝑎𝑒 he/nL + (𝛾% − 𝑎) 𝑒 he/nM

(16)

Where values of t are related to the adsorption and diffusion mechanism describing the process. Regression of these expressions to the asphaltene data only provided meaningful results for Eq. 14 and Eq. 16 which by the magnitudes of t1 and t2 gave results very close to the experimental data. Eq. 15 failed to fit the data in a meaningful way including instances of failure to converge. Figure 12 shows this for the 0.01 wt% solution of asphaltenes in toluene. The characteristic time constant (t) in Eq. 14 (1031 1/s) was approximately 3-10 times higher than as those reported by Yu et al.56 who analyzed the asphaltene concentration range from approximately 0.0005 to 10 %wt for 6 different asphaltenes. They also reported large differences between the different asphaltenes. As reported by Yu et al. t decrease with increasing concentration approaching a constant value. Despite the small number of concentrations investigated the same was observed. For the stearic acid systems, the analysis could not be performed due to the very large and abrupt jump in interfacial tension within the first few milli-seconds.


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39

Interfacial tension (mN/m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

37

Experimental Equation 14

35

Equation 15 Equation 16

33 31 29 27 25 0

1000

2000

3000

time (s)

4000

5000

6000

Figure 12: Fitting of exponential expressions of dynamic interfacial tension (Equations 14, 15 and 16) to data from 0.01 wt % asphaltenes in toluene.

CONCLUSIONS IFT dynamics was analyzed for water drops formed in solutions of stearic acid, asphaltenes and binary mixtures of stearic acid and asphaltenes in toluene. The acidity obtained by varying the stearic acid content covers TAN from 0.1 to 2 mg KOH/g oil. The asphaltene content was below 0.01 wt% in order to secure optical transparency of the outer (oil) phase. The dynamic IFT is not reaching equilibrium for any of the experiment observed. For stearic acid containing systems, the IFT develops initially ballistic within the time of droplet formation. This leads to an initial constant IFT value. Potentially due to initial depletion of the subsurface region, this is followed by an induction period in which the subsurface establishes a new diffusion equilibrium with the bulk. After this, there is a slow development towards an equilibrium, which, in part, could be described by the WardTordai approach. The asphaltenes in acid free solution, on the other hand, do not show any initial adsorption, and the induction period is very long and concentration dependent. Analysis of the individual impacts on total surface pressure from individual surface-active components demonstrates that in the beginning of all the experiments stearic acid contribution is predominant. This suggests that in the binary mixture, small and mobile molecules of stearic acid reach the interface much faster than the large and slow asphaltenes.


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The presence of stearic acids, especially at high concentration, out-performs the asphaltenes. However, at low acid concentration, asphaltenes (even at these very low asphaltene concentrations) have a significant contribution to the interfacial tension, although it appears to be suppressed by the competition with the acid, when the acid is present in large concentrations. The Langmuir-Gibbs analysis of the concentration dependence indicates that the apparent adsorption equilibrium constant KL for asphaltenes is much higher than that of stearic acid. In such a case, where the product of KL and the concentration of two different surface-active species are comparable, but the concentration of the least active component is much higher, one would expect that with time this component could be replaced by the other, leading to additive equilibrium conditions. Even though the Langmuir-Gibbs analysis seems to apply for the individual components, the stearic acid-asphaltene system was not observed to obey this approach, especially at high stearic acid concentrations. Therefore, it seems that there is a significant competition at the interface which cannot be described by a simple monolayer description. This appears as an apparent saturation of the interface at high stearic acid content, even though the pure stearic acid IFT is still decreasing between 0.50 and 1.00 wt%. However, as indicated, isotherms of 0.01 wt% asphaltenes with either 0.25 or 0.50 wt% stearic acids are almost identical beyond 600 seconds. In all cases, the combined effect of stearic acid and asphaltenes in form of binary mixture was smaller than the sum of corresponding individual impacts. Hence, it is possible to conclude, that there is a competition between asphaltene and stearic acid molecules for the adsorption sites at the interface. The mixture surface pressure is closer to the hypothetical additive one, for those cases where one of the components dominates or where both components provide similar contributions of moderate value. On the other hand, competitiveness becomes higher (PBM/PS ratio goes down) for the cases where both components are present at high concentration and where we observe that stearic acid, despite a much lower adsorption equilibrium constant, is the determining factor. This also can be considered as a sign of interface saturation, or in other words, finite size of the interface. One explanation of this observation is that stearic acid, at high concentrations, will form well organized packed interfacial structures, with the hydrocarbon chain extended into the oily media. This alkane-like brush will repel the asphaltenes and may also lead to association of asphaltenes close to the interface when these enter the interfacial region.


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The analysis of the diffusivity clearly indicates that stearic acid has a very fast diffusion to the interface during droplet formation which leads to a very high initial coverage. Then a slow diffusion takes over probably caused by the depletion of the subsurface and diffusion limitations. The interfacial adsorption of asphaltenes is found to be initially barrier limited, probably due to the low hydrophilicity of the asphaltenes compared to other molecules, confirming other reports in the literature. Despite the much larger apparent surface activity of the asphaltenes, giving adsorption equilibrium constants about 2 orders of magnitude higher than that of stearic acid, the latter suppresses the adsorption substantially. The commonly observed effects of desorption of the compound with low surface activity by a compound of high activity, even when the latter is present in low quantities, is not observed for the stearic acid – asphaltene solutions. We examined different approaches of regression of both, diffusion and barrier controlled exponential relations, to obtain estimations of equilibrium data. It was found that there is significant dependence of results upon the approach taken. This especially emphasizes the multicomponent nature of asphaltene solutions which, therefore, may not warrant the application of the pseudo-single component approach to these systems when one wants to derive meaningful properties describing the surface behavior. The above described phenomena are surprising as it was expected that asphaltenes would not be almost completely eradicated at the interface. This may play an important role in highly acidic crude oils with modest asphaltene contents. The extension to higher asphaltene concentrations is required in order to generalize our findings.


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ASSOCIATED CONTENT Supporting Information is available free of charge.

ACKNOWLEDGEMENT The authors would like to thank Saudi Aramco and Schlumberger for the permission to publish this work.

AUTHOR INFORMATION Corresponding Authors * Email: [email protected] (W.A.) * Email: [email protected] (S.A.) ORCID Simon Ivar Andersen: 0000-0002-5943-8088 Wael Abdallah: 0000-0001-7788-6805 Author Contribution B.S. and M.S. contributed equally to the execution of the experimental work and all authors contributed equally to the writing and data analysis. Notes The authors declare no competing financial interest.


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GRAPHICAL ABSTRACT


Dynamic Asphaltene-Stearic Acid Competition at the OilâWater Interface

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Dynamic Asphaltene-Stearic Acid Competition at the OilâWater Interface