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Long term adsorption kinetics of asphaltenes at the oilwater interface: a random sequential adsorption perspective. Vincent O. Pauchard, Jayant P Rane, Sharli Zarkar, Alexander Couzis, and Sanjoy Banerjee Langmuir, Just Accepted Manuscript • Publication Date (Web): 19 Jun 2014 Downloaded from http://pubs.acs.org on June 19, 2014
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Long term adsorption kinetics of asphaltenes at the oil-water interface: a random sequential adsorption perspective. Vincent Pauchard3,4, Jayant P. Rane1,2,4, Sharli Zarkar1,2,4, Alexander Couzis2 and Sanjoy Banerjee1,2,4 1 Energy 2
Institute, City College of New York, New York, NY, 10031, USA Department of Chemical Engineering, City College of New York, New York, NY, 10031, USA
3 Flow
Technology group, Department of Process Technology, SINTEF Materials and Chemistry, Trondheim, Norway the Multiphase Flow Assurance Innovation Center, Norway.
4FACE,
KEYWORDS: Asphaltenes, interfacial rheology, elastic modulus, equation of state, IFT, interfacial coverage, Langmuir trough, jamming, hysteresis. ABSTRACT: Previous studies
1, 2
, indicated that asphaltenes adsorbed as monomers on oil-water interfaces and the early stage kinetics of the process was controlled by diffusion and hence dependent on oil viscosity. By measuring interfacial tension (IFT) as a function of surface coverage during droplet expansions in pendant drop experiments, it was also concluded that the IFT data could be interpreted with a Langmuir Equation of State (EoS), which was independent of oil viscosity, time of adsorption and bulk asphaltenes concentration. The surface excess coverage was calculated to be ~0.3 nm2/molecule which suggested adsorption in face-on configuration of asphaltenes monomers at the interface and average PAH core per molecule of about 6 for the asphaltenes investigated, consistent with the Yen-Mullins model3, 4. The current study focuses on the kinetics of asphaltenes adsorption at longer times and higher interfacial coverage. Long term IFT data have been measured by the pendant drop method for different asphaltenes concentrations and for different bulk viscosities of the oil phase (0.5- 28cP). The data indicate that when coverage reaches 35-40%, the adsorption rates slow down considerably compared to the diffusion controlled rates at the very early stages. The surface pressure increase rate (or IFT decrease rate) at these higher coverages is now independent of oil viscosity but dependent upon both surface pressure itself and asphaltene monomer concentration. The long term asymptotic behavior of surface coverage is found to be consistent with the predictions from surface diffusion mediated Random Sequential Adsorption (RSA) theory which indicates a linear dependency of surface coverage on 1/√t and an asymptotic limit very close to 2D random close packing of polydispersed disks (85%). From these observations RSA theory parameters were extracted that enabled description of adsorption kinetics for the range of conditions above surface coverage of 35%. 1. Introduction and Background: Asphaltenes are indigenous species in crude oils (particularly heavy crude oils) and tar sands. They adsorb at the water-oil interface and stabilize water in oil emulsions. Separation of such emulsions during oil recovery is expensive, and hence considerable research goes into understanding the coalescence and separation behavior of asphaltene-stabilized emulsions. In the literature, there are several studies that qualitatively relate emulsion stability to the slow formation of asphaltene-rich rigid skins on water droplets5-7. However, hypotheses of this nature are not supported by the observation that such emulsions can be stabilized by asphaltenes very rapidly, suggesting that such phenomena are still poorly understood. To clarify the mechanisms involved in asphaltenes adsorption and the effect of the adsorbed layers on emulsion stabilization, we conducted several studies. In the first1,
dynamic interfacial tension (IFT) at oil-water interfaces was measured for different concentrations of asphaltenes in the oil and for different oil viscosities. Nexbase (aliphatic) oils were used as the viscosities could be readily varied. It was found that upon rescaling time by viscosity, the initial dynamic interfacial tension data could be superimposed to form a single curve up to surface pressures of ~57 mN/m. This suggested initial diffusion control, which was supported by the initial proportionality of IFT decay to the square root of time. For larger surface pressures (i.e. at longer times) use of time rescaled by viscosity did not work, suggesting that different mechanisms control asphaltenes adsorption. In more detail, the mechanisms that control adsorption in the long term appeared to be slower than diffusion: in rescaled time units, the deviation from diffusion control was earlier and stronger for low viscosity than for high viscosity (at the same asphaltenes concentration). This could be interpreted qualitatively as indication of a sterically hindered adsorption process rather than a re-conformation or a cross-linking at the interface. This
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interpretation was supported by droplet expansion experiments conducted after variable adsorption times with variations in adsorption conditions (viscosity and concentration). All tests collapsed on to a single master curve relating interfacial tension to relative coverage. In other words a unique surface pressure isotherm was found, irrespective of adsorption conditions, which appeared to rule out interfacial re-conformation/cross-linking. Those experiments also provided some insight about the nature of the asphaltenes adsorbing at the water-oil interface. The slope of initial interfacial tension decay versus square root of time was found to evolve similarly to asphaltene monomer concentration as determined by Nuclear Magnetic Resonance: i.e., it increased almost linearly with nominal concentration up to 80 ppm and leveled off from 80 ppm onward. The values of the slopes were also compared to the prediction of the short time approximation of diffusion controlled adsorption (given in equation 1 below). The values were found to be consistent with those for adsorption of monomers but not with those for the adsorption of nano-aggregates, which would indicate lower diffusivities. The validity of the conclusion that adsorption was primarily of asphaltene monomers was confirmed in a second study2. It was shown that the surface pressure isotherm obtained from droplet expansion experiments could be interpreted by a Langmuir Equation of State (EoS). This Langmuir EoS was found to predict the unique relationship observed between surface pressure and instantaneous (high frequency) dilatational elasticity, irrespective of adsorption conditions. Furthermore the value of the only fitting parameter in the EoS (which was surface excess coverage) corresponded to a molecular area of ~0.3 nm2. Such a value is too small for nano-aggregates8 but could correspond to the flat on (i.e. with polyaromatic cores of the asphaltene monomers parallel to water surface) adsorption of a poly-aromatic cores of an average size of 7 rings. This is consistent with both the average size of asphaltenes core (6 to 8 rings) 3, 4 and their conformation at the interface with aromatic cores and alkyl chains parallel and perpendicular to the water surface, respectively 8. Work still to be published also indicates that the Langmuir EoS holds for petroleum asphaltenes from different origins in different solvents, and with similar molecular areas ~7 rings for the adsorbate. However for coal and model asphaltenes with different monomer core molecular areas, the excess surface coverage from the Langmuir EoS always corresponds to the actual size of the polyaromatic cores in each case This insight about adsorption of asphaltenes (i.e. that the monomers adsorb with their polyaromatic cores lying flat on the interface) at the water oil interface could help towards elucidating the mechanism by which they stabilize water in oil emulsions. For example, there are consistent indications9, 10 that asphaltenes which accumulate at the interface during consecutive coalescence events block further coalescence once surface coverage reaches a critical value of around 3.5 mg/m2 irrespective of solvent nature and initial concentration. Using a reasonable value for the average monomer molecular weight of 750 g/mol, the
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critical mass coverage yields around ~3 molecules/nm2 or ~0.3nm2/molecule. Such values of molecular area are similar to the values estimated from droplet expansion experiments described by the Langmuir EoS. This suggests that asphaltenes block water droplet coalescence when surface coverage approaches the maximum interfacial packing (as do particles, surfactants or proteins11-14). As discussed in 9, 10 such behavior is also consistent with the hole nucleation theory from Derjaguin15-17 which hypothesizes that coalescence rate is controlled by the nucleation rate of surfactant/particle free contact points between droplets or bubbles. Close to maximum packing both the remaining free area and interfacial mobility are expected to decline sharply thus sharply reducing the hole nucleation rate. Interestingly this theory has also been successfully applied to prediction of the dependence of thin film lifetimes with regard to asphaltenes concentration18. The objective of the current work is therefore to measure long term asphaltenes adsorption kinetics and elucidate the controlling mechanisms, particularly for the asymptotic kinetics and surface coverage at long times. Such experimental data would allow the various ideas discussed above to be checked. As an aside, the hole nucleation theory for coalescence kinetics is similar to the theory of Random Sequential Adsorption (RSA) mediated by surface diffusion19-22. RSA theory (described in more detail in section 3) accounts for the fact that interfacial free area is divided into domains that can be smaller than adsorbate molecular area, leading to a rapid increase of steric hindrance to adsorption. If adsorbate can diffuse on the interface, steric hindrance is however mediated by the random nucleation of adsorption sites and adsorption can proceed until the interface jams close to maximum packing. To better understand this process, the dynamic interfacial tension measurements from our previous work1 will be reanalyzed with the help of the EoS from 2 to extract the time evolution of surface coverage. These data will then be compared to the theoretical predictions of diffusion control models at short times, and RSA models at long times. In the following discussion of experimental results, the focus in the analysis of interfacial tension in terms of the EoS is on the first molecular monolayer. This is not meant to exclude the possibility of subsequent multilayer formation or topping of the first molecular layer by nanoaggregates. In this regard, it should also be noted that the alkyl chains at nano-aggregate peripheries would be chemically more compatible interacting with a monolayer presenting alkyl chains protruding towards the oil phase than with bare water. 2. Materials and Methods The experimental procedures are similar to those used in our previous work and can be found in 1. Materials and methods used are summarized below. 2.1. Chemicals
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The aqueous phase contains de-ionized water mixed with 43 g/l of NaCl, 7 g/l of CaCl2. The final pH is adjusted to 7 with 0.1M NaOH. The asphaltenes have been extracted by n-heptane precipitation from a Norwegian crude oil. A stock solution of 1000 ppm asphaltenes in toluene is further diluted with toluene before mixing with an aliphatic medium.to reach the desired nominal concentration (from 10 ppm to 500 ppm) while keeping the toluene content at 15%. For most tests synthetic poly-alpha olefins of variable viscosity (Nexbase® oil 2000 series from Neste oil, Finland) are used. Additional experiments are performed with heptane to decrease further bulk viscosity. The viscosity of the different mixtures studied here is reported in Table 1. For Nexbase mixtures, viscosity has been measured on a TA instruments AR 2000 rheometer. For heptane mixture, a simple mixture law yielded a viscosity of 0.5 cP.
2.2. Interfacial tension measurements Dynamic interfacial tension is measured using the pendant drop technique (Theta Tensiometer, Biolin Scientific, Finland). An inverted 16-gauge needle is submerged in the aqueous phase such that the tip is visible in the frame of capture. A gas tight syringe [1 ml] (Hamilton Company, USA) is mounted in a micro-syringe pump (Harvard Apparatus, USA) to ensure the instantaneous creation of an oil droplet of a preset volume. Before the droplet is formed, the image capture software is triggered collecting images at 2 frames per second for the first 10 minutes and 1 frame per minute thereafter up to 30,000 seconds. Edge detection is used to identify the droplet shape, with the interfacial tension determined using the Young-Laplace equation 23. Experiments are generally repeated 3 times and only those experiments for which droplet volume remains constant are considered. Table 1: Viscosities of different Nexbase® 2000 series oils with 15% of toluene Oil
Viscosity (Pa.s)
85% heptane +15% toluene
0.0005
85% Nexbase 2002 +15% toluene
0.0065
85% Nexbase 2004 +15% toluene
0.0163
85% Nexbase 2006 +15% toluene
0.0201
85% Nexbase 2008 +15% toluene
0.0280
droplet immersed in oil during IFT measurements would be appropriate. Unfortunately the opacity of asphaltenes solutions prevents the use of a water droplet beyond 10 ppm asphaltenes in oil. However, the dimensions of the pendant droplet are much larger than those for asphaltene monomers (or even nano-aggregates). Therefore, curvature effects on asphaltene interfacial configuration, the EoS and maximum packing fraction, which may be brought about because the curvature of oil drops in water is reversed compared to water drops in oil, are expected to be small.. On the other hand, curvature might impact diffusion kinetics (equation 2). As indicated in Figure 4 and Figure 5, these effects manifest themselves only at low concentration and during late stages of diffusion. Given the reported 1 transition to a steric hindrance regime , dynamic interfacial tension should be fairly similar with a water droplet immersed in oil and an oil droplet immersed in water. This has been tested at 10ppm asphaltenes in the 6.5 cP oil (which is transparent, gives maximum curvature effect and 1 for the long-time diffusion controlled regime ). Figure 1 shows that the differences between oil and water droplet configurations are small. To further prove this point the long term data analyzed later in terms of Random Sequential Adsorption correspond to a water droplet in oil for 10 ppm in 6.5 cP oil and to an oil droplet in water for all other concentrations. That little difference arises from these different configurations can be seen in 4
Bulk Viscosity= 0.5 cP 20 ppm 50 ppm Bulk Viscosity= 6.5 cP 10 ppm 20 ppm 40 ppm 100 ppm 200 ppm 500 ppm Bulk Viscosity= 16.5 cP 100 ppm Bulk Viscosity= 20 cP 100 ppm Bulk Viscosity= 28 cP 100 ppm
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above 20 mN/m but never completely vanishes. According to the EoS from previous expansion experiments, a surface pressure of 20 mN/m corresponds to a relative surface coverage of 80%. This first estimate is consistent with surface diffusion mediated RSA in that close to the maximum packing limit, steric hindrance becomes very high and adsorption slows down considerably. It is also noteworthy that such high surface coverage values are reached at all bulk asphaltenes concentrations if the adsorption time is sufficiently long. This observation is consistent with the definition of asphaltenes as a solubility class (soluble in toluene and insoluble in n-alkanes) and with the nature of the aliphatic carrier oil, i.e, the asphaltenes molecules are essentially ‘insoluble’ and the adsorption process can be expected to be largely irreversible. Such conclusionshad previously been drawn from droplet size measurements9, 10.
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Surface pressure (π) (mN/m)
Figure 6 and Figure 8.
Figure 2: Dynamic surface pressure (deduced from IFT) curves for different concentrations of asphaltenes and different viscosities of the droplet oil phase. Figure 1: comparison of oil droplet in water (empty symbols) and water droplet in oil (full symbols) interfacial tension measurements with 10 ppm asphaltenes in 6.5 cP oil. The arrow indicates the transition from early diffusion controlled regime to steric hindrance controlled regime as 1 detected by viscosity rescaling . Dashed and full lines are predictions from coupled equations 2 and 3 for oil droplet in water and water droplet in oil respectively (see procedure for choice of parameters in section 3 below).
3. Results and Discussion Representative dynamic surface pressure curves for asphaltenes adsorption on constant volume pendant drops are shown in Figure 2. In all cases, interfacial tension (surface pressure) never reaches an equilibrium value. The rate of change slows considerably for a surface pressure
In 1, the classical short time approximation of surface pressure evolution given below was shown to capture the initial adsorption kinetics:
πt = γ − γt = 2kTC
Eq.1
Here π(t) is surface pressure at time t, γ0 is clean surface interfacial tension (at time 0 or between pure fluids), γ(t) is interfacial tension between water and asphaltenes solution at time t, k is Boltzmann constant, T is absolute temperature, C is bulk adsorbate concentration, Π is the number pi (3.14) and D is adsorbate diffusion coefficient. In case the adsorbing species can be present in various physical states in bulk solution (e.g., monomer, aggregates or micelles), Equation 1 can be used as a first approximation to extract adsorbate concentration C by assuming a
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value for adsorbate diffusion coefficient D. It was demon1 strated in that assuming monomer diffusion (with diffusion coefficient values calculated from the Einstein equation with a radius of gyration of 1.2 nm1 for asphaltenes monomers and the viscosities indicated in Table 1) yielded adsorbate concentrations that were consistent with the total asphaltenes concentration, particularly at low concentrations when nanoaggregates do not form, and proportional to the “mobile” (monomeric) asphaltenes concentration as determined in our Nuclear Magnetic Resonance studies.
•
Langmuir EoS with surface excess coverage corresponding to the core size of monomers.
•
“Almost insoluble” adsorption.
•
Deviation from diffusion control due to steric hindrance.
However even for diffusion control, this asymptotic behavior only holds for very low coverage (i.e. in the limit of the linearity of diffusion kinetics, EoS and the corresponding Adsorption Isotherm). The non-linearities in diffusion, the EoS and the Adsorption Isotherm can balance each other out to give to an apparently linear regime beyond applicability range of equation 1. This could then introduce some error in the determination of the value of adsorbate concentration C. On the other hand for an “insoluble” adsorbate, the adsorption isotherm can be neglected and the evolution of surface coverage Γ can be calculated directly from Fick’s diffusion equation and mass conservation 24:
Γt = 2C ± Dt
Eq.2
where r is the radius of curvature of the droplet and the sign +/- holds for diffusion from the outside/inside of the droplet onto the interface respectively. Equation 2 can be coupled to the Langmuir EoS from expansion experiment2 to predict the evolution of surface pressure:
π = − kT Γ ∞ ln(1 −
Γ ) Γ∞
Eq.3
with Γ∞~3.3 molecule/nm2 the surface excess coverage (i.e. the inverse of molecular area at the interface). Equations 2 and 3 can then be solved together to extract adsorbate concentration at very low surface pressure and at the same time verify that the obtained value is not dependent upon the choice of other parameters such as surface excess coverage. Figure 3 shows that the very short term kinetics (where π0.8Γjam) the blocking function reads38, 39. ,-
.=
"
/ 0
-
−
1
.
Eq.7
At lower coverage the blocking function for spheres without surface diffusion can be generalized by a simple rescaling of relative coverage40: ,-
. =1−4
+ 3.308 -
/
. + 1.4069 Eq.8
which becomes ,-
. =1−4
.:: 1
.::
1.4069 ;
< Eq.9
.::
+ 3.308 ;
/
< +
While the choice of K is unimportant when coupling equation 7 to equation 4, it is not when coupling equation 9 to equation 4 to predict evolution of surface coverage in the intermediate range. This enables checking of the estimated value of ka. Figure 10 actually shows that prediction compares well to experiments down to low surface coverage.
ior: equation 7). Examples at 100 ppm (same data as Figure 5 (a)).
4. Discussion The analysis of the long-term adsorption kinetics by means of the previously identified Langmuir EoS confirms an expected transition to a regime governed by steric hindrance of adsorption. This regime has been shown to follow surface diffusion mediated RSA kinetics with an asymptotic maximum coverage or jamming limit of 85%. This high value is consistent with the Langmuir EoS based upon localized adsorption, for which coverage can assume values up to 100%. This tends to indicate a fairly large degree of order within the asphaltenes monolayer. With respect to positional order, the molecular area of asphaltenes at the interface is only three to four times higher than the molecular area of water41-44. This finite size limits the number of relative positions that asphaltenes can assume at the water surface as described in Lattice gas simulations (which EoS converges to Volmer’s type at large adsorbate size and to Langmuir’s type at low adsorbate size45). It is also noteworthy that a high degree of orientational and conformational order was observed by surface spectroscopy experiments performed on asphaltene laden interfaces846. An asymptotic limit of 85% is also found to be consistent with theoretical simulations of 2D random close packing (RCP) or maximally random jammed (MRJ) state of polydispersed disks, which might represent asphaltenes with various core sizes. With different simulation techniques and for a large range of size distributions (type, width), RCP or MRJ occur at relative coverage values of 85±1%47-52. Simulations also indicate that compressing a “dilute” ensemble of polydisperse disks yields a glass transition in the vicinity of 80% coverage52. It will be reported in a forthcoming article that almost the same value of coverage is found to cause a deviation from the EoS and a loss of Laplacian shape (hence a transition to a solid-like behavior) upon contraction of aged droplets. Further confirmation of the results presented in this paper can be found in the literature on asphaltenes. During compression in Langmuir troughs, asphaltenes-monolayer exhibits a steep increase in surface pressure for a coverage around 4 mg/m2 (average value from the review presented53). Using a molecular weight of 750 g/mol., which corresponds to the value reported here, this yields a coverage of 3.2 molecule/nm2. Given the uncertainty about the presence of nano-aggregates at the interface, due to the mix of asphaltenes monomers, nano-aggregates and clusters, being forced onto the interface from the spreading solution, the correspondence with our results is remarkable.
Figure 10: comparison of experimental evolution of surface coverage (symbols) with theoretical predictions (in red medium range: equation 9, in blue asymptotic behav-
Another comparison can be made with reported equilibrium interfacial tension values. According to our results, the maximum surface pressure that can be obtained by static adsorption is in the vicinity of 21-23 mN/m. Depending
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Langmuir upon the solvent, reaching this range will require higher or lower concentrations, lower in an aliphatic medium and higher in an aromatic medium. In toluene, corresponding experiments show that a minimum of 13 to 15 mN/m interfacial tension (close to 23 mN/m surface pressure) is reached at concentrations in the order of 10%wt54. Figure 11 below presents some results provided by Prof. Yarranton. In 50/50 heptol an equilibrium surface pressure of 21 to 23 mN/m is reached for 5kg/m3. Finally, the impact of steric hindrance on adsorption kinetics might explain the discrepancy between the proposed surface excess coverage (Γ∞=3.3 molecule/nm2) and the much higher values reported from the Gibbs plot10. In Random Sequential Adsorption models, surface coverage asymptotically reaches a maximum value of Γmax(11/(KLC)1/3) whereas it is Γ∞(1-1/KLC) for a Langmuir type model55.
22 Equilibrium interfacial tension (mN/m)
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to 2D random close packing of disks (~85%)is found to hold. From those observations the adsorption rate constant of asphaltenes can be extracted and coupled to a generalized blocking function. This enables prediction of most of the range of experimental adsorption kinetics data. Those concepts can be used to re-interpret data provided in the literature and in particular the maximum surface pressure that can be reached with asphaltenes in most types of solvents.
Corresponding Author *
[email protected] ACKNOWLEDGMENT This work is a collaboration between the City College of New York and SINTEF under the auspices of the FACE centre - a research cooperation between IFE, NTNU and SINTEF. The centre is funded by The Research Council of Norway, and by the following industrial partners: Statoil ASA, GE Oil & Gas, Scandpower Petroleum Technology AS, FMC, CD-adapco, and Shell Technology Norway AS.
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12 0
5
10
15
20 3
Asphaltene concentration (kg/m )
Figure 11: Equilibrium surface pressure as a function of asphaltenes concentration in 50-50 heptol (data courtesy from Pr. Yarranton and previously reported in 56). Values measured after 4 hours (green) or 16 hours (red). 5. Conclusion On the one hand asphaltenes behave like non cross-linked surfactants with respect to EoS and instantaneous elasticity2. On the other hand their flat on adsorption and rigidity makes them extremely sensitive to steric interactions. At low coverage and for very aliphatic media, adsorption kinetics can be modeled by diffusion of "insoluble" molecules. When coverage reaches ~35%, adsorption considerably slows down following the predictions from RSA theories: the surface pressure increase rate depends upon surface pressure itself and diffusing concentration, and is independent of viscosity. The asymptotic behavior of surface coverage follows the theoretical prediction from Random Sequential Adsorption mediated by surface diffusion: a linear dependency on 1/√t and an asymptotic limit close
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