Kinetics and Thermodynamics of Asphaltene Adsorption on Metal

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Energy & Fuels 2005, 19, 1252-1260

Kinetics and Thermodynamics of Asphaltene Adsorption on Metal Surfaces: A Preliminary Study† Kui Xie and Kunal Karan* Department of Chemical Engineering, Queen's University, Kingston, Ontario, Canada K7L 3N6 Received December 1, 2004. Revised Manuscript Received March 12, 2005

Asphaltene deposition on pipeline surfaces during crude oil production and transportation is considered to be a key Flow Assurance issue. Asphaltene-metal surface interactions including the simplest process of asphaltene adsorption on metal surfaces remains a poorly understood topic. In this study, preliminary results on the kinetics and thermodynamics of asphaltene adsorption from toluene-heptane and toluene-pentane solutions are presented. The kinetics of asphaltene adsorption on gold surface was investigated using a quartz crystal microbalance in a flow-cell system. The kinetics of adsorption was relatively slow and did not achieve equilibrium even after 700 min. The asymptotic analyses indicate that the initial adsorption process is controlled by the diffusion of asphaltenes from the bulk solution to the adsorption surface. A thermodynamic framework to describe asphaltene adsorption on metal surfaces in terms of Lifshitz-van der Waal (LW) and acid-base (AB) free energy interactions is proposed. The LW and AB components of the surface tension parameters of asphaltenes and metal surfaces were determined from contact angle measurements. The free energy of asphaltene adsorption on metal surfaces in the presence of toluene was calculated. It is predicted that asphaltenes will adsorb preferentially in the following order Au > SS > Al.

Introduction Asphaltenes are generally defined as the oil fraction that is insoluble in the low-molecular-weight normal paraffins and that is soluble in aromatics. Asphaltenes can cause a series of problems along the whole production chain from the reservoir to the refinery.1 Reservoir damage and well-bore plugging in the oil production, pipeline and tank clogging in transportation line adversely affect the petroleum industry. Although, deposition of asphaltenes is the source of problems, a majority of the studies so far have been focused on improving our understanding of the asphaltene precipitation process. Asphaltene deposition in general and asphaltenemetal interaction in particular remain a poorly understood topic. One of the early stages in the deposition process and an important interaction is the process of asphaltene adsorption. Although asphaltene adsorption in itself is unlikely to be a major problem from crude oil production and transportation perspective, it can play an important role in influencing the deposition of precipitated asphaltenes on the surface. Moreover, fundamental understanding of asphaltene-metal interactions can provide insight into whether and how surface characteristics can influence asphaltene deposition. † Presented at the 5th International Conference of Petroleum Phase Behavior and Fouling. * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Leontaritis, K. J.; Mansoori, G. A.; Jiang, T. S. J. Pet. Sci. Eng. 1988, 1, 229-239.

Several investigators have studied the adsorption of asphaltenes on various minerals.2-4 Langmuir-type isotherms were obtained showing a maximum adsorption density of 1-2 mg/m2 for most minerals.2 Multilayer formation was also observed on inorganic adsorbent for some kinds of asphaltenes, whereas other sample gave simple Langmuir-type adsorption.3 In a toluene-heptane mixture, a two-stage isotherm was recorded.4 In one of the studies, photothermal surface deformation spectroscopy technique was used to investigate adsorption of asphaltenes on glass surface. In this study, adsorption isotherms for asphaltene in toluene showed stepwise or multilayer adsorption, which has been related to aggregate formation in toluene solution. The aggregate formation and asphaltene adsorption are very slow process often occurring over several days. Previous work suggest that a proper description of asphaltene adsorption on mineral surfaces requires a consideration of aspects such as multilayer formation, aggregates formation, and adsorption.6 The studies of asphaltene adsorption on several kinds of mineral suggested that it is in fact quite distinct from the simple ‘Langmuir-type’ model. The reported adsorption isotherms show Freundlich-type behavior at early stages (2) Gonzalez, G.; Moreira, M. B. C. Colloids Surf. 1991, 58, 293302. (3) Acevedo, S.; Ranaudo, M. A.; Escobar, G.; Gutie´rrez, L.; Ortega, P. Fuel 1995, 74, 595-598. (4) Pernyeszi, T.; Patzko´, A Ä .; Berkesi, O.; De´kańy, I. Colloids Surf., A 1998, 137, 373-384. (5) Acevedo, S.; Castillo, J.; Fernańdez, A.; Goncalves, S.; Ranaudo, M. A. Energy Fuels 1998, 12, 386-390. (6) Acevedo, S.; Ranaudo, M. A.; Garcıá, C.; Castillo J.; Fernańdez, A.; Caetano, M.; Goncalvez, S. Colloids Surf., A 2000, 166, 145-152.

10.1021/ef049689+ CCC: $30.25 © 2005 American Chemical Society Published on Web 04/29/2005

Kinetics and Thermodynamics of Asphaltene Adsorption

and/or inflections characteristic of lateral interactions, as well as multiple steps that may be related to surface phase reorientation, multilayer formation, or hemimicelle formation.7 The study of adsorption kinetics of asphaltene onto water-oil interfaces using interfacial tension method has also been reported in the literature.8,9 These studies show that the interfacial intension is reduced by asphaltene adsorption at the interface of water-oil, which suggests surfactant-like characteristics of asphaltenes. Jeribi et al. reported that adsorption of asphaltene at interfaces is a slow process. The initial diffusion step is rapid, which is followed by a long reorganization and by the progressive building of multilayers.9 In another study, asphaltenes adsorption on a glass surface with respect to time was monitored by contact angle measurements.10 The asphaltene adsorption on silica had been studied by Acevedo et al.6 For initial concentrations of 5, 20, and 50 mg/L, the results led to an average firstorder rate constant of (1.17 ( 0.3) × 10-3 min-1. For more concentrated solutions (200 and 400 mg/L), the same initial rate constant was found. However, at long times, significantly lower rates were apparent. They also found that desorption of asphaltenes from the surface was very slow and could be neglected. However, in a later publication,11 they suggested that results could be adjusted to irreversible second-order adsorption kinetics, where the adsorption rate was strongly dependent on concentration. The previous research results of asphaltene adsorption kinetics are plausible. Interestingly, the possibility of a diffusion-controlled process at the early stages of adsorption was not considered. Few studies have investigated adsorption of asphaltenes on metal surfaces.12,13 In one of the studies,12 a quartz crystal microbalance (QCM) was used to investigate adsorption of asphaltene onto a hydrophilic surface. The study reported that asphaltene forms a rigid layer at lower concentrations, while it is possible to obtain further adsorption which is related to the strong tendency of aggregation of asphaltenes in the bulk solution. Another study reported isotherms for asphaltene adsorption on stainless steel and aluminum from toluene solution.13 Relatively little is known about the kinetics of the asphaltene adsorption on metal surfaces. Also, in the past, almost no effort has been directed toward the development of a thermodynamic framework to describe asphaltene-metal interactions. This is despite the fact the asphaltene deposition on metal surfaces in considered to be a critical Flow Assurance issue by the petroleum industry. This study is part of a research program focused on developing an improved understanding of asphaltene-metal interactions. In this (7) Marczewski, A. W.; Szymula, M. Colloids Surf., A 2002, 208, 259-266. (8) Sheu, E. Y.; Storm, D. A.; Shields, M. B. Fuel 1995, 74, 14751479. (9) Jeribi, M.; Almir-Assad, B.; Langevin, D.; Heńaut I.; Argillier J. F. J. Colloid Interface Sci. 2002, 256, 268-272. (10) Akhlaq, M. S.; Go¨tze, P.; Kessel, D.; Dornow, W. Colloids Surf., A 1997, 126, 25-32. (11) Acevedo S.; Ranaudo M. A.; Garcıá, C.; Castillo J.; Fernańdez A. Energy Fuels 2003, 17, 257-261. (12) Ekholm, P.; Blomberg, E.; Claesson, P.; Auflem, I. H.; Sjo¨blom, J.; Kornfeldt, A. J. Colloid Interface Sci. 2002, 247, 342-350. (13) Alboudwarej, H. Asphaltene Deposition in Flowing Systems, Ph.D. Thesis, The University of Calgary, 2003.

Energy & Fuels, Vol. 19, No. 4, 2005 1253 Table 1. Asphaltenes Yield of Cold Lake Bitumen

asphaltenes yield

C5-asphaltenes (wt%)

C7-asphaltenes (wt%)

15.6 ( 0.2

11.3 ( 0.2

paper, we present preliminary results for asphaltene adsorption on metal surfaces from model asphaltene solutions. The kinetics of asphaltene adsorption on varies metal surfaces was studied using a QCM. In addition, a thermodynamic framework to describe asphaltene adsorption on metal surfaces is proposed. Experimental Section Experiments were conducted to investigate kinetics of asphaltene adsorption on metal surfaces from asphaltene solutions in toluene-pentane and toluene-heptane mixtures. Likewise, the asphaltenes were characterized in terms of van der Waals and acid-base components of the surface tension parameters. The following sections describe the methods for asphaltene extraction, asphaltene solution preparation, asphaltene adsorption experiments, and contact angle measurements for asphaltenes and metal surfaces. In addition, the underlying principle of QCM is discussed. Asphaltene Extraction. Asphaltene samples were extracted from dewatered and inorganic-free Cold Lake Bitumen sample supplied by Imperial Oil Resources Ltd, Calgary, Canada. For asphaltene extraction, reagent-grade toluene, n-heptane, and n-pentane procured from Fisher Scientific Company were used. Briefly, the extraction method involved blending of a known amount of bitumen sample with toluene in a 1:1 ratio and sonicated for 10 min. Next, n-pentane or n-heptane was added to the mixture at 40:1 weight ratio followed by sonication for 30 min. Next, the mixture was allowed to equilibrate with occasional shaking for 24 h in dark. The mixture was filtered under vacuum using a 0.2 µm Nylon filter paper. The filter cake was rinsed by the precipitant (npentane or n-heptane) until the effluent was colorless. For the n-heptane rinse, hot heptane at 60 °C was used to wash the filter cake to ensure any waxes in the asphaltene samples were dissolved out in the filtrate. The rinsed asphaltene samples were dried at room temperature under dry and dark conditions until there was no further change in mass. The extracted asphaltenes were kept in the container in a cool, dry, and dark environment for future use. The n-heptane- and n-pentaneinsoluble fractions of Cold Lake Bitumen, hereafter referred to as C7-asphaltenes and C5-asphaltenes, are presented in Table 1. It is useful to mention that addition of toluene to initially dissolve the oil may affect the nature and amount of asphaltenic material that is extracted in comparison to a process that involves direct addition of heptane to the oil. It has been hypothesized that initial addition of toluene can alter the solvation shell and associated material which do not precipitate upon addition of heptane. Asphaltene Solution Preparation. For asphaltene solution preparation, a known amount of asphaltenes was added to 100 mL of reagent-grade toluene. The mixture was stirred and then sonicated for 20 min. The mixture was allowed to equilibrate overnight, following which, it was filtered using a 0.2 µm Nylon filter paper to remove any undissolved asphaltene entity. After filtration, the filter paper was dried and weighed to calculate the actual mass of asphaltenes in the solution. The filtered solution was transferred into a 250 mL volumetric flask and the required amount of toluene was added to make a stock solution of known concentration. The stock solution was stored in dark, cool place for future use. At least one week before performing an adsorption experiment, the stock asphaltene-toluene solution was first diluted by toluene and then a known amount of n-heptane was added slowly with continuous stirring. Upon addition of heptane, no

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Energy & Fuels, Vol. 19, No. 4, 2005

Xie and Karan sensitivity factor for the crystal (56.6 Hz µg -1 cm2 for a 5 MHz AT-cut quartz crystal at room temperature). The frequency of QCM can change when the sensor electrode is exposed to a liquid. The frequency change is dependent upon the viscosity and density of the liquid. Kanazawa’s solution15 for the change in resonant frequency of the crystal due to liquid loading is shown in following equation:

∆f ) - f3/2 u

Figure 1. Experimental setup with flow cell. visual sign of precipitation was observed. After being mixed, the solution was sonicated for 20 min. Once prepared, the sample was sonicated 3-4 times per day, 20 min per time in the following week. Asphaltene Adsorption Experiments. The asphaltene adsorption experiments were conducted in a flow system. A schematic diagram of the experimental setup is shown in Figure 1. The experimental setup comprises the following key components: a quartz crystal microbalance and associated data-acquisition system, a temperature-controlled bath, and a peristaltic pump. Other auxiliary components include flasks, tubings, valves, etc. The heart of the system is a research quartz crystal microbalance (RQCM) acquired from Maxtek, Inc. The RQCM system employed in this study utilizes a crystal of 5 MHz characteristic frequency. The fluid is circulated through the system using a peristaltic pump and controlled by 3-way valves. The QCM flow cell and flasks containing asphaltene and blank solutions are immersed in a temperature-controlled water bath which can maintain the temperature within (0.2 °C. The blank solution is essentially a mixture of the same composition as that of asphaltene-free solution. Briefly, the adsorption experiment involves equilibration of the crystal in air followed by flowing blank solution into the QCM flow-cell until the system is equilibrated. The system was deemed to have been equilibrated if the crystal frequency varied by less than (5 Hz over a 1 h period. Next, the asphaltene sample fluid is allowed to flow through the flow cell while frequency response is continuously monitored and recorded. Basic Principle of a Quartz Crystal Microbalance (QCM). A QCM is a piezoelectric resonator device consisting of an AT-cut quartz crystal sandwiched between two electrodes. Upon excitation by application of alternating voltage, the crystal vibrates with a characteristic frequency. The frequency change can be related to one or more of the following factors: (i) mass change, (ii) change in viscosity densityproduct of the media exposed to the crystal surface, and (iii) pressure change. The mass change per unit area at the QCM electrode surface can be related to the observed change in oscillation frequency of the crystal according to the Saurbrey equation:14

∆f ) - Cf∆m

(1)

where ∆f ) the observed frequency change in Hz, ∆m ) the change in mass per unit area in µg/cm2, and Cf ) the (14) Sauerbrey, G. Z. Phys. 1959, 155, 206.

x

ηLFL πµqFq

(2)

where fu ) resonant frequency of unloaded crystal in Hz, Fq) density of quartz ) 2.648 × 103 kg/m3, µq ) shear modulus of quartz ) 2.947 × 1010 Pa, FL ) density of the liquid in contact with the electrode in kg/m3, and ηL) viscosity of the liquid in contact with the electrode in N‚S/m2. The frequency of the crystal can also change due to changes in pressure. The pressure dependence of frequency, ∆fp, increases linearly with increasing pressure for gases up to 15 psi, as discussed by Stockbridge.16 A similar relationship for liquids up to 1.5 × 104 psi was presented by Susse.17 Thus, ∆fp can be written as

∆fp ) f0R∆P ) CP∆P

(3)

where R is the proportionality constant and CP is the pressure sensitivity of the QCM crystal, both of which are independent of the type of fluid in contact with the crystal. CP is calculated to be 0.36 for a 5 MHz crystal from the value of R proposed by Stockbridge when pressure (∆P) is expressed in psi. Contact Angle Measurement. The asphaltene and metal surfaces were characterized in terms of van der Waals and acid-base components of the surface tension parameters. The + three surface tension component of the material γLW S , γS , and γS were obtained by measuring the contact angle of the surface using three liquids of varying polarity and known surface tension parameters. The description of the theory underlying these parameters estimation is provided later. The three liquids used in this study were water (polar), glycerol (polar), and diiodomethane (apolar). Contact angle measurements were carried on a VCA-Optima (AST Products, Inc.) instrument. All of the measurements were carried out at room temperature of 22 ( 1 °C. The substrates of asphaltenes were prepared by coating a high-concentration asphaltene-toluene solution on the quartz crystal surfaces and then slowly evaporating and drying for 24 h in fume hood.

Asphaltene Adsorption Kinetics Typical Adsorption Run The frequency response from QCM during a typical adsorption run is presented in Figure 2. The figure shows three distinct regions corresponding to frequency changes during equilibration in air and in blank solution followed by slow change during the adsorption process. As can be observed from the figure, the QCM equilibrates rapidly upon being exposed to the blank solution. The change in frequency is due to the change in viscosity-density product of the media and can be estimated from eq 2. When the QCM is exposed to asphaltene solution, the change in frequency is attributed only to mass adsorbing on the crystal surface. This is true because the blank solution and the asphaltene solution have density-viscosity (15) Kanazawa, K. K.; Gordon, J. G. Anal. Chem. 1985, 57, 17701771. (16) Stockbridge, C. D. Effects of gas pressure on quartz crystal microbalances. In Vacuum Microbalance Techniques; Behrndt, K. H., Ed.; Plenum Press: New York, 1966; p 147. (17) Susse, C. J. Phys. Radium 1955, 16, 348-349.


Figure 2. Typical frequency response during an adsorption experiment.

Figure 3. Asphaltene adsorption kinetics: effect of concentration [C5-insoluble asphaltenes in a 1:1 n-heptane-toluene mixture; 25 °C; flow rate: 0.9 mL/min].

products very close to each other. Applying eq 1, one can then calculate the mass change from the frequency change data. Asphaltene Adsorption: Effect of Asphaltene Concentration. A set of experiments were performed with C7-asphaltene solutions containing 10-200 ppm of asphaltene in 1:1 volume of C7-toluene mixture. Figure 3 shows the kinetics of the adsorption process for these experiments. The key feature to note is that there is a very rapid initial response followed by a gradual change in mass. As asphaltene concentration increases, both the initial rate and the amount of asphaltene adsorbed at any given time increases. At lower concentration (10 ppm), the adsorption curve appears to attain close to equilibrium conditions after 700 min. However, at higher concentration (200 ppm), it is evident from the trajectory of the plots that even after 700 min there is no indication that the process is getting close to equilibrium. As stated earlier, literature data for asphaltene adsorption on metals are essentially nonexistent barring those reported by Alboudwarej13 and Elkholm et al.12 These two studies were not concerned with the kinetics of the adsorption process, and as such, there is limited information available. Elkholm et al. report that equilibrium-like conditions were achieved in their experiments in less than 10 min, whereas Alboudwarej13 reports that equilibrium was

Energy & Fuels, Vol. 19, No. 4, 2005 1255

achieved in less than 24 h. Studies on asphaltene adsorption on minerals report that it can take up to 5400 min to achieve the equilibrium level. One of the interesting results of our study was that the amount of asphaltene adsorbed even at less than equilibrium levels is significantly higher than that obtained by Alboudwarej.13 We attribute this difference to the different types of solvents utilized in the experiments. The experiments by Alboudwarej were carried out with asphaltene solutions in toluene as opposed to a toluene-heptane mixture. It is generally accepted now that asphaltenes may be present in an associated state even at low concentrations (as low as 50-100 ppm) when dissolved in toluene. Therefore, it is very plausible that, in a toluene-heptane mixture, the degree of association is expected to be significantly higher. Thus, there are few possible explanations for larger amounts of asphaltene adsorbed. One possibility is that, because the asphaltenes are in an associated state, the monolayer mass of adsorbed asphaltenes in C7-toluene solvent would be higher than that in toluene. A second possibility is that in the associated state the asphaltenes follow a multilayer adsorption process similar that reported for adsorption on certain minerals.3 It is also possible that, in the associated state, the asphaltenes behave as another phase, and therefore, the apparent adsorption process is somewhat similar to deposition process, which is not restricted to monolayer formation. Unfortunately, with the limited data we have, it is difficult to provide a conclusive explanation. Adsorption Kinetics in a Flow Cell. Regardless of the actual factor that leads to increased amount of asphaltene adsorption, further analyses of kinetic data were performed. The mass change data for QCM was considered to be a result of adsorption process. In particular, the interest was to determine whether the rate of adsorption was limited by the kinetics of adsorption at the surface or by mass transport limitations (i.e., diffusion). For the analyses, the methodology proposed by Fillipov18 was adopted. A detailed mathematical model describing adsorption in a flow cell is provided in the Appendix. It is recognized that a complete solution of the coupled partial differential equations requires a numerical method. The initial rates can, however, be analyzed for two cases: (i) adsorption kinetics are finite, and (ii) adsorption kinetics are infinite. Asymptotic analyses of the first case indicate that the initial rate (mass change) will vary linearly with time (refer to eq A.11), whereas for the second case, the initial rate will vary linearly with square root of time (refer to eq A.15). The first case corresponds to a kineticcontrolled process, while the second case corresponds to a diffusion-controlled process. A third case may arise wherein both diffusion and kinetics can play an equally important role. An implicit assumption in the development of eqs A.11 and A.15 is that the initial rate process should be independent of convective parameters, viz., flow rate. To investigate whether the initial rates of adsorption in our experiments were independent of the convective parameters, experiments at three different flow rates of 0.8, 2, and 4 mL/min were performed. The experi(18) Filippov, L. K. J. Colloid Interface Sci. 1995, 174, 32-39.

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Figure 4. Effect of flow rate on asphaltene adsorption kinetics [C5-insoluble asphaltenes in a 1:1 n-heptane-toluene mixture; 25 °C; concentration: 200 ppm].

mental results are shown in Figure 4. It can be seen from the figure that the rate of adsorption is independent of the flow rates, although at long times, there is a significant effect of the flow rates. The independence of initial asphaltene adsorption rates on flow rates allows asymptotic analyses of the experimental data. Asymptotic Analyses of Initial Rates. To evaluate whether kinetics or diffusion dominates the initial adsorption process, the asphaltene adsorption data were plotted as a function of time and square root of time, as shown in Figure 5a and b, respectively. For both a and b of Figure 5, the data over same range of time was employed. It can be observed from Figure 5 that mass adsorbed does not follow a linear relationship with time but it does with square root of time. Thus, it can be concluded that for the conditions encountered in our experimental system, asphaltene adsorption is limited by the diffusion of asphaltene molecules from the bulk solution to the substrate. Further, these results imply that the rate constant for asphaltene adsorption on gold surface is very large. Estimation of Asphaltene Diffusion Coefficient and Particle Size. Equation A.15 allows us to estimate

Xie and Karan

the diffusion coefficient of asphaltenes. The estimated asphaltene diffusion coefficients are presented in Figure 6. The asphaltene diffusion coefficient is on the order of 10-11 m2/s and is found to be a function of concentration. The concentration dependence of diffusion coefficients can be explained in terms of the concentrationdependent size of the asphaltene entity. At low concentrations, the degree of association of asphaltenes is small but increases with increase in concentration until a critical size is reached. The higher the state of association, the larger the entity size and the lower the diffusion coefficient. Ostlund et al.19 have reported diffusion coefficients of asphaltenes in toluene-d8 solutions to be on the order of 10-10 m2/s. In a more recent study, Ostlund et al.20 estimated the diffusion coefficients of various fractions of Cold Lake asphaltenes in dichlorobenzene-d4 to be on the order of 10-11 m2/s, which is closer to the diffusion coefficient estimated in the present study. Although strictly applicable to steady-state condition, we have applied the Stokes-Einstein equation21 to estimate the asphaltene entity size:

D)

kBT 3πµd0

(4)

where D is the diffusion coefficient of the particles, d0 is the particle diameter, µ is the solvent viscosity, and kB is Boltzmann’s constant. Assuming asphaltenes are spherical in shape, a questionable assumption, the particle size can be calculated from eq 4. The calculated particle size as a function of asphaltene concentration is plotted in Figure 7. It is interesting to note that the asphaltene entity at 10 ppm in the toluene-heptane mixture has an equivalent diameter of around 30 nm, which is 2-3 times the size of Safanya asphaltene fractions in tetrahydrofuran as determined by Ravey et al.22 using small angle neutron scattering. Asphaltene particles size can vary significantly depending on the concentration and solvent. The association and solvation shell of asphaltenes at 10 ppm in the heptane-toluene mixture is probably more significant than in tetrahydrofuran. Therefore, it is plausible that the estimated

Figure 5. Mass of asphaltene adsorbed as a function (a) time and (b) square root of time. Error bars represent (7% variation of intermediate flow rate data. (Initial time period data of Figure 4).



action, ∆G132, can be written as a sum of a number of interactions23 Tot LW AB EL ∆G132 ) ∆G132 + ∆G132 + ∆G132 + ...

Figure 6. Asphaltene diffusion coefficient as a function of concentration [C5-insoluble asphaltenes in a 1:1 n-heptanetoluene mixture; 25 °C; flow rate: 0.9 mL/min].

(5)

Only the first two terms of the right-hand side of eq 5 account for the Lifshitz-van der Waal (LW) and acidbase (AB) interactions, while the third term is the electrostatic interaction. The LW interaction includes London dispersion, Keesom, and Debye components of the van der Waal interactions. The AB interaction represents the electron-donor electron-acceptor behavior that may be important owing to the electron donor capability of metals. The LW and AB interactions can be calculated from eqs 6 and 7, respectively,23 provided the surface tension components of adsorbent, adsorbate, and solvent are known. LW ) 2(xγLW γLW + xγLW γLW - xγLW γLW - γLW ∆G132 1 3 2 3 1 2 3 )

(6) AB + ∆G132 ) 2(xγ+ 3 (xγ1 + xγ2 - xγ3 ) + xγ3 (xγ1 +

xγ+2 - xγ+3 ) - xγ+1 γ-2 - xγ-1 γ+2 )

(7)

As a first simplification, assuming that there is no electrical charge or ions in the gold-toluene-asphaltene EL system, the term of ∆G132 in eq 5 can be neglected and the total free energy for adsorption can be written as follows TOT LW AB ∆G132 ) ∆G132 + ∆G132 ) 2[xγLW γLW + 1 3

Figure 7. Asphaltene particle size at different concentrations [C5-insoluble asphaltenes in a 1:1 n-heptane-toluene mixture; 25 °C; flow rate: 0.9 mL/min].

particle size in this work is much bigger than those reported by other researchers. Asphaltene-Metal Interaction: Development of a Thermodynamic Framework The thermodynamic framework to describe asphaltene-surface interaction is essentially nonexistent in the literature. We are interested in developing a theoretical framework that allows us to answer essentially two questions: (i) whether asphaltenes have a tendency to adsorb or adhere to a given metallic surface, and (ii) if they do, what is the maximum amount adsorbed. In this paper, we proposed building a thermodynamic framework that accounts for various types of interactions between the adsorbate (asphaltene ) 1) and adsorbent (metal surface ) 2) in the presence of a medium (solvent ) 3). The total free energy of inter(19) Ostlund, J.-A.; Lofroth, J. E.; Holmberg, K.; Nyden, M. J. Colloid Interface Sci. 2002, 253, 150-158. (20) Ostlund, J.-A.; Wattana, P.; Nyden, M.; Fogler, H. S. J. Colloid Interface Sci. 2004, 271, 372-380. (21) Cussler, E. L. Diffusion Mass Transfer in Fluid System, 2nd ed.; Cambridge University Press: New York, 1997. (22) Ravey, J. C.; Ducouret, G.; Espinat, D. Fuel 1988, 67, 15601567.

+ γLW - xγLW γLW - γLW xγLW 2 3 1 2 3 ] + 2[xγ3 (xγ1 + xγ-2 - xγ-3 ) + xγ-3 (xγ+1 + xγ+2 - xγ+3 ) - xγ+1 γ-2 xγ-1 γ+2 ] (8)

Tot If the calculated value of ∆G132 is negative, the overall interaction, in our case adsorption, is spontaneous. From separate experimental studies, the adsorption isotherm can yield the adsorption equilibrium constant, Keq, and the maximum surface coverage concentration, Cmax. The free energy of adsorption ∆Gads can be calculated from Keq. Thus, the adsorption experiments can be employed to validate the thermodynamic model for asphaltene-metal interaction. Determination of Surface Tension Components. To calculate the free energy of interaction or adsorption, surface tension data of adsorbent, adsorbate and solvent have to be known. Surface tension data of the solvent (toluene) can be obtained from the literature. However, surface tension data of metals and asphaltenes are not readily available. However, these parameters can be extracted through contact angle measurements. In what follows, we present the method of determination of these parameters; a similar approach was presented by Askvik24

(23) van Oss, C. J. Interfacial Forces in Aqueous Media, 1st ed.; Marcel Dekker, Inc.: New York, 1994. (24) Askvik, K. M.; Fotland, P. Experimental Determination of Hamaker Constants for Asphaltenes and Crude Oils, Presented at the 4th International Conference on Petroleum Phase Behaviour and Fouling, Trondheim, Norway, June 23-26, 2003.

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Xie and Karan Table 2. Surface Tension Data of Asphaltenes, in mJ/m2

C7-asphaltene C5-asphaltene

γLW S

γ+ S

γS

γAB S

γTOT S

30.00 29.67

0.200 0.003

0.72 2.51

0.75 0.18

30.75 ( 1.30 29.84 ( 0.90

Table 3. Surface Tension Data of Metals, in mJ/m2

gold stainless steal aluminum

γLW S

γ+ S

γS

γAB S

γTOT S

39.33 35.85 39.14

0.11 1.26 0.88

7.91 11.66 7.37

1.89 7.66 5.11

41.22 ( 2.10 43.51 ( 1.20 44.24 ( 3.80

Table 4. Calculated Adsorption Free Energies of C7-Asphaltene on Various Metal Surfaces, in mJ/m2 material

∆G132

Au SS Al

-0.957 ( 0.050 -0.361 ( 0.020 -0.059 ( 0.010

Figure 8. C7-asphaltene contact angle data.

Thomas Young23 described the relationship between the surface tension of a solid (γS) and a liquid (γL), the interfacial tension between the solid and the liquid (γSL), and the contact angle, θ, according to the following equation:

γL cos θ ) γS - γSL

(9)

Dupre´ expressed the relation between the work of adhesion, surface tension, and interfacial tension of solids and liquids as follows23

∆GSL ) γSL - γS - γL

(10)

Substituting eq 10 into eq 9, one obtains the well-known Young-Dupre´ equation:

-∆GSL ) γL(1 + cos θ)

(11)

Taking ∆GLW and ∆GAB into account, the Young-Dupre´ equation can be more precisely expressed as AB -∆GLW SL - ∆GSL ) γL(1 + cos θ)

(12)

LW LW ∆GLW SL ) - 2xγS γL

(13)

+ - + ∆GAB SL ) - 2(xγS γL + xγS γL )

(14)

Also,

Substituting eqs 13 and 14 into eq 12, one obtains23 LW + - + ) 2(xγLW (1 + cos θ)γTOT L S γL + xγS γL + xγS γL )

(15) + The surface tension components, γLW S , γS , and γS , of the solid material can be obtained from contact angle (θ) measurements with three liquids of known surface LW + tension components γTOT L , γL , γL , and γL . In this study, the contact angle data of C7-asphaltenes were measured using three liquidsswater, glycerol, and diiodomethanesof varying polarity but known surface tension parameters. The experimental data are plotted in Figure 8. The LW and AB components of surface tension of C7-asphaltenes and C5-asphaltenes are listed in Table 2. The LW components for both types of asphaltenes are very close; however, the AB compo-

nents are significantly different. Although C5-asphaltenes have higher γ-, the total acid-base component γAB is lower than that of C7-asphaltene. The surface tension parameters of metal surfaces were obtained similarly and are presented in Table 3. Predicted Free Energy of Asphaltene-Metal Interaction. The free energy for interaction or adsorption of C7-asphaltene from asphaltene-toluene solution on gold (Au), stainless steel (SS), and aluminum (Al) was calculated using eq 8. Table 4 lists the estimated adsorption free energy of metal-toluene-asphaltene systems. From the data in Table 4, it can be seen that Al, SS, and Au have the increasing absolute values of adsorption free energy. This indicates that the adsorption amount of asphaltene on the metals will increase as Al < SS < Au. Asphaltene adsorption experiments are underway to verify whether these calculated ∆Gads compare well with those obtained from adsorption isotherm data. Conclusions This study reports preliminary findings of kinetics and thermodynamics of asphaltene adsorption on metal surfaces. The kinetics of adsorption of asphaltenes from solutions of toluene-heptane mixtures was investigated using a QCM flow system. Asymptotic analyses of the initial rates of process indicated that adsorption was limited by the diffusion of asphaltene and not by the adsorption kinetics. Asphaltene diffusion coefficients were estimated to be on the order of 10-11 m2/s. A thermodynamic framework to describe asphaltene adsorption on metal surfaces in terms of LW and AB free energy interactions was proposed. The LW and AB components of the asphaltene surface tensions were obtained from contact angle measurements. The free energy of interaction or adsorption of asphaltene on metal surfaces in the presence of toluene was calculated. It is predicted that asphaltenes will adsorb preferentially in the following order Au > SS > Al. Experimental work is underway to test the validity of these predictions. Appendix: Mathematical Model for Asphaltene Adsorption in a Flow Cell An unsteady-state model incorporating diffusionconvective mass transport and adsorption phenomenon



backward rate of the adsorption and desorption process, respectively.

R+ ) KadRad[c(0,t), Γ(t)], R- ) KdesRdes[Γ(t)]

Figure 9. Geometry of the flow cell.

proposed by Fillipov18 has been adopted here to describe adsorption in flow cell. The flow cell geometry is represented in Figure 9. The convective-diffusive mass transfer equations based on a mass balance on the adsorbate can be described by the following equation: 2 ∂c(x, y, t) y ∂c(x, y, t) D∂ c(x, y, t) + γy 1 ) ∂t b ∂x ∂y2

(

)

(A.1)

where c(x, y, t) is the concentration of the adsorbate, γ is the wall shear rate, D is the diffusion coefficient of the adsorbate in the solution, b is the thickness of the flow cell, and γ is wall shear rate. The initial condition is

at t ) 0, c ) 0 for all y, x > 0

(A.2)

The boundary conditions are

at x ) 0, c ) c0 for all y, t

{

(A.3)

0 for t < tm, tm ) x/Vm b at y ) , c ) c0 for t g tm 2

(A.4)

at y ) 0, c ) 0

(A.5)

where c0 is the adsorbate concentration in the bulk and Vm is the maximum axial velocity in a flow cell. For the asphaltene solution that is Newtonian, the shear rate of fluid near the adsorbing surface is25

V(y) )

6Q y y12 b bd

(

)

(A.6)

where Q is volumetric flow rate of solution through the rectangular flow channel and d is the width of the flow cell. In the general case, the processes of adsorption are governed by the kinetics of adsorption and desorption of adsorbate molecules at the interface and the diffusion of these molecules in the adsorbed layer. Therefore, in the general case, the adsorption and desorption kinetics on a metal surface is described by

dΓ(t) ) R+ - Rdt

(A.7)

where Γ(t) is the amount of adsorbate adsorbed on the metal surface and R+ and R- are the forward and (25) Brodkey, R. S.; Hershey, H. C. Transport Phenomena; McGrawHill: New York, 1988.

(A.8)

where Kad and Kdes are the forward and backward rate constants of the adsorption and desorption process, respectively, Rad and Rdes depend on the adsorption model that applied, and c(0,t) is the adsorbate concentration at the surface (x ) 0). For the adsorption and desorption kinetics, the common isotherm models are considered here. The generalized expression for the Henry, Langmuir, and Freundlich adsorption kinetics may be written as,26

dΓ(t) ) Kads[c(0,t)]m[Γ0m - Γ(t)]s - KdesΓ(t) dt

(A.9)

where, Γ0m is the maximum adsorption and m and s are the parameters of adsorption and desorption kinetics constants, respectively. For the Henry’s Law isotherm, m ) 1, s ) 0; for the Langmuir isotherm, m ) s ) 1; and for the Freundlich isotherm, 0 e m e 1, s ) 0. To obtain a complete solution of adsorption kinetics, eqs 1-9 must be solved with appropriate boundary and initial conditions. The solution of the coupled partial differential equations is not straightforward. However, an asymptotic analysis of the solution at short times and very long times are relatively simple. Here the discussions are limited to short time asymptotic analyses. Finite Adsorption Kinetics. If the rates of adsorption and desorption are finite,18

Γ(L,t g tm) ≈ S*(t - tm) Γ0 d

[

]

Γ(L,t g tm) /dt ≈ S* Γ0 S* ) Kadcm 0

(Γ0m)r Γ0

(A.10)

(A.11)

(A.12)

where, S* is the slope of the relative adsorption versus time at short times. The rate of adsorption depends on Kad and does not depend on diffusive and convective parameters. Therefore, in this case, the adsorption process is controlled by the adsorption kinetics and the relation of relative adsorption versus time should be linear. Infinite Adsorption Kinetics. If the rates of adsorption and desorption are infinite (Kad, Kdes f ∞), from the system of equations, the asymptotic solution can be described by the following equations:18

Γ(L,t g tm) ≈ S0(t - tm)1/2 Γ0

(A13)

d[Γ(L,t g tm)/Γ0] ≈ S0(t - tm)1/2 dt

(A14)

(26) Eyring, H. Basic Chemical Kinetics. Wiley: New York, 1980.

1260


c0 S0 ) 2 (D/π)1/2 Γ0

Xie and Karan

(A15)

where S0 is the slope of the relative adsorption versus (t - tm)1/2. Therefore, the rate of adsorption depends on diffusion coefficient, D, and does not depend on parameters characterizing the kinetics and convective transfer. In this case, the adsorption process is controlled by the diffusion since the convective term is negligible. Nomenclature b ) thickness of the flow cell [m] c(x,y,t) ) concentration of adsorbate [ppm] c0 ) adsorbate concentration in the bulk [ppm] Cmax ) maximum surface coverage concentration [µg/cm2] D ) diffusion coefficient [m2/s] d ) the width of the flow cell [m] d0 ) particle diameter [nm] Kad ) rate constant of the adsorption kB ) Boltzmann’s constant [1.3807 × 10-23 J/K] Kdes ) rate constant of the desorption Keq ) adsorption equilibrium constant Q ) volumetric flow rate [ml/min] R- ) rate of the desorption R+ ) rate of the adsorption Rad ) adsorption rate Rdes ) desorption rate S* ) slope of the relative adsorption versus time S0 ) slope of the relative adsorption versus time t ) time tm ) lag time V(y) ) axial velocity [m/s] Vm ) maximum axial velocity in a flow cell [m/s] ∆G132 ) free energy of interaction of 1 adsorbing on 2 in medium 3 [mJ/m2] ∆Gads ) free energy of adsorption [mJ/m2]

∆GSL ) work of adhesion [mJ/m2] µ ) solvent viscosity [Pa‚s] γ ) wall shear rate [s-1] γL ) surface tension of liquid [mJ/m2] γS ) surface tension of solid [mJ/m2] γSL ) interfacial tension of liquid and solid [mJ/m2] θ ) contact angle [deg] Γ(t) ) the amount of adsorbate adsorbed on the metal surface [µg/cm2] Γ0 ) the amount of adsorbate adsorbed at the concentration c0 [µg/cm2] Γ0m ) maximum adsorption [µg/cm2] Superscripts - ) electron-acceptor parameter of acid-base interaction + ) electron-donor parameter of acid-base interaction AB ) acid-base interaction EL ) electrostatic interaction LW ) Lifshitz-van der Waals interaction TOT ) total interaction Subscripts 1 ) adsorbent 2 ) adsorbate 3 ) medium L ) liquid S ) solid

Acknowledgment. The authors acknowledge financial support from Imperial Oil University Research Award, Queen’s Advisory Research Committee Award, and Natural Sciences and Engineering Council of Canada (NSERC). The authors thank Dr. Aristides Docoslis for valuable technical discussion and granting access to contact angle measurement device. EF049689+

Kinetics and Thermodynamics of Asphaltene Adsorption on Metal

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