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Rheology of Asphaltene-Toluene/Water Interfaces Danuta M. Sztukowski‡ and Harvey W. Yarranton*,† Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4 Received July 15, 2005. In Final Form: September 26, 2005 The stability of water-in-crude oil emulsions is frequently attributed to a rigid asphaltene film at the water/oil interface. The rheological properties of these films and their relationship to emulsion stability are ill defined. In this study, the interfacial tension, elastic modulus, and viscous modulus were measured using a drop shape analyzer for model oils consisting of asphaltenes dissolved in toluene for concentrations varying from 0.002 to 20 kg/m3. The effects of oscillation frequency, asphaltene concentration, and interface aging time were examined. The films exhibited viscoelastic behavior. The total modulus increased as the interface aged at all asphaltene concentrations. An attempt was made to model the rheology for the full range of asphaltene concentration. The instantaneous elasticity was modeled with a surface equation of state (SEOS), and the elastic and viscous moduli, with the Lucassen-van den Tempel (LVDT) model. It was found that only the early-time data could be modeled using the SEOS-LVDT approach; that is, the instantaneous, elastic, and viscous moduli of interfaces aged for at most 10 minutes. At longer interface aging times, the SEOS-LVDT approach was invalid, likely because of irreversible adsorption of asphaltenes on the interface and the formation of a network structure.
Introduction Water-in-crude oil emulsions can be stabilized by several components including asphaltenes,1-3 solids such as clays or corrosion products,4-9 and organic acids.10 The density and viscosity of the oil are also factors. Heating and the addition of flocculants can overcome unfavorable density and viscosity conditions but cannot always promote satisfactory coalescence. In many cases, coalescence likely depends on the rheological properties of the interface as well as the size and concentration of solids on or near the interface. Recent research has focused on the rheology of asphaltene interfacial films. Asphaltenes appear to adsorb at the interface (at least initially) as a monolayer varying between 2 and 9 nm.11 Over time, the asphaltenes appear to rearrange into a rigid mechanical film. These films have a large elastic modulus12-16 and visibly crumple when the interface is contracted.17-22 It has been widely hypothesized that these * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: (403) 220 6529. Fax: (403) 282 3945. † University of Calgary. ‡ Now with Shell Canada Research, 3655 36 Street NW, Calgary, Alberta, Canada T2L 1Y8. (1) Yarranton, H. W.; Hussein, H.; Masliyah, J. H. J. Colloid Interface Sci. 2000, 228, 52. (2) McLean, J. D.; Kilpatrick, P. K. J. Colloid Interface Sci. 1997, 196, 23. (3) Taylor, S. D.; Czarnecki, J.; Masliyah, J. J. Colloid Interface Sci. 2002, 252, 149. (4) Kotlyar, L. S.; Sparks, B. D.; Woods, J. R.; Raymond, S.; LePage Y.; Shelfantook, W. Pet. Sci. Technol. 1998, 16, 1. (5) Kotlyar, L. S.; Sparks, B. D.; Woods, J. R.; Chung, K. H. Energy Fuels 1999, 13, 346. (6) Yan, Z.; Elliot, J. A. W.; Masliyah, J. H. J. Colloid Interface Sci. 1999, 220, 329. (7) Yan, N.; Gray, M. R.; Masliyah, J. H. Colloids Surf., A 2001, 193, 97. (8) Gu, G.; Zhiang, Z.; Xu, Z.; Masliyah, J. H. Colloids Surf., A 2003, 215, 141. (9) Bensebaa, F.; Kotlyar, L.; Pleizier, G.; Sparks, B.; Deslandes, Y.; Chung, K. Surf. Interface Anal. 2000, 30, 207. (10) Horva´th-Szabo´, G.; Masliyah, J. H.; Czarnecki, J. J. Colloid Interface Sci. 2001, 242, 247. (11) Sztukowski, D. M.; Jafari, M.; Alboudwarej, H.; Yarranton, H. W. J. Colloid Interface Sci. 2003, 265, 179.
films are largely responsible for long-term emulsion stability.1,17,21,23-25 Interfaces with a large elastic modulus experience a relatively large increase in energy when the interfacial area increases or surfactants such as asphaltenes are spread more thinly on the interface. Therefore, a droplet with an elastic film is less likely to deform during a collision with another droplet. Also, the Gibbs-Marangoni effect is likely to be stronger so that asphaltenes will migrate to depleted areas more rapidly. Both factors will reduce the coalescence rate and enhance emulsion stability. Attempts to quantify interfacial film compressibility and elasticity have been made via Langmuir film balance techniques,26-30 shear viscometric measurements,14,31-34 (12) Freer, E. M.; Radke, C. J. J. Adhes. 2004, 80, 481. (13) Freer, E. M.; Svitova, T.; Radke, C. J. J. Pet. Sci. Eng. 2003, 39, 137. (14) Spiecker, P. M.; Kilpatrick, P. K. Langmuir 2004, 20, 4022. (15) Bouriat, P.; El Kerri, N.; Graciaa, A.; Lachaise, A. Langmuir 2004, 20, 7459. (16) Bauget, F.; Langevin, D.; Lenormand, R. J. Colloid Interface Sci. 2001, 239, 501. (17) Taylor, S. E. Chem. Ind. London 1992, October 19, 770. (18) Reisberg, J.; Doscher, T. M. Prod. Mon. 1956, November, 43. (19) Strassner, J. E. J. Pet. Technol. 1968, 20, 303. (20) Jeribi, M.; Almir-Assad, B.; Langevin, D.; Henaut, I.; Argillier, J. F. J. Colloid Interface Sci. 2002, 256, 268. (21) Yeung, A.; Dabros, T.; Czarnecki, J.; Masliyah, J. Proc. R. Soc. London, Ser. A 1999, 455, 3709. (22) Khristov, Khr.; Taylor, S. D.; Masliyah, J. Colloids Surf., A: 2000, 174, 183. (23) Siffert, B.; Bourgeois, C.; Papirer, E. Fuel 1984, 63, 834. (24) Nordli, K. G.; Sjo¨blom, J.; Kizling, J.; Stenius, P. Colloids Surf. 1991, 57, 83. (25) Sheu, E. Y.; De Tar, M. M.; Storm, D. A.; DeCanio, S. J. Fuel 1992, 71, 299. (26) Jones, T. J.; Neustadter, E. L.; Whittingham, K. P. JCPT 1978, April-June, 100. (27) Ese, M.-H.; Galet, L.; Clausse, D.; Sjoblom, J. J. Colloid Interface Sci. 1999, 220, 293. (28) Ese, M.-H.; Yang, X.; Sjoblom, J. Colloid Polym. Sci. 1998, 276, 800. (29) Zhang, L. Y.; Lawrence, S.; Xu, Z.; Masliyah, J. H. J. Colloid Interface Sci. 2003, 264, 128. (30) Zhang, L. Y.; Xu, Z.; Masliyah, J. H. Langmuir 2003, 19, 9730. (31) Eley, D. D.; Hey, M. J.; Lee, M. A. Colloids Surf. 1987, 24, 173. (32) Mohammed, R. A.; Bailey, A. I.; Luckham, P. F.; Spencer, S. E. Colloids Surf., A 1993, 80, 237.
10.1021/la051921w CCC: $30.25 © 2005 American Chemical Society Published on Web 11/04/2005
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and oscillatory drop measurements,12,13,15,16,35 Generally, these studies indicate that the elastic and viscous moduli increase when the continuous phase becomes more paraffinic and when the interface is aged. The measured elastic and viscous moduli also depend on the crude oil (or asphaltene) concentration in the continuous phase. Some authors have observed an increase in the elastic modulus with an increase in asphaltene or crude oil concentration,13,14 whereas others have noted variable behavior.35 Although the effects of solvent quality, time, and continuous-phase composition on interfacial elasticity have been examined, few attempts have been made to model the rheology. Most notably, Freer and Radke12 examined asphaltene adsorption and the rheology of model toluene-water interfaces in terms of a combination of purely diffusional relaxation and viscoelastic behaviors. Their study of an aged, 0.005 wt % asphaltene-toluenewater interface showed that the total, elastic, and viscous moduli at different frequencies could be modeled successfully with the Lucassen-van den Tempel (LVDT) and Maxwell viscoelastic models. The need for a mechanical component in their model showed clearly the importance of irreversible adsorption effects and was consistent with previous visual observations of interfacial “rigid” skins.17-22 The purpose of this work is to (1) examine the effect of asphaltene concentration and aging time on the rheology of the water/hydrocarbon interface and (2) extend the LVDT approach to these systems. The hydrocarbon phases consisted of 0.002 to 20 kg/m3 (approximately 0.0002 to 2 wt %) asphaltenes in toluene. The interfaces were aged up to 16 h. Experimental Methods Materials. Asphaltenes were precipitated from Athabasca bitumen, a coker-feed bitumen that has been treated to remove most of the large solids and all of the water. As discussed in previous studies,36-39 native solids are usually associated with the asphaltene fraction and coprecipitate with asphaltenes. Hence, because the material precipitated from bitumen is actually a mixture of asphaltenes and solids, it is referred to as asphaltene-solids. To precipitate asphaltene-solids, reagent-grade n-heptane purchased from Van Waters & Rogers Ltd. (VWR) was added to Athabasca bitumen in a 40:1 (cm3/g) ratio. The mixture was sonicated for 45 min at room temperature and then left to equilibrate for 24 h. After settling, the supernatant was filtered through a Whatman no. 2 filter paper without disturbing the whole solution. At this point, approximately 10% of the original mixture remained unfiltered. Additional n-heptane was added to this solution in a 4:1 (cm3/g) ratio of n-heptane to the original bitumen mass. The mixture was sonicated for 45 min, left overnight, and finally filtered using the same filter paper. The yield of asphaltene-solids from bitumen was 15.1% as reported previously.37 To separate asphaltenes from fine solids, asphaltene-solids were dissolved in reagent-grade toluene purchased from VWR in a ratio of 100 cm3 of toluene per gram of asphaltene-solids. The mixture was sonicated for 20 to 40 min to ensure complete asphaltene dissolution and solids dispersion. The mixture was allowed to stand for 1 h, after which it was centrifuged at 4000 rpm (1640 RCF) for 6 min. To recover asphaltenes, the super(33) Acevedo, S.; Escobar, G.; Gutierrez, L. B.; Rivas, H.; Gutierrez, X. Colloids Surf., A 1993, 71, 65. (34) Li, M.; Xu, M.; Ma, Y.; Wu, Z.; Christy, A. Fuel 2002, 81, 1847. (35) Aske, N.; Orr, R.; Sjoblom, J. J. Dispersion Sci. Technol. 2002, 23, 809. (36) Sztukowski, D. M.; Yarranton, H. W. J. Dispersion Sci. Technol. 2004, 25, 299. (37) Sztukowski, D. M.; Yarranton, H. W. J. Colloid Interface Sci. 2005, 285, 821. (38) Gafonova, O. V.; Yarranton, H. W. J. Colloid Interface Sci. 2001, 241, 469. (39) Yarranton, H. W.; Masliyah, J. H. AICHE J. 1996, 42, 3533.
Sztukowski and Yarranton natant was decanted and the solvent evaporated until only dry asphaltenes remained. Asphaltenes and fine solids made up 97 and 3 wt %, respectively, of the asphaltene-solids mixture.37 Only solids-free asphaltenes were used in this work. Interfacial Tension. Interfacial tension (IFT) was measured using an IT Concept Tracker drop shape analyzer (DSA). The hydrocarbon phase was loaded into a syringe and injected through a U-shaped needle into an optical glass cuvette containing reverse osmosis water provided by the University of Calgary water plant. A droplet was formed at the tip of the needle and illuminated. The profile of the droplet was captured using a CCD camera and analyzed using a video image profile digitizer board connected to a personal computer. The bench was placed on a wooden platform and a foam mat in order to remove potential vibrations. The shape of the drop results from the balance between the forces of interfacial tension and gravity. The interfacial tension force acts to minimize the surface area and tends to pull the droplet into a spherical shape. The gravity force acts upward on the droplet and therefore tends to elongate the droplet because the droplet phase is less dense than the phase in the cuvette. The equations determining the drop profile can be solved from the Laplace equation and hydrostatic calculations.40 As long as the density of the two phases and the shape of the droplet are known, the equations can be fitted to the measured drop profile, and the interfacial tension can be obtained from the best-fit parameters. A Laplacian shape was observed for drops varying from 8 to 30 µL. In the current work, 22 µL droplets were employed for all measurements. IFT values of several organic solvents over distilled water were measured with the DSA and found to be within 1% of published values. In the current work, the DSA was used to gather the interfacial tension of asphaltene-toluene solutions over water for times up to 16 h. Measurements were made every second during the first 2 to 3 min after drop formation and then every 10 s. Elasticity. Interfacial elasticity, , is defined as follows
)
dγ dγ )A d ln A dA
(1)
where γ is the interfacial tension and A is the interfacial area. Elasticity is a measure of the change in interfacial energy with a change in interfacial area. In an oscillating system, elasticity is a complex quantity and has both a real and an imaginary component defined as follows
) ′ + i′′
(2)
where ′ is the real component, or elastic modulus, and ′′ is the imaginary part, or viscous modulus. The total modulus represents a change in the energy of the system with a corresponding change in area. The elastic modulus can be thought of as the energy stored in the system, and the viscous modulus, as the loss energy. The elastic and viscous moduli can also be expressed in terms of the total modulus, ||, and phase angle, φ, as follows:
′ ) d ) || cos φ
(3)
′′ ) ωηd ) || sin φ
(4)
and
The viscous modulus is the product of the frequency of oscillation, ω, and the interfacial viscosity, ηd. In this work, sinusoidal oscillations were employed. The measured total modulus depends on a number of experimental parameters including the size of the drop, the amplitude of oscillations, the frequency of oscillations, and the interface aging time. As mentioned earlier, the initial size of the drop was 22 µL. This corresponds to an interfacial area of approximately 38 mm2. Jafari41 examined the effect of the (40) Bashforth, F.; Adams, J. C. An Attempt to Test the Theories of Capillary Action; Cambridge University Press: Cambridge, England, 1883. (41) Jafari, M. MSc. Thesis. University of Calgary, Calgary, 2005.
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tension to the bulk concentration of asphaltenes, (2) calculation of the instantaneous elasticity, and (3) calculation of the elastic and viscous moduli. Relation of Interfacial Tension to Bulk Asphaltene Concentration. First, the interfacial tension is modeled using the binary form of the Butler surface equation of state (SEOS)42,44
[
Figure 1. Sinusoidal oscillation of drop area and IFT response for 1 kg/m3 Athabasca asphaltenes at a toluene/water interface. Interface aging time ) 1 h, ω ) 0.1 Hz. amplitude of the oscillation on the measured elastic and viscous moduli. For amplitudes up to 45% of the initial area, a Laplacian drop was maintained, and the total modulus did not vary significantly from that measured when the amplitude was as low as 2%. However, most experimenters have used amplitudes that do not exceed 10% of the initial area.13,35,42 In the current work, the amplitude of oscillations was 4 mm2, or 11% of the initial area. The elastic and viscous moduli can be measured as long as the interfacial tension does not change significantly during the interval in which the drop is oscillated. In the current study of asphaltene-toluene/water systems, the minimum time after which measurements were made was 10 min; that is, a droplet was formed at the tip of the capillary, and the IFT was recorded for 10 min. No oscillations were applied during the aging time because it has been shown that for systems containing asphaltenes at concentrations exceeding 0.1 kg/m3, continuous oscillation results in erroneous measurements that are excessively affected by diffusion.35,41 In the current study, the interface aging time was varied from 10 min to 16 h. Note that a fresh drop was created for each aging time. After the desired aging time had elapsed, the droplet was oscillated at a chosen frequency for a total of 10 complete cycles. The frequencies employed in the current study were 0.02, 0.033, 0.1, 0.2, and 0.5 Hz (periods of 50, 30, 10, 5, and 2 s, respectively). Note that 50 s oscillation periods were applied only to drops aged for 4 or more hours. Also note that elasticity at a frequency higher than 0.5 Hz could not be measured because there was too much scatter in the IFT response. Figure 1 presents a typical example of the data collected with the DSA. The example system is a droplet of a solution of Athabasca asphaltenes and toluene in a water medium. The droplet was aged for 1 h and then oscillated at a frequency of 0.1 Hz (10 s period) with an amplitude of 4.1 mm2. The initial drop area was 37.8 mm2. The measured phase angle was 16.6°, and the measured total modulus was 10.2 mN/m. Figure 1 shows that the DSA data has some scatter, a byproduct of minor inertial effects and the finite speed of the motor. However, the data can be smoothed using the Tracker’s internal algorithms, as shown by the ideal sinusoids imposed on both the area and IFT curves. It was found that data smoothing was important for frequencies exceeding 0.2 Hz and at asphaltene concentrations lower than approximately 0.01 kg/m3; under all other conditions unsmoothed data and smoothed data resulted in the same phase angle and elasticity.
(42) Lucassen-Reynders, E. H.; Cagna, A.; Lucassen, J. Colloids Surf. 2001, 186, 63.
]
)
where subscripts 1 and 2 refer to the solvent and surfactant, respectively, and Π is the surface pressure, that is, the difference between the interfacial tension between the pure solvent (toluene) and water, γo, and the interfacial tension of the solvent and surfactant versus water, γ. R is the universal gas constant, T is temperature, a1 is the interfacial area of a solvent molecule, S2 is the ratio of the interfacial area of the surfactant molecule to the area of the solvent molecule, θ2 is the fractional area surface coverage by the surfactant, and H is the enthalpy of mixing at infinite dilution. The first, second, and third terms in eq 5 represent the ideal entropy of mixing, the nonideal entropy of mixing caused by the difference in size between solvent and surfactant molecules, and the enthalpy of mixing, respectively.42 The fractional surface coverage of the solute, θ2, is related to the surfactant concentration in solution, c2, through the following equation
c′2 )
c2 c2,θ)0.5
)
2θ2 [2(1 - θ2)]
S2
[
exp
]
S2H (1 - 2θ2) RT
(6)
where c′2 is the reduced concentration and c2,θ)0.5 is the half-saturation concentration. Note that the concentration given in eq 6 is the molar concentration. Also note that, for ternary or higher-order systems, equations similar to eq 6 apply for the reduced concentration of the surfactant molecules in question.45 Equation 6 reduces to the Frumkin equation when the solvent and surfactant molecules are of equal size (i.e., S2 ) 1) and further to the Langmuir equation when the enthalpy of mixing is ignored (H/RT ) 0). Calculation of Instantaneous Elasticity. The SEOS is used to establish the relationship between the surfactant concentration (or fractional surface coverage) and the reduction in interfacial tension (or increase in surface pressure). The second step is to find the instantaneous elasticity, which is given by
o )
dγ d ln Γ
(7)
or the derivative of interfacial tension (eq 5) with respect to the natural logarithm of the molar area of the interface, Γ. Note that eq 7 is independent of the SEOS used. For the binary form of the Butler SEOS, the resultant instantaneous elasticity is given by
Theory The interfacial tension and elasticity data of the asphaltene/toluene system was modeled using the Lucassen-van den Tempel (LVDT) approach.43 Three major steps were applied: (1) relation of the interfacial
(
RT 1 H 2 θ ln(1 - θ2) + 1 θ + a1 S2 2 RT 2 (5)
Π ) γo - γ ) -
o ) -
[
(
)
]
θ2 RT 1 H θ + 2 θ22 + 1a1 (θ2 - 1) S2 2 RT
(8)
(43) Lucassen, J.; Van Den Tempel, M. Chem. Eng. Sci. 1972, 27, 1283. (44) Butler, J. A. V. Proc. R. Soc. London, Ser. A 1932, 135, 348. (45) Lucassen-Reynders, E. H. Colloids Surf., A 1994, 91, 79.
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Figure 2. Asphaltene apparent (self-associated) molar mass as a function of asphaltene concentration.
Calculation of Elastic and Viscous Moduli. The final step is to calculate the total, elastic, and viscous moduli. A key assumption is that relaxation is purely diffusional. The effect of diffusion is accounted for as follows43
|| )
o [1 + 2ζ + 2ζ2]1/2
(9)
where ζ is a diffusion parameter given by
ζ2 )
D dc 2ω dΓ
2
( )
(10)
and D is the diffusivity of the surfactant. Also, the characteristic time of diffusion, τD, is related to the diffusional parameter and the frequency, ω, through the following:
τD )
1 ζ2ω
(11)
The elastic and viscous moduli can be found individually from
1+ζ ′ ) d ) o 1 + 2ζ + 2ζ2
(12)
ζ ′′ ) ωηd ) o 1 + 2ζ + 2ζ2
(13)
and
Note that for an SEOS and the above elasticity expressions to be valid the adsorption of the surfactant on the interface must be reversible, equilibrium must be attained, and there can be no mechanical film present. Results and Discussion All asphaltene concentrations were measured on a mass basis; however, the surface equation of state is based on molar concentrations. The relationship between asphaltene molar mass and asphaltene concentration was determined with vapor pressure osmometry (VPO) and is presented in Figure 2.46 Consistent with previous work,11 the molar mass increases with increasing concentration, (46) Sztukowski, D. Ph.D. Thesis. University of Calgary, Calgary, 2005.
Figure 3. Effect of frequency on the total modulus of Athabasca asphaltenes dissolved in toluene at concentrations from 0.005 to 20 kg/m3. The interface was aged for 10 min. The lines are visual aides.
suggesting that asphaltene monomers self-associate into larger aggregates as their concentration in the bulk solution increases. Because there is some controversy over asphaltene molar mass, the data are presented in terms of molar concentration (mol/m3) when compared with modeling results but in mass concentration (kg/m3) otherwise. Interfacial Rheology at 10 Minute Aging Time. Figure 3 shows the effect of frequency on the measured total modulus of asphaltenes in toluene after 10 min of interface aging. At low frequencies, the interfacial area changes relatively slowly, and there is sufficient time for diffusion from the bulk phase or within the interface to affect the measurement. Diffusion acts to reduce the change in interfacial tension and therefore reduces the measured elasticity. As the frequency increases, the total elasticity eventually reaches a plateau where diffusion no longer affects the measurement. The plateau can be considered to be the instantaneous elasticity, o. The instantaneous elasticity is an intrinsic property of the interfacial film. Figure 3 shows that diffusion effects are apparent in all of the measurements except at asphaltene concentrations below 0.01 mol/m3 (0.02 kg/m3) and then only at frequencies above 0.1 to 0.2 Hz. These results are consistent with those of Freer and Radke.12 Figure 3 also shows that the trends with concentration are approximately the same at any given frequency. Nonetheless, the effect of concentration was examined in detail at four different frequencies: 0.033, 0.1, 0.2, and 0.5 Hz. The total, elastic, and viscous moduli versus asphaltene concentration after 10 min of interface aging are shown in Figure 4. At low concentrations, the measured total modulus corresponds to the instantaneous elasticity because the effects of diffusion are negligible. However, as the concentration (or correspondingly the surface pressure) increases, the effects of diffusion increase. During drop expansion, the interface is stretched, and asphaltene-free pockets develop on the interface. At high concentrations, there is a large supply of asphaltenes in the bulk; therefore, a large concentration gradient exists between the stretched areas of the interface and the bulk solution. Hence, molecules migrate to the interface quickly (i.e., diffusion is very fast), and interfacial tension increases less than it would if no diffusion occurred. During expansion and contraction, the effect is to reduce the total modulus.
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Figure 4. Measured and modeled elasticity of solutions of Athabasca asphaltenes in toluene over water for oscillation frequencies f of (a) 0.033, (b) 0.1, (c) 0.2, and (d) 0.5 Hz. The interface was aged for 10 min.
Figure 4 shows that the interface is mostly elastic (i.e., negligible viscous modulus) for asphaltene concentrations less than 0.01 mol/m3 (0.02 kg/m3). Diffusion begins to affect the measurements at approximately 0.01 mol/m3, and a viscous modulus appears. Modeling Interfacial Rheology. Interfacial Tension. The SEOS is first fit to interfacial tension data. The fit for interfacial tension measurements of asphaltenes in toluene versus water after 60 s, 10 min, and 4 h of contact is shown in Figure 5. The fit parameters are the enthalpy of mixing, the area of an asphaltene molecule, the shape factor, and the half-saturation concentration. For lack of a better value and the sake of simplicity, the enthalpy of mixing was assumed to be negligible. The average interfacial area of an asphaltene that best fit the data was 1.4 nm2. This value is within the range reported in the literature27,47,48 and is within 7% of the area obtained from a plot of interfacial tension versus the logarithm of asphaltene concentration for the same Athabasca asphaltenes.11 Hence, it appears that the Gibbs isotherm is a good approximation of the molecular area of an adsorbed asphaltene, even if the Gibbs isotherm assumes Langmuirtype adsorption (because S2 ) 1). However, the Gibbs isotherm would not fit the IFT for concentrations less than 0.01 mol/m3. The ratio of the molecular areas, S2, was set to 5 so as to obtain a realistic interfacial area for toluene, 0.28 nm2. (47) Rogel, E.; Leo´n, O.; Torres, G.; Espidel, J. Fuel 2000, 79, 1389. (48) Bhardwaj, A.; Hartland, S. Ind. Eng. Chem. Res. 1994, 33, 1271.
Figure 5. Measured and modeled interfacial tension of Athabasca asphaltenes dissolved in toluene versus water at 23 °C and interface aging times of 60 s, 10 min, and 4 h.
The area of toluene is expected to be slightly larger than the area of benzene. On the basis of the lengths of the bonds between carbon atoms in the benzene molecule, the area is about 0.15 nm2. Also, the average area occupied by a molecule on an interface will likely be larger than the size of the molecule itself. The half-saturation concentrations were then adjusted to fit the low-concentration data. Concentrations of 0.07, 0.03, and 0.007 mol/m3 were found to fit the data at 60 s, 10 min, and 4 h, respectively. Note that theoretically the
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Figure 6. Diffusion coefficient for Athabasca asphaltenes dissolved in toluene as a function of asphaltene concentration, determined from eq 14.
half-saturation concentration is applicable at equilibrium and should therefore be constant. However, the equilibrium value of the interfacial tension of asphaltene solutions over water is difficult to assess because mechanical rigidity affects the measurements relatively quickly. Hence, the half-saturation constant has been used as a fitting parameter. In fact, as discussed later, the LVDT model assuming purely diffusional relaxation is valid only at short interface aging times (i.e., before the formation of mechanical films). Hence, the half-saturation constants are only physically meaningful at very short aging times. Elastic and Viscous Moduli. To use the LVDT model, the diffusion coefficient must be known for asphaltenetoluene solutions over water. The diffusion coefficient, D, can be deduced from the interfacial tension at short times using the equation given by Campanelli and Wang49
x3Dt 7π
γ(t) ) γo - 2RTco
(14)
where γ and γo are the interfacial tension of the surfactant-solvent solution and pure solvent over water (or another immiscible liquid), respectively, R is the universal gas constant, T is the temperature, co is the bulk concentration of surfactant, and t is the time. Equation 14 shows that for the short-time diffusion approximation to apply, a plot of γ versus t1/2 should be linear. The diffusion coefficient can then be deduced from the slope of the plot. Figure 6 shows the calculated diffusion coefficient as a function of bulk asphaltene concentration. Equation 14 was found to be useful only at low asphaltene concentrations. At asphaltene concentrations greater than 0.2 kg/m3 (0.1 mol/m3), the interfacial tension decreased during droplet formation, and the value of IFT at time zero (i.e., when the droplet was fully formed) was less than the pure-solvent IFT. Norinaga et al.50 used pulsed field gradient spin-echo NMR to determine the diffusivity of Kafji vacuum residue asphaltenes in pyridine. They found that the diffusivity decreased from about 1.4 × 10-10 to 0.9 × 10-10 m2/s when the bulk asphaltene concentration increased from roughly 1 to 20 kg/m3. The data in Figure 6 show a similar decrease in diffusion coefficient with concentration but are approximately 1 order of magnitude smaller than the values given in the work of Norinaga et al. (49) Campanelli, J. R.; Wang, X. H. J. Colloid Interface Sci. 1999, 213, 340. (50) Norinaga, K.; Wargardalam, V. J.; Takasugi, S.; Iino, T.; Matsukawa, S. Energy Fuels 2001, 15, 1317.
Figure 7. Measured and modeled elasticity of solutions of Athabasca asphaltenes in toluene over water. The oscillation is frequency 0.033 Hz, the interface was aged for 10 min, and D ) 3 × 10-11 m2/s.
As a first pass, the diffusion coefficient was taken to be 3 × 10-11 m2/s, which falls in the range shown in Figure 6. The instantaneous elasticity, the elastic modulus, and the viscous modulus were then determined from eqs 8, 12, and 13, respectively. The predictions are compared with the experimental data for 10 min of aging and an oscillation frequency of 0.033 Hz in Figure 7. It is obvious from Figure 7 that the match was successful only for asphaltene concentrations less than 0.005 mol/m3. To determine if the whole range of asphaltene concentration could be matched, the diffusion coefficient was treated as a fitting parameter. It was found that a concentrationdependent asphaltene diffusivity of the following power law form
D ) ac2b
(15)
was required to fit the elastic and viscous moduli in Figure 7 where a and b are constants. The numerical values of a and b that best fit the elasticity data are 3 × 10-14 m2/s and -0.6, respectively. Equation 15 indicates that the required diffusivity at the lowest asphaltene concentration considered here is approximately 10-12 m2/s and decreases to approximately 10-14 m2/s at the highest concentrations. Hence, the diffusivity required to match the full range of asphaltene concentration is anywhere from two to four orders of magnitude lower than the values of Norinaga et al.50 or the values obtained from the short-time diffusion approximation shown in Figure 6. Why is the diffusivity needed to match the full range of asphaltene concentration so much smaller? One reason is that the diffusion coefficient relevant to the relaxation of asphaltenes at the interface is not the bulk diffusion coefficient as deduced from the short-time diffusion approximation. Although asphaltenes diffuse to the interface quite quickly, their movement at the interface during droplet expansion/contraction may be retarded because of the formation of skins at the interface. The formation of viscous films may result in slower diffusion along the interface during oscillation; therefore, the bulk diffusion may not be representative during interfacial relaxation. Sheu et al.51 speculated that the rearrangement of asphaltenes on the interface may be slower than the (51) Sheu, E. Y.; Storm, D. A.; Shields, M. B. Fuel 1995, 74, 1475.
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Figure 8. Effect of interface aging time on the elastic and viscous moduli of Athabasca asphaltenes dissolved in toluene. The oscillation frequency is 0.033 Hz. Closed symbols - elastic modulus, open symbols - viscous modulus. The lines are visual aides.
diffusion process and can therefore become the “bottleneck” of the equilibrium kinetics. This argument is supported by the work of Freer and Radke.12 As mentioned previously, they measured the elastic and viscous moduli of an asphaltene-toluenewater interface at an asphaltene concentration of 0.005 wt % (approximately 0.05 kg/m3) over six decades of frequency. They used a combination of the LVDT model and a Maxwell viscoelastic model to match their data. Because their data was collected at a constant asphaltene concentration, the instantaneous elasticity predicted from a surface equation of state was not required. Rather, they regressed o, the characteristic time of diffusion, τD, (eq 11), and two other parameters that were required for the Maxwell viscoelastic part of the model until a satisfactory match was obtained over the entire frequency range. They found a characteristic diffusion time of 25 s. In our work, a similar characteristic time of diffusion of 88 s is obtained at a concentration of 0.05 kg/m3 (0.03 mol/m3). Hence, both applications of the LVDT model require similar diffusivities. Figure 4a-d compares the predicted instantaneous, elastic, and viscous moduli with experimental data for asphaltene-toluene over water interfaces aged for 10 min. The same values of a and b in eq 15 are used for each oscillation frequency. The model matches appear to be satisfactory, although the viscous modulus is slightly overpredicted at lower frequencies. Effect of Interface Aging. The elastic and viscous moduli of asphaltenes at a toluene/water interface are given in Figure 8 for an oscillation frequency of 0.033 Hz. The data are reported versus mass concentration because the apparent asphaltene molar masses were not measured over time. The elastic modulus increases significantly over 16 h, whereas the viscous modulus increases only marginally. The largest increases in the moduli occur for “intermediate” asphaltene concentrations, that is, concentrations varying between 0.01 and 1 kg/m3 (0.05 and 0.5 mol/m3). The rise in the moduli is consistent with other work.12-15,35 Unfortunately, a quantitative comparison of the data shown in Figure 8 with the literature is difficult because the asphaltene source, concentration, and solvent vary significantly. Furthermore, some of the studies were conducted on crude oil drops rather than asphalteneheptol drops.13,35 The effect of resins and other surfaceactive constituents of the oil impedes meaningful com-
Figure 9. Measured and modeled elasticity of solutions of Athabasca asphaltenes in toluene over water for oscillation frequencies f of (a) 0.033 and (b) 0.1 Hz. The interface was aged for 4 h.
Figure 10. Film ratio of the interface of droplets of Athabasca asphaltenes in toluene surrounded by water.41
parisons. Nonetheless, the general trends regarding the effect of contact time are consistent. The increase in the moduli over time could not be predicted with the Lucassen-van den Tempel model, as shown in Figure 9. A likely explanation for the model failure is that irreversible adsorption occurs and a mechanical film forms. Figure 10 shows the film ratio of asphaltene-toluene/water interfaces as a function of time and asphaltene concentration.41 The film ratio is the area of the interface at which the interfacial film crumples over the initial area of the interface. Such crumpling is evidence of rigid, irreversible film formation. Figure 10
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shows that film ratios appear even at very short aging times (less than 10 min). For the SEOS-LVDT approach to be valid, asphaltenes must be adsorbed reversibly. Therefore, it is not surprising that the modeling approach required modified diffusivities at short aging times and failed at longer times. The small diffusion coefficients required to match the data suggest that asphaltene diffusion along the interface, rather than bulk diffusion to and from the interface, dominates the rheology. Therefore, an SEOS-LVDT modeling approach does not strictly apply to asphaltene interfacial films. It is possible to use a viscoelastic models such as the Maxwell model used by Freer and Radke;12 however, curve-fitted parameters are required. Conclusions The rheological properties of asphaltene-toluene/water interfaces are sensitive to asphaltene concentration and aging time. The elastic modulus reached a maximum at asphaltene concentrations of approximately 0.1 to 0.2 kg/ m3 (0.05 to 0.1 mol/m3) and decreased over the range of concentrations typically encountered in oil field emulsions. Hence, oils with higher asphaltene concentrations can potentially form less stable emulsions than oils with low asphaltene concentrations. The elastic modulus increases with aging at all asphaltene concentrations. The increasing modulus is consistent with the gradual formation of interfacial skins. The trend is also consistent with the observation that aged emulsions are typically more stable than fresh emulsions. The viscous modulus did not increase with aging time. The interfacial rheology of fresh asphaltene-toluene/ water interfaces can be modeled with the LVDT approach. However, it is necessary to use a concentration-dependent asphaltene diffusivity that is orders of magnitude smaller than the expected bulk-phase diffusivity. The low diffusivity suggests that diffusion at the interface rather than diffusion in the bulk phase controls the time-dependent interfacial behavior. There may be resistance to mass transfer at the interface because the asphaltenes have formed a surface network. LVDT does not account for molecular interactions at the interface; therefore, strictly speaking, the model is invalid for the asphaltene-toluene/
Sztukowski and Yarranton
water interfaces. Furthermore, aging effects cannot be accounted for with this type of model. Acknowledgment. The financial support of NSERC, Alberta Ingenuity, and the Alberta Energy Research Institute is greatly appreciated. We also thank Syncrude Canada Ltd. for bitumen samples. Nomenclature a ) fitting parameter a ) interfacial area of a molecule (nm2/molecule) A ) area of the drop at any given time (mm2) b ) fitting parameter co ) bulk concentration of surfactant (mol/m3) c′2 ) reduced concentration (-) c2,θ)0.5 ) half-saturation concentration (mol/m3) D ) diffusion coefficient (m2/s) H ) enthalpy of mixing (J/mol) R ) universal gas constant (8.314 J/mol‚K) S2 ) shape factor, ratio of the area of a surfactant molecule to the area of a solvent molecule t ) time (s) T ) temperature (K) Greek Symbols γo ) interfacial tension of pure solvent over water (mN/m) γ ) interfacial tension of surfactant-solvent solution over water (mN/m) Γ ) moles adsorbed per area of interface (mol/m2) ) total modulus (mN/m) ′ ) elastic modulus (mN/m) ′′ ) viscous modulus (mN/m) d ) interfacial elasticity (mN/m) ζ ) diffusion parameter (-) ηd ) interfacial viscosity (mN/m‚s) θ ) fractional surface coverage (-) τD ) characteristic time of diffusion (s) φ ) phase angle (rad) Π ) surface pressure (mN/m) ω ) frequency (rad/s) Subscripts 1 ) solvent (toluene) 2 ) surfactant (asphaltenes) LA051921W
