Some Preliminary Results on a Physico-Chemical Characterization of

To reassure the legitimacy of the hard sphere model, Sheu used Campbell and ..... It is still in the ballpark of the 495 and 290 Da obtained using the...
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Energy & Fuels 2000, 14, 845-853

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Some Preliminary Results on a Physico-Chemical Characterization of a Hassi Messaoud Petroleum Asphaltene Y. Bouhadda,† D. Bendedouch,† E. Sheu,*,‡ and A. Krallafa† Laboratoire de Physico-Chimie et de Modelisation, Institut de Chimie Universite´ d’Oran (Es-Senia), Oran 31000, Algeria, and Vanton Research Laboratory, #7 Olde Creek Place, Lafayette, California 94549 Received October 6, 1999. Revised Manuscript Received January 26, 2000

Viscosimetry, tensiometry, and X-ray diffraction have been employed to determine physicochemical and structural properties of an Algerian asphaltene in solution. A new viscosity analysis scheme was adopted to extract information about the shape of the asphaltene aggregates, the solvation, and the inter-aggregate interactions. The average molecular weight (MW) was deduced by combining the surface tension and viscosity studies. The average MW of this asphaltene appears to be small in comparison with those measured by vapor pressure osmometry (VPO) but comparable with the recent results from mass spectroscopy, atomic force microscopy, and fluorescent spectroscopy. X-ray measurements show that asphaltene molecules aggregate, even in the neat phase, and an average aggregate is composed of 4-5 aromatic sheets. The viscosity study suggests that asphaltenes in toluene solutions behave in accordance with a spherical micellar model containing aggregated asphaltene molecules with a substantial amount of solvation.

Introduction In the past two decades, petroleum asphaltenes have been extensively studied because of their impact on the oil industry. In addition to changing the physical properties, such as density and viscosity of crude oils, it is also responsible for several technical problems commonly encountered during production, recovery, pipeline transportation, and even in refining.1-8 These problems usually arise from phase separation and/or precipitation of asphaltene, which likely result from its strong self-association propensity. Asphaltene is conventionally defined as the fraction of crude insoluble in low-boiling n-paraffin solvents but soluble in toluene under certain conditions.8 It is a class of material with varieties of molecular structures, rather than a substance with a well-defined molecular struc* Corresponding author. † Institut de Chimie Universite ´ d’Oran (Es-Senia). ‡ Vanton Research Laboratory. (1) See, for examples, the chapters in AsphaltenesFundamentals and Applications; Sheu, E. Y.; Mullins, O. C., Eds.; Plenum Press: New York, 1995. (2) See, for examples, the chapters in Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998. (3) Speight, G. The Chemistry and Technology of Petroleum; Marcel Dekker: New York, 1980. (4) Speight, J. G. Fuel Science and Technology Handbook; Marcel Dekker, New York, 1993; pp 1190. (5) Yen, T. F. In The Future of Heavy Crude and Tar Sands; Meyer, R. F., Steele, C. T., Eds.; McGraw-Hill: New York, 1980; pp 174-179. (6) Hassket, C. E.; Tartera, M. J. Pet. Technol. 1965, April, 387391. (7) Tuttle, R. N. J. Pet. Technol. 1983, June, 1192-1196. (8) Aczel, T.; Williams, R. B.; Chamberlain, N. F. Chemistry of Asphaltenes, Advances in Chemistry Series 195; Bunger, J. W., Li, N. C., Eds.; American Chemical Society: Washington, DC, 1981; p 237.

ture. The first hypothetical colloidal structure of asphaltene dispersions was proposed by Saal and Pfeiffer in the 1940s.9 Since then, many molecular models have been proposed to describe their physicochemical properties. Among them, the commonly accepted one was proposed by Dickie and Yen.10-11 They described an asphaltene “particle” as a superposition of many aromatic sheets containing heteroatoms attached with aliphatic chains. Metals such as iron, vanadium, and nickel under porphyrinic structures are often present as the heteroatoms.12-13 Other than the molecular structures, the solution behavior appears to be crucial and likely responsible for many practical problems. To reveal microscopically the structural behavior and their relevance to industrial practices, many techniques have been applied to characterize these complex molecules,14-19 as well as their physical and chemical properties in solutions. Through these studies, it gradually becomes clear that the impact of asphaltenes heavily depends on their molecular weight and self-association propensity. It is thus neces(9) Pfeiffer, J. P.; Saal, R. N. J. J. Phys. Chem. 1940, 44, 139. (10) Dickie, J. P.; Yen, T. F. Anal. Chem. 1982, 39 (14), 1487-1852. (11) Erdman, J. G.; Pollak, S. S.; Yen, T. F. Anal. Chem. 1961, 33, 1587-1594. (12) Pearson, C. D.; Green, J. B. Energy Fuels 1993, 7, 338. (13) Freedman, D. A.; Saint Martin, D. C.; Boreham, C. J. Energy Fuels 1993, 7, 194. (14) Brown, J. K.; Ladner, W. L. Fuel 1960, 36, 79. (15) Maekawa, Y.; Yoshida, T.; Yoshida, Y. Fuel 1979, 58, 864. (16) Barron, P. F.; Bendall, M. R.; Armstrong, R. J.; Athkins, A. R. Fuel 1984, 63, 1276. (17) Cookson, D. J.; Smith, B. E. Fuel 1987, 1, 11. (18) Overfield, R. E.; Sheu, E. Y.; Sinha, S. K.; Liang, K. S. Fuel Sci. Technol. Int. 1989, 7, 611. (19) Ravey, J. V.; Decouret, G.; Espinat, D. Fuel 1988, 67, 1560.

10.1021/ef9902092 CCC: $19.00 © 2000 American Chemical Society Published on Web 05/06/2000

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sary to accurately estimate the MW and the phase behavior whenever dealing with an asphaltene-rich petroleum liquid, in order to set up an appropriate process to avoid negative impact. Because both selfassociation phenomenon and the MW determination require microscopic measurement, the spectroscopic methods become handy. However, using spectroscopic methods to characterize a complex system requires intensive and complicated data analyses. As a result, combination of microscopic and macroscopic measurements becomes an alternative. On one hand, the microscopic measurements can reveal the characteristics on the molecular/colloidal length scales, and on the other hand the macroscopic measurements can provide thermodynamic and transportation properties on larger length scale. More importantly, the macroscopic measurements are often simple and portable, which is convenient for field applications. In many cases, one can combine these measurements to reasonably describe the colloidal structures and their corresponding physicochemical properties which is important for practical applications. As mentioned earlier, asphaltenes have high tendency to self-associate, even in dilute solutions1,20-21. This makes it very difficult to determine the true MW.22-24 To date, the techniques considered suitable for MW determination are tensiometry,25 microcalorimetry,20 mass spectrometry,26 and fluorescence spectroscopic techniques.27-29 Even though these techniques are considered credible, they often arrive at different MW, critical micellar concentration (CMC), and solution properties. This is largely due to variation of asphaltenes from different sources and their molecular complexity. Despite these difficulties, the combination of surface tension and viscosity studies can still provide viable information about the MW, as well as the solution properties of these complicated materials as demonstrated previously.30-31 Since Sheu et al.32 and Bardon et al.27 succeeded in applying tensiometric and viscosimetric theories to characterize asphaltene solutions, certain asphaltene behaviors are understood. Their results are in favor of Yen’s structural model. In this paper we present the preliminary results of tensiometry, X-ray, and viscosity investigation on an Algerian asphaltene recovered from a deposit. The (20) Anderson, S. I.; Birdi, K. S. J. Colloid Interface Sci. 1991, 142, 497. (21) Speight, J. G.; Moschopedis, S. E. Fuel 1977, 56, 344. (22) Chung, K. E.; Anderson, L. L.; Wiser, W. H. Fuel 1978, 58, 847. (23) Moschopedis, S. E.; Freyer, J. F.; Speight, J. G. Fuel 1976, 55, 227. (24) Scotti, R.; Montanari, L. In Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998. (25) Sheu, E. Y.; De Tar, M. M.; Storm, D. A. Surface Activity and Dynamics of Asphaltenes. In Asphaltene Particles In Fossil Fuel Exploration, Recovery, Refining, and Production Processes; Sharma, M. K., Yen, T. F., Eds.; Plenum Press: New York, 1994; 115 pp. (26) DeCanio, S. J.; Nero, V. P.; DeTar, M. M.; Storm, D. A. Fuel 1990, 69, 1233-1236. (27) Bardon, C.; Barre´, L.; Espinat, D.; Guille, V.; Li, Min Hui; Lambard, J.; Ravey, J. C.; Rodenberg, E.; Zemb, T. Fuel Sci. Technol. Int. 1996, 14 (1 and 2), 203. (28) Xu, Y.; Koga, Y.; Strausz, O. P. Fuel 1995, 74 (7), 960-964. (29) Groenzin, H.; Mullins, O. C. Book of Abstracts; 218th ACS National Meeting, New Orleans, Aug 22-26, 1999. (30) Sheu, E. Y.; Storm, D. A. Fuel 1994, 73 (8), 1368. (31) Reenrik, H. Ind. Eng. Chem. Prod. Res. Dev. 1973, 12 (1), 82. (32) Sheu, E. Y.; De Tar, M. M.; Storm, D. A.; DeCanio, S. J. Fuel 1992, 71, 299.

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intention was to characterize this asphaltene and to critically test the available analysis schemes for treating surface tension and viscosity data. Other than the analysis scheme used by Sheu et al.,30 a new analysis scheme based on Huggin’s equation was applied to interpret the low shear viscosity, which can better describe the solvation and interparticle (in this case the asphaltene aggregates) interactions. Because both viscosity and surface tension measurements are simple and handy and if the analyses presented in this work can provide reasonably accurate information, one can apply them in the field. Samples and Experiments Samples. The asphaltenes used in this study were derived from a deposit recovered from an oil well in the Hassi Messaoud field (Algeria) at a 3077 m depth. The deposit was washed with hot chloroform (T ) 50 °C) to separate minerals. Asphaltene extraction was performed with a Soxhlet extractor with n-heptane followed by toluene. This was a modified procedure described by M. Neurock et al.33 with the extraction time extended to 32 h. For surface tension and viscosity experiments, stock solutions of 1 and 20 wt %, respectively, in toluene were prepared at room temperature, and diluted afterward by adding toluene (analytical reagent). In the surface tension experiment, measurements were taken 24 h after dilution to avoid the kinetic effect. Measurements. The X-ray diffraction measurements were performed on a Philips PW X-ray diffractometer using the KR ()1.54 Å) wavelength. The sample measured was in neat phase with diffraction angle range scanned from 2° to 80°. The measurements were performed at ambient temperature. The density (mass/unit volume) of solid asphaltene was measured using an Ohaus densitometer. From the measured density and using the Van Crevelin34 correlation functions, the hydrogen percentage was calculated and from which the carbon percentage can be derived. Surface tension was measured using a De Nuoy tensiometer (Kru¨ss K10). The measurements were performed as a function of asphaltene concentration in toluene by dilution of the stock solution. Low shear viscosity of the Hassi Messaoud asphaltene solutions was measured using an unblholde Viscologic TI Viscometer. A series of solutions of different asphaltene concentrations were measured (from 0.01 to 0.15 asphaltene volume fraction). In this concentration regime, the asphaltenic solutions were found to be Newtonian. Theories and Analysis Schemes X-ray Diffraction. To quantitatively analyze the X-ray diffraction data, the areas under the peaks and the reticular distances were calculated, from which the procedure established by Dickie and Yen10 can be used (33) Neurock, M.; Nigam, A.; Trauth, D.; Klein, M. T. Chem. Eng. Sci. 1994, 49 (24A), 4153-4177. (34) Van Crevelin, D. H. Coal; Elsevier: Amsterdam, 1961.

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to determine the aromaticity. Yen defined the aromaticity:

Ar ) Car/(Car + Ca)

(1)

) (002)band area/[(002)band area + γ band area] where Car is the percentage of aromatic carbons [from (002) band] and Ca the percentage of aliphatic carbons [from γ band]. Bragg peak positions were used to evaluate reticular distances

d ) (λ sin θ)/2

(2)

where θ is the diffraction angle and λ is the X-ray wavelength. The inter-sheet distance d002 and the interchain distance dγ can be calculated from the (002) peak and γ bands, respectively. The Scherrer equation was applied for calculation of the average number of sheets per cluster and the average area of a sheet. The average size of the aromatic clusters perpendicular to the plane of the sheet Lc can be deduced from the (002) band using the Scherrer equation:

Lc ) 0.9 λ/(w cos θ)

(3)

where w is the width of the peak at half-maximum (fwhm). From d002 and Lc one can determine the average number of associated sheets in a single micelle:

n ) Lc/d002

(4)

The average diameter of an aromatic sheet La is calculated from the (10) or the (11) peak as

La ) 1.84 λ/(w cos θ)

can then be determined according to

H/C ) 11.92 H%/C%

(8)

Ar ) 0.09 × 1201/C% - 1.15 H/C + 0.77

(9)

Surface Tension. Surface tension provides information about the asphaltene concentration near the surface sublayer, and is intimately related to the molecular arrangement at the liquid-air surface. In principle, one can deduce the average molecular weight of asphaltene from the surface tension data alone, provided an appropriate structural model and the intermolecular interactions at the air-liquid interface are known. The starting point of MW calculation using the surface tension data is the Gibbs35 adsorption equation. It calculates the area per molecule at the interface using the measured surface tension data. The Gibbs’s adsorption equation for a reversible system reads:

Γ ) (- 1/RT) × [dγ/d(ln C)]

where dγ is the surface tension variation and d(ln C) the logarithmic concentration variation (C expressed in wt %). One should note that Gibb’s equation is only applicable to the concentration below CMC (critical micelle concentration). Once Γ is obtained, the average area occupied by an asphaltene molecule at the toluene/ air interface can be easily calculated,

Γ ) 1/(N × A)

For details of eq 1-5, one can refer to Dickie and Yen’s paper.10 Density and H/C Analysis. With the density measurement one can estimate the hydrogen content (percentage) using Van Crevelin’s method,34 and subsequently can calculate the carbon percentage. Although this approach is simple, there are many assumptions involved. Thus, the results obtained should be considered qualitative and approximate in indicating the relative abundance of various atomic fractions in asphaltene. Van Crevelin’s approach is in general satisfactory for coal and graphite carbon systems, whereas for an asphaltene system it can only help to predict some asphaltenic properties. Adopting Crevelin’s approach, the measured density can be related to the hydrogen and carbon percentages by:

F ) 1.45 - 0.045 H%

(6)

C% ) 100 - (H% + O% + S% + N%)

(7)

where F is the density of asphaltene in toluene expressed in g/cm3; C%, H%, O%, S%, N% are the weight percentages of carbon, hydrogen, oxygen, sulfur, and nitrogen, respectively. The atomic ratio and aromaticity

(11)

where N is Avogadro’s number and A is the molecular area. From A, one can construct a conformational model for the molecule at the interface to compute the molecular volume; and from the volume, one can determine the average molecular weight:36

MW ) density × N × particle volume (5)

(10)

(12)

Although eq 12 provides a simple method for MW estimation, Sheu and Storm30,36 pointed out that the solvation effect and the intermolecular interaction can greatly impact the accuracy of MW obtained from this approach. They took into account the effect from solvation and intermolecular interaction, for the Ratawi asphaltene, by

MW ) density × N × particle volume/S/ξ3

(13)

S represents the degree of solvation and ξ stands for the interparticle interaction effect.28 S can be estimated from

S ) (0.74/φm)

(14)

where φm is the maximum packing volume fraction. It can be determined from analysis of the viscosity measurement. The number 0.74 was chosen because it represents the maximum packing of a FCC crystal. The factor ξ can be extracted from the viscosity measurements provided an appropriate model for the interparticle interaction is in place and that the interaction parameter obtained from the bulk analysis can be used (35) Gibbs, W. Collected Works, Vol. 1; Yale University Press: New Haven, 1948; pp 219-237. (36) Taylor, S. E. Fuel 1992, 71, 1338.

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for the intermolecular interaction at the surface. For different asphaltene systems this interaction factor may differ. We will discuss how to extract S and ξ from the viscosity measurements. Viscosity. As we mention earlier, both solvation parameter S and the intermolecular interaction parameter ξ can be determined from the low shear viscosity measurements. However, it is well-known that analysis of low shear viscosity data is always a challenge. Since Einstein derived the viscosity equation for the hard sphere diluted solution,37 much effort has been given to constructing satisfactory analysis schemes for unfolding the microscopic world from the viscosity data. Although many equations have been proposed,38 the majority of them are empirical and often provide no or minimum physical information on the system, except some constants. A physically meaningful parameter that is obtainable from these equations is the intrinsic viscosity which somewhat represents the shape of the suspended particles (aggregates). However, the contribution of this parameter to the viscosity is often coupled with other contributions, such as the interparticle interactions and solvation. It is thus very difficult to rigorously determine its true value. To de-couple all contributions from a viscosity measurement, more than one analysis scheme (or experiment) is needed. In a previous report, Sheu et al.39 adopted the Pal and Rhodes40 equation, the Eiler’s equation.41 the Campbell and Forgac’s equation,42 and the Grimson-Barker equation43 to paint a picture for the asphaltene aggregates in solution. In that approach, the contribution of the particle shape and the solvation was considered de-coupled through the analysis using the Pal and Rhodes’ equation. Although this is approximately correct, the impact of the particle shape on the overall viscosity was overlooked because its contribution was at the exponent (see eq 15) which, after taking the logarithm, substantially loses its sensitivity. To reassure the legitimacy of the hard sphere model, Sheu used Campbell and Forgac’s equation42 to argue that the asphaltene colloids are similar to a hard sphere as long as the concentration is low enough. This merely provides a necessary condition but not sufficient. As for interparticle interactions, Sheu et al.44 used the Grimson-Barker equation43 to extract the interaction parameter ξ, and used it to calculate the MW using eq 13. This approach suffers a drawback that the Grimson-Barker equation presets the interparticle potential to be a Columbic-like potential which may not be representative. In this work, we decided to use the Huggin’s equation, combined with Pal and Rhodes’ and Eiler’s equations. This approach is less subjective since the Pal and Rhodes’ and the Eiler’s approach describe the interparticle interaction differently, so are their sensitivities in differentiating the contributions from the particle shape and interparticle interactions. (37) Einstein, A. Ann Phys. 1911, 34, 519. (38) Rutgers, R. Rheol. Acta 1962, 2, 305. (39) Sheu, E. Y.; De Tar, M. M.; Storm, D. A. Fuel 1991, 70, 1151. (40) Pal, R.; Rhodes, E. J. Rheology 1989, 33, 1021. (41) Eiler, H. Kolloid-Z Z. Polym. 1941, 97, 313. (42) Campbell, G. A.; Forgas, G. Phys. Rev. A 1990, 41, 8. (43) Grimson, M. J.; Barker, G. C. Europhys. Lett. 1987, 3, 511. (44) Sheu, E. Y.; De Tar, M. M.; Storm, D. A. Fuel Sci. Technol. Int. 1992, 10 (4-6), 607.

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We still start with the Einstein equation to construct our analysis scheme on the viscosity data. The Einstein equation37 expresses ηr, the relative viscosity, as a function of the volume fraction φ as

ηr ) 1 + 2.5 φ

(15)

where φ is the particle volume fraction. For nonhard, nonspherical solvated particles, the Pals and Rhodes’ equation30 gave the following equation:

ηr ) (1 + Kφ)-2.5

(16)

In this equation, the particle is assumed spherical. A coefficient R accounting for the particle shape can be introduced to give a modified Pal-Rhodes equation:

ηr ) (1 + Kφ)-R

(17)

In both cases the constant K represents the solvation effect. If no solvation occurs, K is equal to unity, otherwise it is greater. An increase in polydispersity may vary the R and/or the K value. One should note that the polydispersity of the particle has been implicitly accounted for in the Pal-Rhodes’ equation as indicated in Roscoe’s equation.45 This is to say that the effect of polydispersity is included in R and/or K. The Eiler equation41 took a different approach and gave an empirical equation which provides the intrinsic viscosity and the maximum packing volume fraction simultaneously:

ηr ) [1 + k(φ/φm)/(1 - (φ/φm)]2

(18)

the constant k is related to the intrinsic viscosity,

k ) [η]φm/2

(19)

This formula can also be written as

(ηr1/2 - 1)/φ ) [η]/2 + (ηr1/2 - 1)/φm

(20)

where [η] and φm can be obtained simultaneously through the intercept and the slope of a (ηr1/2 - 1)/φ versus (ηr1/2 - 1) plot. From φm, the solvation shell thickness can be calculated:

∆R/R ) (φ0/φm)1/3 - 1

(21)

with R being the particle radius. Mooney’s equation, on the other hand, provides an opportunity to extract [η], φm, and an explicit polydispersity parameter, λ, simultaneously. This empirical equation46 is applicable to all uncharged concentrated systems. λ is equal to unity for a monodisperse system and > 1 when polydispersity becomes significant. Unfortunately, λ does not quantitatively represent polydispersity. Instead, it is only an indicator. The Mooney’s equation reads

ηr ) exp[[η]φ/(1 - λ(φ/φm))]

(22)

This equation requires three adjustable parameters to fit the data, [η], λ, and φm. Since the shape of the asphaltene aggregates in solution play an important role and they may behave like polymers in solution, the Kuhn and Kuhn equa-

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Figure 1. The X-ray diffraction spectrum as a function of the angle 2θ. Table 1. Partial Chemical Element Composition of Hassi Messaoud Asphaltene Deduced from Density Measurements; E is the Heteroatoms

Figure 2. (Use caption from Figure 2.)

density(g/cm3)

H (%)

E (%)

C (%)

H/C

aromaticity

1.094

8.42

8.42

83.16

1.20

0.57

Table 2. Average Structural Parameter Values Extracted from the X-ray Spectrum

tion47

was an alternative for characterization of shape. The Kuhn and Kuhn equation links the specific viscosity ηsp to the particle aspect ratio p, p ) a/b, where a is the major axis and b the minor one:

(ηsp/φ) ) 2.5 + 0.4075(p - 1)1.508

(23)

The limitation of this equation is that it does not take into account the solvation at all which severely restricts its applicability to asphaltene solutions. Both the Mooney and the Kuhn-Kuhn equations will be used to compare with a new analysis scheme applied in this work, which will be described below. Results Table 1 shows the partial chemical composition of the asphaltene deduced from the density measurement and Van Crevelin calculation.34 Because of lacking comprehensive chemical composition analysis, we simply assumed that the total percentage of the hetero-elements is of the same order as that of hydrogen. This assumption was made to be compliant with the majority of cases available in the literature.8 It allows us to calculate the structural parameters using eqs 6-9. The main parameter interested in this work is the H/C ratio which reveals the degree of aromaticity of the sample. Theoretically, the H/C value can span from ∼2 (long alkyl chains) to unity (e.g., benzene) and to much smaller than unity (e.g., the condensed aromatic rings such as peri, 0.55, and kata, 0.33, systems). The H/C value for the asphaltene studied here (see Table 1) is 1.20 indicating that this asphaltene fraction is not very aromatic. The aromaticity obtained from eq 9 is 0.57. This means that the solubility of Hassi Messaoud asphaltene in a good solvent such as toluene is likely high and the CMC should be relatively high as well. Another method for determination of the aromaticity is by X-ray diffraction. Figure 1 shows the corresponding X-ray spectrum. The γ, (10), (11), and (002) bands were observed. From areas under these bands. We followed Dicki and Yen’s analysis procedure10 to calculate the

number of inter-sheet inter-chain sheet sheets per aromaticity Ar distance distance diameter micelle 0.40

3.56 Å

16,5 Å

9.5 Å

4-5

structural parameters. The results are tabulated in Table 2. The aromaticity obtained was 0.4, again, indicating relative low aromaticity, and is ∼30% lower than the result obtained from density analysis. This is largely due to the sensitivity of the (002) peak. It is only sensitive to the large aromatic molecules. The inter-sheet distance obtained was d002 ) 3.56 Å, and the average sheet diameter value La ) 9.5 Å. From the particle height (Lc ) 16.5 Å) and d002 ()3.56 Å) the average number of aromatic sheets per single particle was estimated to be 4.5. The relatively low aggregation, though in the neat phase, suggests that the MW of this asphaltene may be low, which in turn may mean a high CMC in toluene compared with other reported asphaltenes. A similar trend was indicated by Speight et al.48 from X-ray analysessthe molecular weight increases with increasing La. The fact that our data show La to be 9.5 Å, a rather small value, it means that the MW should be low. Figure 2 shows the surface tension as a function of the asphaltene concentration in toluene. The variation of the surface tension is small as already observed by other authors for various asphaltenes.25,27,49 A clear critical micelle concentration (CMC) appears at 0.17 wt %. This value is greater by approximately an order of magnitude than those obtained by Sheu et al.25,49 and Bardon et al..27 They obtained CMC values to be between 0.015 and 0.03 wt % for their asphaltenes. This rather high CMC may be attributed to the relatively high H/C ratio (∼120), smaller MW, and low number ring molecules. It also indicates that Hassi Messaoud asphaltene may have a relative high solubility in a good solvent such as toluene. (45) Roscoe, R. Brit. J. Appl. Phys. 1952, 3, 267. (46) Mooney, M. J. Colloid Sci. 1951, 20, 162. (47) Khun, W.; Khun, H. Helv. Chim. Acta 1945, 28, 97. (48) Speight, J. G.; Moschopedis, S. E. Chemistry of Asphaltenes; Advances in Chemistry Series 195; Bunger, J. W., Li, N. C., Eds.; American Society: Washington, DC, 1981; p 4. (49) Sheu, E. Y. J. Phys: Cond. Matter 1996, 8, A125-A141.

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Figure 3. 3. (a) Relative viscosity variations as a function of concentration in volume fraction. (b) Pal and Rhodes analysis. The exponent was ∼0.4, indicating a sphere-like particle structure. The K ) 2.89 suggests a substantial amount of solvation. (c) Mooney analysis using λ ) 1.0. Again, the particle appears to be spherical. (d) Eiler’s plot quantified the solvation.

From the surface tension data one can calculate MW using eqs 10-12. The average molecular weight was estimated to be approximately 2550 Da and the particle radius about 9.74 Å. These data were calculated assuming that the molecules at the air-toluene interface are more or less spherical. The MW obtained, though not corrected for solvation effect, is small compared to those values reported in the literature by the surface tension method36 or some other27 measurements. It, however, is qualitatively consistent with the X-ray data which predicts a relatively low molecular weight. The same conclusion is reached when assuming a cylindrical shape for the molecules at the interface. Taking the height of the molecular cylinder as h ) 2d002, the molecular weight was calculated to be 1500 Da. To take into account the effect of solvation for a more accurate estimate of the MW, the low shear viscosity was analyzed as follows. The relative viscosity as a function of concentration is illustrated in Figure 3a. It is noted from Figure 3a that the linear regime is up to φ ) 0.05, beyond which a noticeable deviation is observed. The first step in this analysis was to apply the Pal-Rhodes equation for shape and solvation evaluation. The Pal-Rhodes plot is illustrated in Figure 3b. A simple linear regression fit to the experimental data leads to an R value of 2.5 which means that the particles

could be considered as spherical, even at volume fractions up to ∼0.15. The solvation constant K derived from this analysis is 2.89 which clearly indicates that solvation does occur. Though the K parameter obtained from Pal-Rhodes does not quantify the degree of solvation, it nevertheless serves as a basis for comparison with a polydisperse nonsolvated hard sphere system where K is equal to unity.45 The polydispersity effect was analyzed by the Mooney46 equation as depicted in Figure 3c. It was found that eq 21 can fit the data satisfactorily using λ ) 1. This indicates that both the Pal-Rhodes and Mooney equations conclude that the asphaltenic particles rheologically behave like monodisperse spheres for volume fraction up to 0.15. To quantitatively determine the degree of solvation, the Eiler eq 17 was used. The slope of the Eiler plot (Figure 3d) corresponds to the quantity 1/φm from which the maximum packing volume fraction φm ) 0.39 was obtained. If one assumes the ideal packing to be facecentered-cubic (FCC), the maximum packing volume fraction φo should be 0.74. Thus, the degree of solvation can be calculated (S ) φo/φm). S was found to be 1.89 in our case. Using S obtained and taking ξ to be 1.4 as used by Sheu et al.,44,49 it is possible to recalculate the average

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molecular weight of the adsorbed asphaltene molecule, assuming the degree of solvation of the molecules at the toluene-air interface is the same as that of an asphaltene aggregate in the bulk. From eqs 12 and 13, the new molecular weight values for spherical and cylindrical molecules were calculated to be 495 and 290 Da, respectively. These values are comparable with those deduced from mass spectroscopy measurements.26 One, however, needs to note that the interaction parameter was taken as 1.4 as used by Sheu.49 This number may differ from one asphaltene to another, though we expected it to be similar when the surface is saturated near CMC. As we pointed out earlier, the interaction parameter ξ is usually coupled to the shape parameter as well as the solvation parameter. It is thus necessary to separate these contributions. A sensible method of determining the contribution from each effect is to extract them using equations that provide a similar degree of sensitivity and that these two parameters are clearly separated in the equation. One such method is to use the Huggin’s equation,50 in which the shape effect is relevant to the linear term while the interaction is at the quadratic term. Huggin’s equation can be combined with the Jeffery equation51 which provides by far the most accurate intrinsic viscosity for an ellipsoid. The process is as follows. One can write the Huggin’s equation as

ηr ) 1 + [η]p3φ + kH[η]2f 2

Figure 4. Huggin’s and Jeffery’s analysis.

(24)

where p is the aspect ratio (the ratio between the major axis a and the minor axis b), kH is the Huggin’s coefficient (the interaction parameter), and [η] is the intrinsic viscosity calculated from the Jeffery’s equation,

[η] )

[

4β2 14 + 15 p2(4p2 - 10 + 3R) 3β + p2(p2 + 1)[(2p2 - 1)R - 2] 6 + 2 2 (p + 1)(2p + 4 - 3p2R) 4p2 + 2 - (4p2 - 1)R p2(4p2 - 10 + 3R)[(2p2 + 1)R - 6]

Figure 5. Khun and Khun’s analysis using eq 23. The aspect ratio extracted was 7.5.

]

(25)

where β ) p2 - 1 and R ) ln[(p + xβ)/(p - xβ)]/[pxβ]. In view of the Huggin’s equation, the solvation effect was taken into account according to the hydrodynamic diameter of the particle and scaled by the aspect ratio p. This argument is plausible since the low shear viscosity at low concentration (