Liquid-Phase Behavior during the Cracking of Asphaltenes - Industrial

Samina Rahmani, William McCaffrey, Janet A. W. Elliott, and Murray R. Gray*. Department of Chemical and Materials Engineering, University of Alberta, ...
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Ind. Eng. Chem. Res. 2003, 42, 4101-4108

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GENERAL RESEARCH Liquid-Phase Behavior during the Cracking of Asphaltenes Samina Rahmani, William McCaffrey, Janet A. W. Elliott, and Murray R. Gray* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 2G6 Canada

Asphaltenic material from Athabasca bitumen, with and without fine solids, was reacted at 430 °C under a nitrogen environment in the liquid phase, mixed with either 1-methyl naphthalene or maltene fractions from Athabasca. Phase behavior during coke formation was investigated by examining the coke produced from selected reactions by scanning electron microscopy (SEM). Both fine solids and solvents were found to assist the dispersion of liquid coke spheres in an oil medium. Phase inversion, to an oil-in-coke structure, was observed in some sections of coke produced from pure asphaltenes. The thermodynamic feasibility of phase inversion was confirmed by calculating the entropy difference for a set of representative conditions. Qualitatively, as the volume fraction of coke increases, the probability of a phase inversion is increased. This result agrees with the behavior of polymer blends, where phase inversion occurs at high concentration. Introduction Phase behavior plays an important role in coke formation. Reactions such as cracking and polymerization can lead to incompatibility in the liquid phase, resulting in phase separation.1,2 Coking follows the formation of a new phase either by liquid-phase separation1,2 or by flocculation of asphaltene micelles.3 Subsequent reactions and phase separation within the coke material lead to the formation of an anisotropic mesophase that appears bright under cross-polarized light.4 Storm et al.3 suggested an alternative mechanistic view of coke formation. Judging from data on the size of dispersed asphaltenes and rheological measurements, they suggested that an asphaltenic phase forms by flocculation at around 200 °C, well below the temperatures at which chemical reactions occur. This flocculated phase is the precursor to the coke-producing phase in the reacting residue. An alternative explanation of the rheological changes observed by Storm et al.3 is the formation of dispersed droplets of liquid phase. For example, Rand5 found that the viscosity tends to increase as the volume fraction of the mesophase increases. If fine solids are present during coking, the developing coke components in the new phase can interact with fine solids via mechanisms such as nucleation of the coke phase, dispersion of the coke, or flocculation with coke solids. Fine solids are originally present in Athabasca bitumen as mineral clays coated with strongly bound toluene-insoluble organic materials.6 Several studies have indicated the importance of fine solids in the liquid-liquid behavior of carbonaceous systems. For example, the addition of fine solids was found to interfere with the coalescence of mesophase in coal tar7,8 and bitumen fractions.9 Tanabe and Gray10 suggested * To whom corresponding should be addressed. Tel.: (780) 492-7965. Fax: (780) 492-2881. E-mail: murray.gray@ ualberta.ca

that fine solids might prevent coalescence of tolueneinsoluble coke material at the early stages of reaction, as observed in mesophase formation at longer reaction times, thereby altering the coking kinetics. They showed that fine solids inhibited the formation of tolueneinsoluble coke from Athabasca vacuum residue during reaction in a batch reactor at 430 °C. The reduction in coke yield was as much as 7-9 wt % after 20-30 min when compared to the coke yield from residue without fine solids. Sanaie et al.11 observed reductions in coke yield as large as 25% due to the presence of hydrophobic clays. Fine solids are potentially important in affecting the coalescence of the coke phase, which, in turn, affects the total coke formation kinetics. Normally, when two immiscible components form a dispersion, the major component forms the continuous phase. The average droplet size increases with the volume fraction of the dispersed phase. A dual-phase continuity of the two phases is commonly observed during the mixing of polymer blends at approximately 50/50 composition.12 At higher concentrations, phase inversion generally takes place, i.e., the dispersed droplets form the continuous phase after they disintegrate and coalesce. Dispersed droplets will disintegrate when the total force acting on the droplet is greater than the surface tension. The phase inversion point generally depends on the concentrations and viscosity ratio of the components under the conditions of blending.12 In analogy to polymer blends, a situation can arise during coke formation when the coke material will form the continuous phase, i.e., a phase inversion can take place. The objective of this study was to investigate the phase behavior of coke during the cracking of asphaltenic material. Two aspects of the phase behavior were studied: (1) the influence of fine solids and diluent on the morphology of the coke phase and (2) the possibility of phase inversion during coking. Two sets of experiments were conducted. First, Athabasca asphaltenes were mixed with 1-methyl naphthalene or maltenes and reacted. In a subsequent series of experiments, a

10.1021/ie020921d CCC: $25.00 © 2003 American Chemical Society Published on Web 07/24/2003

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Table 1. Composition of Supercritical Fluid Extraction Fractions of Athabasca Vacuum Residue (524 °C +), after Chung et al.14 fraction

molecular weight

S (wt %)

MCR (wt %)

asphaltene (wt %)

1 10 (end cut)

506 4185

4.1 6.51

5.64 48.94

0 88.03

mixture of two supercritical fluid extraction (SFE) fractions of Athabasca vacuum residue were subjected to coking. Scanning electron microscopy (SEM) was used as the main tool for examining the phase behavior. SEM gives three-dimensional images that are easier to analyze than the two-dimensional micrographs obtained by most optical and TEM techniques.13 Experimental Methods Materials. In one series of experiments, Athabasca asphaltenes mixed with maltenes or 1-methyl naphthalene were used to study the influence of diluents on the phase behavior. The asphaltenes were separated from Athabasca vacuum residue. First, the mineral solids were removed by digesting the residue in 40 parts of toluene overnight and then filtering it through 0.22-µm filter paper. Toluene was removed by a rotary evaporator. Heptane-insoluble asphaltenes were prepared by adding 40 parts of heptane and mixing overnight; then the solid fraction was separated by filtration through a 0.22-µm Millipore filter. In a second series of experiments, two supercritical fluid extraction (SFE) fractions were selected from a series of 10 fractions.14 The lightest fraction, fraction 1, and the heaviest, the asphaltenerich end-cut fraction, were used as feed materials to study the role of fine solids. Supercritical fluid extraction using pentane is capable of cutting deep into bitumen at a temperature much lower than the cracking temperature of the feedstock. Fraction 1 and the endcut fraction constitute approximately 10 and 40 wt % of the vacuum residue, respectively. Syncrude Research Center in Edmonton, Canada, provided the fractionated samples. The properties of the two fractions used in this study are listed in Table 1. Coking Experiments. Experiments were carried out batchwise in a 15-mL microreactor made from Swagelock fittings and tubing. The reactor was loaded with 3 g of reactant, and then the pressure tested with nitrogen at 4 MPa. The gas was then vented, and the reactor was pressurized twice more with nitrogen and vented to purge residual oxygen. The initial cold pressure of nitrogen was atmospheric when the diluent was fraction 1 of SFE fractions or maltene and 3-4 MPa when 1-methyl naphthalene was used as the diluent. The reactor was heated in a fluidized sand bath and agitated at ca. 1 Hz for the duration of the reaction interval. The contents of the reactor reached the final temperature within 5 min. The reaction was then quenched by plunging the reactor into cold water, giving cooling to less than 100 °C in 15 s. All of the reactions were carried out at 430 °C under a nitrogen environment. Approximately 85% of the solvents was estimated to be in the liquid phase at 430 °C using the Peng-Robinson equation of state (ASPEN Plus software, Aspen Technology, Cambridge, MA). Separation. Liquid product and coke were washed out of the reactor with 40 parts of toluene and then kept overnight at 70 °C to ensure the extraction of liquid products from the solid coke. Coke was then removed

Figure 1. SEM micrograph of coke from 30 wt % asphaltene in 1-methyl naphthalene at 430 °C and 40 min.

from the toluene solution by filtration on a 0.22-µm Millipore filter. The coke yield was determined by weighing the filter after it had been dried in a vacuum at 70 °C for 12 h. Scanning Electron Microscopy (SEM). Coke samples were prepared for SEM analysis by being dried and then dispersed in ethanol by sonication for approximately 15 min. A drop of the resulting mixture was placed on a plate and dried in air. The sample holder was then coated with gold. The samples were then observed under a Hitachi S-2700 SEM with energydispersive X-ray (EDX) analysis by a Princeton GammaTech EDX analyzer. Image analysis software (Sigma ScanPro 4, Jandel Scientific) was used to calculate the mean diameters of the coke spheres from the captured images. The number-mean diameter derived from the projected areas of the spheres can be defined as follows i)k

Dn )

niDi ∑ i)1 i)k

(1)

ni ∑ i)1 where Dn is the mean diameter, ni is the number of particles measured in size range i, Di is the middle size of class range i, and k is the number of particle size ranges. The sample size was 60 or greater for each case. Experimental Observation of Coke Morphology Coke Formation with Solvent Dilution. Coke samples from different reactions were observed by SEM to determine the morphology of the coke phase. Coke samples from the thermal cracking of Athabasca asphaltenes mixed with different solvents at different dilution ratios were chosen for this study. Selected solvents were heptane-soluble maltenes, which is the naturally occurring solvent in the vacuum residue, and the aromatic solvent 1-methyl naphthalene. Selected micrographs of representative coke morphologies are presented in Figures 1-4. Figure 1 shows an SEM micrograph of tolueneinsoluble coke produced from the coking reaction of 30 wt % Athabasca asphaltenes in 1-methyl naphthalene. Spherical domains of coke were observed, mostly on the order of 1 µm in diameter. Most of the spheres were

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Figure 2. SEM micrograph of coke from 75.6 wt % Athabasca asphaltene in maltene at 430 °C and 40 min.

lightly attached to each other, indicating a low rate of coalescence in the presence of solvent, although some coalescence of spheres was also observed (Figure 1). Observation of coke spheres and agglomerated spheres suggests that this material was liquid or plastic at reactor conditions. A liquid phase of toluene-insoluble coke that is dispersed in a continuous oil phase will seek to minimize the surface energy. The shape with the smallest area, and hence, the lowest energy, would be an emulsion of spheres, analogous to spheres of mesophase in pitch at similar temperatures.15 Frequent coalescence, flowing features, and larger coke domains were observed for 75.6 wt % asphaltenes in maltenes (Figure 2). During coalescence, attractive dispersion forces as well as Brownian, hydrodynamic, and surface forces act as the driving forces for the droplets to merge, whereas a high viscosity of the phase existing between the droplets will inhibit the transition to a single spherical droplet. Because of the two opposing forces, a relaxation time is required to merge the coalescing droplets into a single sphere. It is well-known that any two droplets of like phase separated by a second continuous phase have an attractive dispersion force (van der Waals force) that is proportional to 1/Γ,6 where Γ is the separation distance between them. Thus, stronger attractive forces should exist between the droplets in concentrated mixtures. Hence, coalescence was more prominent for the coke produced from the thermal cracking of asphaltene with a lower concentration of solvent phase (Figure 2). The average size of coke domains was found to be larger for coke from asphaltenes at higher concentration compared to the coke from 30 wt % asphaltenes in 1-methyl naphthalene, consistent with the higher concentration of coalescing material. The extent of coalescence is a function of the viscosity of the polymeric phase, and coalescence requires that the polymer remain sufficiently deformable to respond to the requirements of minimum surface energy and hence develop the new spherical shape.16 Figure 3 shows SEM micrographs of coke from asphaltenes without solvent. The two images from the same experiment exhibit very different morphologies. Figures 1, 2, and 3a show examples where coke separated out as spheres or a coalesced structure from the continuous oil phase. In contrast, Figure 3b suggests a situation in which coke was the continuous phase and oil was dispersed in it. The voids in the SEM image are

Figure 3. SEM micrographs of coke from Athabasca asphaltene at 430 °C and 40 min: (a) domain of coalesced coke material, (b) structure consistent with phase inversion.

consistent with the presence of spherical droplets of oil phase dispersed in the continuous coke phase. Examples of phase inversion are abundant in polymer science,12,17 and its occurrence depends on the concentrations and viscosities of the dispersed and continuous phases. During filtration, the oil droplets would be washed out, leaving honeycomb-like structures. An alternative explanation for the structures in Figure 3b is a foam of gas bubbles, evolved from the formation of volatile components during cracking of the liquid phase. The small size of the vacant pockets in the coke, on the order of 1 µm, is consistent with an emulsion rather than a foam. The larger interfacial tensions in gas-liquid systems favor much larger bubbles, on the order of 100 µm or larger;18 therefore, formation of a liquid-liquid microemulsion is the most likely explanation. All of the SEM images were taken after the reaction had been quenched and the tolueneinsoluble material washed. Although we cannot absolutely rule out artifacts due to this procedure, the rapid quenching of the reactor in water reduces the temperature at initial rates in excess of 20 K/s. Cooling could increase the amount of insoluble material by changing the solvent properties of the oil, but this factor cannot account for the changes in morphology observed in this study.

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Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 Table 2. Average Diameters of the Spherical Coke Domains Produced from Reactions of Mixtures the SFE End Cut and SFE Fraction 1

Figure 4. SEM micrograph of coke from the end cut of the SFE fraction at 430 °C and 40 min.

Role of Fine Solids in Coke Morphology. Coke samples from the thermal cracking of the end cut from the SFE of vacuum residue were compared with coke from asphaltenes to study the role of fine solids in coke morphology. The end cut of the vacuum residue contained almost 88 wt % asphaltene and 4.9 wt % toluene insolubles. These toluene insolubles, commonly referred to as bitumen solids, are predominantly aluminosilicate clay particles (0, then, from a thermodynamic point of view, configuration 2 can spontaneously form from configuration 1. Note that we have chosen to use an entropy approach rather than a free energy approach because entropy is the more fundamental quantity. Free energy is defined as the energy that, when minimized subject to the constraints of the problem, corresponds to a maximization of entropy. Free energies for multiphase systems can be quite complicated (23); the entropy approach

allows us to investigate the assumptions required for the entropy difference to reduce to a simple equation that includes only surface energies, which we will derive here. From the Euler equation of thermodynamics, the entropy for a bulk phase consisting of multiple components can be represented by the following equation

S)

U

+

T

PV

-

T

∑j

µjNj

(2)

T

where U is the internal energy, T is the temperature, P is the pressure, and V is the total volume of the phase and mj is the chemical potential and Nj is the number of moles of component j. The summation is performed over the components in the phase. The Euler equation for an interface would thus be

S)

U

-

T

γA

-

T

∑j

µjNj

(3)

T

where A is the interfacial area and γ is the interfacial tension. The total entropy contains five contributions R Si ) SRi + Sβi + Sσi + SG i + Si

(4)

where i ) 1 or 2 for each of the two configurations (coke dispersed and coke continuous); the coke phase is represented by the superscript R; the oil phase is represented by the superscript β; σ indicates the cokeoil interface (effects of the gas-liquid interface and all interfaces involving the reactor vessel walls have been neglected, since we assume that the areas involved will be small compared to the area of the coke-oil interface because of high dispersion); and the superscripts G and R denote the gas phase and the reservoir, respectively. Introducing eqs 2 and 3 into eq 4, one can obtain the entropy for either configuration as follows

Si )

∑j

URi

+

TRi µβji Nβji Tβi

PRi VRi

-

TRi +

Uσi

-

Tσi

∑j

∑j

µRji NRji

γσi Aσi

-

Tσi G µG ji Nji

TG i

+

TRi

+

∑j

Uβi

+

Pβi Vβi

Tβi

Tβi

µσji Nσji

UG i

URi

+

TRi

+

TG i

Tσi +

-

PRi VRi TRi

-

G PG i Vi

-

TG i

∑j

µRji NRji TRi

(5)

where i ) 1 or 2. Certain constraints can be imposed from the definition of the system. Because we are considering the possibility of a phase inversion at a given temperature, we assume that R R β σ TR1 ) Tβ1 ) Tσ1 ) TG 1 ) T1 ) T2 ) T2 ) T2 ) R TG 2 ) T2 ) T (6)

By definition, for the reservoir

PR1 ) PR2

(7)

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µR1 ) µR2

(8)

R R ) Nj2 Nj1

(9)

VR1 ) VR2

where the superscripts Rσ and βσ indicate molecules in the interface of the same types as found in bulk phases R and β, respectively. We assume that

(10)

R Rσ µj2 ) µj2

(20)

Because the reservoir plus the reactor forms an isolated system, internal energy is conserved

β βσ ) µj2 µj2

(21)

R UR1 + Uβ1 + Uσ1 + UG 1 + U1 ) R UR2 + Uβ2 + Uσ2 + UG 2 + U2 (11)

Forming the difference between S2 and S1 from eq 5 making use of eqs 6-11 yields

1 S2 - S1 ) (PR2 VR2 T

∑j µj2R Nj2R + Pβ2 Vβ2 -

Assuming that all of the liquid-phase components can be assumed to be incompressible substances k k - µj1 ) v/j (Pk2 - Pk1) µj2

(22)

for k ) R or β. v/j is the partial molar volume of component j. Assuming that the number of moles of each compnent is conserved during the phase inversion

∑j µj2β Nj2β - γσ2 Aσ2 - ∑j µj2σ Nj2σ + PG2 VG2 -

R Rσ R Rσ + Nj1 ) Nj2 + Nj2 Nj1

(23)

∑j µj2G Nj2G - PR1 VR1 + ∑j µj1R Nj1R - Pβ1 Vβ1 +

β βσ β βσ + Nj1 ) Nj2 + Nj2 Nj1

(24)

∑j µj1β Nj1β + γσ1 Aσ1 + ∑j µj1σ Nj1σ - PG1 VG1 + ∑j µj1G Nj1G) (12) Certain further constraints can be assumed in view of the reactor conditions and the feed properties. We assume that the two liquid phases are nearly incompressible and that there is therefore no volume change of either liquid phase as a result of the phase inversion. This also results in no volume change of the gas phase.

VR1

)

VR2

R

≡V

R Rσ v/j (Nj2 + Nj2 ) ) VR ∑ j in R

(25)

β βσ v/j (Nj2 + Nj2 ) ) Vβ ∑ j in β

(26)

Substituting eqs 20-26 into eq 19 and further assuming

(13)

Vβ1 ) Vβ2 ≡ Vβ

(14)

G VG 1 ) V2

(15)

We further assume that there are no compositional changes of the gas upon inversion so that G G ) Nj2 Nj1

(16)

Equations 5, 14, and 15 imply G PG 1 ) P2

(17)

µG 1

(18)

)

Assuming additivity of the partial molar volumes (and neglecting the volume of the molecules in the interface, as required by the Gibbs dividing surface approach)

µG 2

Next, we assume that the liquid phases are immiscible so that, upon substitution of eqs 13-18, eq 12 becomes

1 S2 - S1 ) [VR(PR2 - PR1 ) + Vβ(Pβ2 - Pβ1) T R R Rσ Rσ R R Rσ Rσ (µj2 Nj2 + µj2 Nj2 - µj1 Nj1 - µj1 Nj1 )∑ j in R β β βσ βσ β β βσ βσ (µj2 Nj2 + µj2 Nj2 - µj1 Nj1 - µj1 Nj1 )∑ j in β

γσ2 Aσ2 + γσ1 Aσ1] (19)

γσ1 ) γσ2

(27)

γ S2 - S1 ) (Aσ1 - Aσ2) T

(28)

yields

Although it is tempting to simply write down eq 28 from the outset, the approach that we have taken is valuable because it clearly indicates the assumptions that are inherent in eq 28, most importantly, eqs 16, 22, and 25-27 and the immiscibility of the liquid phases. Literature Cited (1) Magaril, R. Z.; Aksenova, E. I. Study of the Mechanism of Coke Formation in the Cracking of Petroleum Resins. Int. Chem. Eng. 1968, 8, 727-729. (2) Wiehe, I. A. A Phase Separation Kinetic Model for Coke Formation. Ind. Eng. Chem. Res. 1993, 44, 2447-2457. (3) Storm, D. A.; Barresi, R. J.; Sheu, E. Y. Flocculation of Asphaltenes in Heavy Oil at Elevated Temperatures. Fuel Sci. Technol. Int. 1996, 14, 243-260. (4) Brooks, J. D.; Taylor, G. H. Formation of Graphitizing Carbons from the Liquid Phase. Nature 1965, 206, 697-699. (5) Rand, B. The Pitch-Mesophase-Coke Transformation as Studied by Thermal Analytical and Rheological Techniques. In Petroleum Derived Carbons; Bacha, J. D., Newman, J. W., White, J. L., Eds.; American Chemical Society: Washington, DC, 1986; pp 45-61. (6) Kotlyar L. S.; Sparks, B. D.; Woods, J. R.; Raymond, S.; Le Page, Y.; Shelfantook, W. Distribution and Types of Solids Associated with Bitumen. Pet. Sci. Technol. 1998, 16, 1-19.

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(7) Bradford, D. J.; Greenhalgh, E.; Kingshott, R.; Senior, A.; Bailey, P. A. Interaction of Carbon Black with Coal Tar Pitch. In Proceedings of the 3rd Conference on Industrial Carbons and Graphite; Society of Chemical Industry: London, 1971; pp 520527. (8) Dubois, J.; Ahache, C.; White, J. L. The Carbonaceous Mesophase Formed in the Pyrolysis of Graphitizable Organic Materials. Metallography 1970, 3, 337-368. (9) Rahimi, P.; Gentzis, T.; Fairbridge, C. Interaction of Clay Additives with Mesophase Formed during Thermal Treatment of Solid-Free Athabasca Bitumen Fraction. Energy Fuels 1999, 13, 817-825. (10) Tanabe, K.; Gray, M. R. Role of Fine Solids in the Coking of Vacuum Residues. Energy Fuels 1997, 11, 1040-1043. (11) Sanaie, N.; Watkinson, A. P.; Bowen, B. D.; Smith, K. J. Effect of minerals on coke precursor formation. Fuel 2001, 80, 1111-1119. (12) Hietaoja, P. T.; Holsti, M. R. M.; Seppala, J. V.; Ikkala, O. T. Effect of Viscosity Ratio on the Phase Inversion of Polyamaide 66/Polypropylene Blends. J. Appl. Polym. Sci. 1994, 54, 16131623. (13) Sawyer, L. C.; Grubb, D. T. Polymer Microscopy; Chapman and Hall: New York, 1987. (14) Chung, K. H.; Xu, C. M.; Hu, X. Y.; Wang, R. N. Supercritical fluid extraction reveals resid properties. Oil Gas J. 1997, 95 (1), 66-69. (15) Mochida, I.; Oyama, T.; Korai, Y.; Fei, Y. Q. Study of Carbonization Using a Tube Bomb: Evaluation of Lump Needle Coke, Carbonization Mechanism and Optimization. Fuel 1988, 67, 1171-1181. (16) Marsh, H. A Review of the Growth and Coalescence of Mesophase (Nematic Liquid Crystals) to Form Anisotropic Carbon and Its Relevence to Coking and Graphitization. In Proceedings

of the 4th London International Conference on Carbons and Graphite, 1974; Society of Chemical Industry: London, 1976; pp 2-38. (17) Willis, J. M.; Caldas, V.; Favis, B. D. Processing-Morphology Relationships of Compatibilized Polyolefin/Polyamide Blends. J. Mater. Sci. 1991, 26, 4742-4750. (18) Bohm, S.; Timmer, B.; Olthuis, W.; Bergveld, P. A closedloop controlled electrochemically actuated micro-dosing system. J. Micromech. Microeng. 2000, 10, 498-504. (19) Bensebaa, F.; Kotlyar, L. S.; Sparks, B. D.; Chung, K. H. Organic Coated Solids in Athabasca Bitumen: Characterization and Process Implications. Can. J. Chem. Eng. 2000, 78, 610-616. (20) Wang, S.; Chung, K.; Masliyah, J. H.; Gray, M. R. TolueneInsoluble Fraction from Thermal Cracking of Athabasca Gas Oil: Formation of a Liquid-in-Oil Emulsion that Wets Hydrophobic Dispersed Solids. Fuel 1998, 77, 1647-1653. (21) Dutta, R. P.; McCaffrey, W. C.; Gray, M. R.; Muehlenbachs, K. Use of 13C Tracers to Determine Mass-Transfer Limitations on Thermal Cracking of Thin Films of Bitumen. Energy Fuels 2001, 15, 1087-1093. (22) Gray, M. R.; Le, T.; McCaffrey, W. C.; Berruti, F.; Soundararajan, S.; Chan, E.; Huq, I. Coupling of mass transfer and reaction in coking of thin films of Athabasca vacuum residue. Ind. Eng. Chem. Res. 2001, 40, 3317-3324. (23) Gray, M. R. Upgrading Petroleum Residues and Heavy Oils; Marcel Dekker Inc.: New York, 1994. (24) Hunter, R. J. Introduction to Modern Colloid Science; Oxford University Press: New York, 1999; p 155.

Received for review November 12, 2002 Revised manuscript received April 23, 2003 Accepted June 9, 2003 IE020921D