Asphaltene Aggregation under Vacuum at Different Temperatures by

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Energy & Fuels 2003, 17, 1346-1355

Asphaltene Aggregation under Vacuum at Different Temperatures by Molecular Dynamics J. H. Pacheco-Sańchez,* I. P. Zaragoza, and J. M. Martıńez-Magadań Programa de Ingenierıá Molecular, Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, A.P. 15-805, D.F. 07730, Me´ xico Received October 11, 2002. Revised Manuscript Received July 10, 2003

Asphaltene aggregation under vacuum at different temperatures was obtained using classical molecular dynamics (MD) simulations under nonperiodic boundary conditions in a monodisperse system of 96 hypothetical asphaltene molecules. Identical asphaltenes were originally set as an array, where the separation between each other was ∼40 Å. Simulations under the canonical ensemble at NVT conditions, using the Verlet numerical method to solve the motion equations, were conducted. Aggregated systems formed by several asphaltene monomers after 100 ps of classical MD simulations were found. The structure of the solution was analyzed using the radial distribution function. Simulations at four different temperatures (273, 312, 342, and 368 K) were accomplished. Another similar MD simulation at a temperature of 310 K for 300 ps was performed, to validate the stability in the previous systems. After this run, good structures for explaining asphaltene interactions were also observed; these structures were never before proposed. The following effects can be observed from the results: (i) aggregates that have different structures indicate different types of interactions; (ii) decreasing aggregation number values with increasing temperature is consistent with experimental reality; (iii) the average molecular weights obtained for different temperatures agree with the expected range of experimental values; and (iv) the minimum of the potential energy well, in the range of 3.5-4.0 Å, is consistent with the Yen model.

Introduction Mineral oil residues are produced in oil refineries via the (vacuum) distillation of virgin crude oils and streams that have already undergone processing (Brandt et al.1). These residues contain heavy polyaromatic compounds that are insoluble in n-alkane solvents called asphaltenes. The asphaltene issue is one of the main reasons for research in the petroleum industry to determine a way to avoid asphaltene aggregation and precipitation. The asphaltene problem usually causes solid carbon to be adsorbed into the internal walls of the pipes that are being used to produce and refine crude oil,2-3 which, as a consequence, occludes the petroleum flows into them. One way to resolve part of this problem is through the use of simulation techniques such as molecular dynamics (MD). Computer experiments of classical MD can provide information about asphaltene aggregation phenomena. Yen’s phenomenological model continues being one of the most useful approaches to unveil the molecular mechanisms by which asphaltene aggregation occurs into the petroleum fluids.4,5 The main issues stated by Yen and co-workers are the following: (i) the asphaltene * Author to whom correspondence should be addressed. (1) Brandt, H. C. A.; Hendriks, E. M.; Michels, M. A. J.; Visser, F. J. Phys Chem. 1995, 99, 10430-10432. (2) Pacheco, J. H.; Mansoori, G. A. Presented at the SPE-LACPEC International Symposium of the Society of Petroleum Engineers, Rıó de Janeiro, Brazil, 1997; Paper No. 38966. (3) Speight, J. G. The Chemistry and Technology of Petroleum; Marcel Dekker: New York, 1999; Chapter 11.

stacking formation is through unitary cells from 3-6 sheets; (ii) the asphaltene spacing is 3.5-3.8 Å; (iii) distances for short-range bonding are 0.5-20 Å; and (iv) the range for the minimum energy is 14-20 kcal/mol. It must be mentioned that Yen’s model has been deduced from investigations on powdered asphaltene (solid). This fact leads us to think that they found stabilized asphaltene aggregates. On the other hand, Scotti and Montanari6 conducted X-ray diffraction (XRD) measurements and concluded that more-aromatic asphaltenes have a more-pronounced tendency to aggregate in graphitelike structures of condensed aromatic rings. In addition, they also show a spatial order of the graphitic nuclei of the asphaltene aggregates, with a spacing of ∼27-30 Å. These two different experimental measurements give confidence about the distances over which asphaltenes are interacting between themselves to get dimers, trimers, tetramers, etc., of asphaltene aggregates. A study of molecular simulation developed by Brandt et al.1 for asphaltene aggregation under vacuum was conducted. They worked with an open number of stacked asphaltene molecules of six unit sheets; however, they did not considerate any possible change in the configurations of the asphaltene number of unit (4) Yen, T. F. Prepr.-Am. Chem. Soc., Div. Pet. Chem. 1979, 24, (2), 901-909. (5) Yen, T. F.; Erdman, J. G.; Pollack, S. S. Anal. Chem. 1961, 33, (11), 1587-1594. (6) Scotti, R.; Montanari, L. In Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998.

10.1021/ef020226i CCC: $25.00 © 2003 American Chemical Society Published on Web 08/20/2003

MD Study of Asphaltene Aggregation under Vacuum

sheets per stacking due to aggregation. Moreover, for their stacking of six unit sheets, they reported a linear size of 11 Å, which is an inconsistent result, with respect to the Yen model. Yen et al.5 reported a distance of 1620 Å to be the linear size of four unit sheets for a stacking that is not exactly face to face, as the Brandt model was. The studies of these investigators led to analyses of the interactions and stability of asphaltene aggregates of six sheets that were initially induced when the aggregates did not undergo spontaneous formation. Another study that was similar to the latter was accomplished by Rogel;7 in the Rogel study, the use of a vacuum and different solvents was reported. In yet another study, which was completed by Murgich et al.,8 the use of resins, in addition to a vacuum and solvents, was examined. These studies exhibit stable aggregate structures; however, they worked with only a few molecules, because they used r0, an attractive effect is observed until a certain distance is reached. In model b, which consists of 96 asphaltene molecules, the dielectric constant ( ) 1) indicates that asphaltene under vacuum behaves more similar to asphaltene in n-heptane ( ) 1.92 at 20 °C) than to asphaltene in toluene ( ) 2.379 at 25 °C). The simulation of asphaltene aggregates under vacuum results in energetically favored structures.7 Asphaltene conformations do not change significantly when they are transferred from the vacuum to the bulk of the solvent or the core of the aggregates.1,8 To model asphaltene aggregation, the COMPASS force field was applied to our system of 96 hypothetical asphaltene molecules under vacuum, arbitrarily using a cut-off distance of 20 Å. In this particular case, seven covalently bonded aromatic rings and at least one S heteroatom13 constitute the asphaltene molecule. The original positions of the 96 asphaltenes were set into a volume of 500 Å × 180 Å × 45 Å (approximated dimensions before MD simulations), for a separation distance of ∼40 Å between the nearest S neighbors in the asphaltene molecules. After the energy of the system in model b was minimized, simulations for nonperiodic conditions under both the NVT canonical ensemble and the velocity Verlet18 method for integrating the motion equations were then done. The conju(16) (a) Sun, H.; Rigby, D. Spectrochim. Acta A 1997, 53, 1301. (b) Rigby, D.; Sun, H.; Eichinger, B. E. Polym. Int. 1997, 44, 311. (c) Sun, H.; Ren, P.; Fried, J. R. Comput. Theor. Polym. Sci. 1998, 8, (1-2), 229. (d) Sun, H. J. Phys. Chem. B 1998, 102, 7338. (17) Mansoori, G. A. J. Pet. Sci. Eng. 1997, 17, 101-111. (18) Verlet, L. Phys. Rev. 1967, 165, 98-103.

MD Study of Asphaltene Aggregation under Vacuum gate gradient method was used in the latter process. The NVT canonical ensemble is an appropriate choice to use to obtain MD simulations at different temperatures. The NVT method works very well without periodic boundary conditions and gives enough information to determine if temperature has any effect. In this way, asphaltene monomers can self-associate in freedom, just with the velocity Verlet restrictions. A general procedure for MD simulations can be described as follows. First, a minimization of the system energy is achieved, where convergence after 3061 iterations was successfully obtained. In this system, the number of atoms (16 416) exceeds the maximum number (200) allowed for the Newton minimization convergence method. The convergence strategy of energy minimization then starts with the latter method and switches to a conjugate gradient (Polak-Ribiere) numerical method. Second, general conditions for both equilibration and production processes include the following: temperature in turn; NVT canonical ensemble; NOSE as the thermostat control method; velocity Verlet as an integration method; random velocities from Boltzmann distribution as initial velocities; and an energy deviation of 5000 kcal/mol. The particular conditions were 5000 steps for equilibration and 100 000 steps for production, with a time step of 1 fs. Using all these conditions as the data input for model b, the following initial temperatures were used in the MD simulation: 298, 340, 370, and 400 K. The basic idea of these simulations is to observe the spontaneous formation of asphaltene aggregation under vacuum, as a function of distance and temperature. The final results are analyzed using the radial distribution function (RDF)19 between S atoms. The RDF is a structural property and is determined from the trajectory file data.15,16 This RDF gives a spherically averaged distribution of interatomic sulfur vector lengths. The aggregation number on each system was obtained by counting the number of asphaltene clusters that are observed with more than one single monomer. To decide if they form an aggregate, we run those frames which we automatically take as photographs during the simulation to watch the video and observe more precisely the stability of the aggregates formed in the final conformation. Distances between asphaltenes then were fully measured. The ranges of distances utilized are the same as those mentioned before in the Introduction. Furthermore, useful measurements for the last positions of asphaltene molecules in a given volume can be used to obtain knowledge about the aggregation number of each system. However, we have performed another similar MD simulation at a temperature of 310 K for 300 ps, for two basic purposes: (i) to validate the stability in the previous systems, and (ii) to analyze the structure of some asphaltene aggregates formed under these conditions. The RDF was not calculated in this case; however, very important results about the structure of aggregates are analyzed with this system.

Results and Discussion It is important to stress that, in our case, a spontaneous formation of the asphaltene aggregates is observed, because it was designed to be an initial regular arrangement of 96 asphaltene molecules within a separation of ∼40 Å between the nearest neighbors. Such distance is ∼10 times greater than the known distance proposed by the Yen model between two unit sheets, which is 3.5-3.8 Å; however, after molecular simulation for nonperiodic conditions, the aggregation of asphaltenes was observed. Yen4 also reported distances of 0.520 Å for short-range bonding; these distances were (19) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976; Chapter 13.

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Figure 2. Energy minimization for a face-to-face asphalteneasphaltene interaction under vacuum.

chosen arbitrarily for characterization of the microstructure. The molecular interaction at a distance of 40 Å, which is in the range of long-range bonding, then pertains to the macrostructure. The main orientations in asphaltene aggregates observed in the final results are face-to-face, are edge-on or T-shaped, or have an offset π-stacked geometry. These effects are corroborated in some examples that have been developed in this report, where the distances agree with experimental results. The number of asphaltenes that self-associated in every small cluster formed was counted. This was done to determine if the cluster was a dimer, trimer, tetramer, or pentamer. By counting the number of monomers, dimers, trimers, etc. at the end of every MD sinulation at a certain temperature, it was then possible to obtain the size distribution of asphaltene aggregates under vacuum. Furthermore, several distributions at different temperatures were also obtained. On the other hand, the molecular weight of asphaltene aggregates varies as the temperature changes. The latter behavior is similar to the effect of temperature for asphaltene in aromatics, which were measured experimentally by Espinat et al.14 Asphaltene Interactions. Asphaltene interactions were directly obtained for two identical asphaltene molecules that were placed exactly parallel, one in front to the other, and the interaction energy was determined, as a function of the distance, using energy minimization, as was previously mentioned in the methodology. The results are shown in Figure 2. An actually important analysis in Figure 2 involves those points obtained in the range of 3-4 Å in the graph for asphalteneasphaltene interaction. In this case, when the distance was 40 Å in a long-range interaction. One simulation started at a temperature of 298 K and ended at a temperature of 273 K for an NVT canonical ensemble, at 5000 steps of equilibration plus 100 000 steps of production, within a time step of 1 fs. The final positions of the asphaltene molecules at the latter temperature are exhibited in Figure 3, where aggregated asphaltenes are identified, using circles, triangles, and rectangles, respectively corresponding to the

Figure 4. Radial distribution function g(r), showing the regular behavior for an NVT canonical ensemble after a simulation of 100 000 steps.

aggregation of two, three, and four asphaltene monomers (forming dimers, trimers, and tetramers, respectively). The RDF in this case, calculated for a cut-off radius of 24.7 Å and an interval distance of 1.9 Å, is shown in Figure 4. The highest peak is located at 2.9 Å in this graph of RDF versus distance. This result is consistent with the Yen model and is also a good indication of the formation of asphaltene aggregates. Molecular simulations, for initial temperatures of 340, 370, and 400 K, which ended at 312, 342, and 369 K,



Figure 5. Image obtained at conformation 1500 and a final temperature of 284 K, showing dimers (Di), trimers (Ti), and tetramers (Qi).

respectively, were performed. The RDFs at these final temperatures, for a cut-off radius of 30 Å and an interval distance of 2 Å, are shown in Figure 4. For example, when a temperature of 400 K was the input in the MD simulation, the initial and final temperatures for equilibration were 400 and 404 K, respectively, and the final temperature after production of the MD simulation was 369 K. The RDF of this last stage is the dashed-dotted line reported in Figure 4. In such a graph, one peak (at 7 Å) and two more smaller peaks (one at 11 Å and another at 15 Å) can be observed. These two last, very well-distinguished peaks indicate a strong local density of asphaltenes and they also provide evidence of the aggregation process that has been observed. The largest peak in this case is not consistent with the Yen model. However, the largest peaks, at 312 and 342 K, corresponding to 3.4 and 3.6 Å, respectively, are consistent with the Yen model. As shown in Figure 4, the RDF approaches zero as the value of r increases. This phenomenon is due to the nonperiodic system that has been used for this report. It is important to mention

that, for periodic systems, the RDF approaches unity as the value of r increases. Structure of the Asphaltene Aggregates. The structure of the asphaltene aggregates will be described and analyzed for three dimers, one trimer, and one tetramer, all of which were extracted from conformation 1500 of our MD simulation that was conducted at a temperature of 310 K, within 150 000 time steps of 1 fs for equilibration plus 150 000 time steps of 1 fs for production. Therefore, in this case, the MD simulation was accomplished for 300 time steps of 1 ps. Figure 5 shows conformation 1500 at the end of the production of the MD simulation. This conformation has 12 dimers (Di), although only 7 were noted in Figure 5. Four trimers (Ti) and two tetramers (Qi) are depicted; the other notations represent monomers. Trimers and tetramers are all very clearly observed in Figure 5. Almost all distances for the dimers in Figure 5 are clearly noticed; however, distances for trimers and tetramers are not clear. The fact is that all these distances are in the range of 2-27 Å, which is the range that was

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Figure 6. Two aromatic rings observed at three different geometric positions, showing different interactions.

Figure 8. Schematic depiction showing several distances between two asphaltene monomers that form dimer D1 in T-shaped or edge-on geometry. For example, the distance between S atoms in this depiction is 17.10 Å. Figure 7. Schematic depiction of two monomers in a crossparallel, face-to-face geometry. (Dimer D2.)

observed in the RDF that we found. Dimers D1, D2, and D3, trimer T1, and tetramer Q1 in Figure 5 were selected, because of their final geometry. These were extracted and described by visualizing each one of these aggregates and measuring some distances at different positions. It must be also mentioned that the asphaltene aggregates did not suffer a considerable variation in their transition from conformation 1 to conformation 1500. This effect occurs because the asphaltene aggregates remained almost stabilized since conformation 1 after 150 000 time steps of 1 fs. The radius of gyration for each one of the aggregates in conformation 1500 shown in Figure 5 is generally 7.8-12.1 Å, which is very similar to those experimentally reported for different asphaltenes. The minimum experimental values for the radius of gyration reported by Espinat et al.20 for several classes of asphaltenes were 10, 13, and 14 Å; however, they did not give any indication of the number of self-aggregated asphaltenes. The latter numbers are in agreement with the radius of gyration of our tetramers Q1 and Q2, whose values are 11.2 and 12.1 Å, respectively. Moreover, Carnahan et al.21 reported experimental values of the radius of gyration of 20.6-22.1 Å as the pressure decreased from 400 bar to 25 bar; however, their statements clearly indicate that they considered at least six asphaltene sheets to obtain an aggregate. Therefore, their experimental values of the radius of gyration are in good agreement with our results. Furthermore, Barre´ et al.22 (20) Espinat, D.; Tchoubar, D.; Boulet, R.; Freund, E. Proceedings of Symposium International, Lyon, France, June 25-27, 1984; pp 147152. (21) Carnahan, N. F.; Quintero, L.; Pfund, D. M.; Fulton, J. L.; Smith, R. D.; Capel, M.; Leontaritis, K. Langmuir 1993, 9, (8), 20352044.

Figure 9. Schematic showing two monomers oriented in an offset π-stacked geometry. (Dimer D3.)

reported that the average radius of the log-normal distribution was 6.3-12.1 Å for asphaltene in toluene. At this point, it is important to comment that there are three preferential orientations for dimers D1, D2, and D3, which are very similar to those orientations mentioned by Leach11 for aromatic-aromatic interactions. The best conclusion in regard to this fact is that of Hunter and Saunders,10 who summarized the results of their investigations on porphyrins in three rules: (i) π-π repulsion dominates in a face-to-face geometry, (ii) π-σ attraction dominates in an edge-on geometry, and (iii) σ-σ attraction dominates in an offset π-stacked geometry. These rules were applied to many systems by Vinter.23 A sketch of these three geometric configurations, for single aromatic rings, is shown in Figure 6. Supposing that these three rules are valid for asphaltene-asphaltene interactions, then a π-π repulsion interaction dominates in the asphaltene-dimer D2 (22) Barre´, L.; Espinat, D.; Rosenberg, E.; Scarsella, M. Rev. Inst. Fr. Pet. 1997, 52, (2), 161-175. (23) Vinter, J. G. J. Comput.-Aided Mol. Des. 1994, 8, 653-668.



Table 1. Radius of Gyration, Distance between Sulfur Atoms, and Shortest Length between Two Asphaltenes for Dimers D1, D2, and D3, Trimer T1, and Tetramer Q1 in Conformations 1 and 1500

n-mer

radius of gyration (Å)

Distance between Sulfur Atoms (Å) conformation 1 conformation 1500

D1 D2 D3

8.93 8.22 8.04

21.419 6.416 11.67

Dimers 17.062 6.811 11.79

T1 (Z-X)a T1 (Z-Y)a T1 (Y-X)a

8.50 8.50 8.50

14.627 8.63 9.794

Trimer 14.447 9.256 9.411

Shortest Length between Two Asphaltenes (Å) conformation 1 conformation 1500 4.132 3.661

4.173 3.392 3.6

3.23 3.21 3.72

3.32 3.05 4.20

Tetramer Q1 a

11.20

Letters X, Y, and Z correspond to the asphaltene monomers in trimer T1, shown in Figure 10.

Figure 10. Schematic depiction of conformation 1500, showing that the trimer T1 (taken from Figure 5) is a mixture of the following geometric forms: T-shaped and offset π-stacked geometries.

interaction for a face-to-face geometry, as shown in Figure 7. A π-σ attraction dominates in the asphaltene-dimer D1 interaction for a T-shaped or edge-on geometry, as shown in Figure 8, and, finally, a σ-σ attraction dominates in an asphaltene-dimer D3 interaction for an offset π-stacked geometry, as exhibited in Figure 9. The radius of gyration, the distance between sulfur atoms (dbs), and the shortest length between two asphaltenes (slbta) are given in Table 1. The numbers 1 and 1500 given in the last four columns in Table 1 denote the corresponding conformations. Comparison of the dbs values (columns 3 vs 4) and the slbta values (columns 5 vs 6) in this table validate the stability of this system. Two facts can be observed from Table 1: (i) the radius of gyration of dimer D1 is greater than that of trimer T1, and (ii) the dbs values are greater than the slbta values. This observation occurs because the geometric shape of the asphaltene orientation is due to the asphaltene-asphaltene interaction. Table 1 was obtained from the structures shown in Figures 7-11, which have been obtained for conformation 1500. Dimer D1, which is exhibited in Figure 8, has the same orientation of a T-shaped structure. In this case, their longest aliphatic chains clearly remained interacting, in an almost-parallel manner. At least 10 distances between their parallel longest aliphatic chains are in the range of 4-5 Å. Dimer D2, which is exhibited in

Figure 11. Schematic depiction of conformation 1500, showing that the tetramer Q1 is a combination of several forms of T-shaped or edge-on geometries.

Figure 7, is initially in a face-to-face stacking geometry, forming a cross very similar to that mentioned previously by Rogel (theoretically) and Yen (experimentally). Dimer D3 stacks in a form most similar to those mentioned by Rogel7 and Murgich.8 In this case, one monomer is not exactly positioned over the other. They adopted a cofacial arrangement, with their centers offset, as observed in the dimer in Figure 9. The longest aliphatic chainsof 12 C atoms, connected with monomer Y and located in front of the aromatic rings of the monomer Xsinduces a ∼45° fold on asphaltene molecule X, as shown in Figure 9. Distances of 3.7-5 Å between monomers X and Y are marked in Figure 9. Monomer Y in the trimer T1 is penetrating between monomers X and Z, as shown in Figure 10. Tetramer Q1 clearly has aliphatic chains in the interior of a boundary formed by aromatic cores (see Figure 11). These chains stop all possibilities of stacking in the face-to-face geometry. Although asphaltene monomers W and X are shown in a T-shaped geometry, its aliphatic chains and the other biggest aliphatic chains do not allow any stacking in a face-to-face geometry because they are pushing the asphaltene monomers Y and Z. Generally, we are simply observing a very small compression in the transition from conformation 1 to

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Table 2. Variation of Both the Number of Aggregates and the Aggregate Distribution Observed with Increasing Temperature Simulation Temperature (K) initial final 298 340 370 400 a

273 312 342 369

number of aggregates at the final stage of the simulation

aggregate distributiona

22 18 19 18

12 dimers, 3 trimers, 7 tetramers 11 dimers, 2 trimers, 2 tetramers, 3 pentamers 11 dimers, 5 trimers, 2 tetramers, 1 pentamer 12 dimers, 5 trimers, 1 pentamer

Given in terms of the n-mers built at the end of the simulation.

Figure 12. Plots of the concentrations of asphaltene under vacuum versus the aggregation number at different temperatures.

conformation 1500. Otherwise, this is the first time, however, that a result without induced interaction is shown, because, in the very initial conformation before applying MD simulation, the average distance between asphaltenes was ∼40 Å in a regular configuration. All these analyses on asphaltene structures are sufficient to confirm that the nearest bond distances for interaction between Groenzing-Mullins asphaltenes are located in the range of 3-4 Å. This range includes the 3.55-3.7 Å range reported by Yen for an asphaltene model that was based on three different classes of asphaltenes. Moreover, Rogel indicated a range of 3.63.8 Å after optimization of the structure of one asphaltene average molecule and its aggregates, via calculations that used Biosym facilities. Effect of Temperature on Asphaltene Aggregation. Table 2 shows the results that were found for molecular simulations of those temperatures already mentioned. A similar table, which was proposed by Pacheco et al.,24 was also reported on their results for a separation of ∼50 Å between S atoms in the asphaltenes. Therefore, a larger aggregation number was expected if asphaltenes were placed as close together as 40 Å, using this type of calculation. For possible future calculations, a larger aggregation number is now expected if asphaltenes are placed as close together as 30 Å. The data for aggregate distribution at every temperature in Table 2 show that the asphaltene monomer is the most abundant species, and it is followed in abun(24) Pacheco, J. H.; Zaragoza, I. P.; Magadań, J. M. Memorias del XVI Congreso Nacional de Termodina´ mica; Sociedad Mexicana de Termodina´mica: Colima, Me´xico; 2001.

Figure 13. Plots of the effect of concentration of n-mers, relative to changes in temperature.

Figure 14. Plot describing the effect of the apparent molecular weight, relative to variations in temperature.

dance by the asphaltene dimer. This sequence is more formally observed both in Figure 12, for concentration versus aggregation number, and in Figure 13, for concentration of n-mers versus temperature. Concentration levels for the monomers and dimers are clearly observed in Figure 13, whereas the concentration levels of the other n-mers are mixed. A better definition of a model of more than 96 asphaltene monomers is expected. The abundance of trimers increases as the temperature increases, whereas the abundance of tetramers decreases as temperature increases. The change of apparent molecular weight, with respect to the change in temperature, is exhibited in Figure 14 for asphaltene under vacuum. Using the number of aggregates and the aggregate distribution in Table 2, it



Conclusions

Table 3. Variation of Temperature Observed, As a Function of Density final temperature (K)

densitya (mol/cm3)

radius of gyration (Å)

273 312 342 369

0.004980718 0.004766331175 0.004603885139 0.004198597889

196.820831 199.58 201.900284 208.198212

a Calculated using the radius of gyration of the 96-asphaltene system after the simulation.

was possible to determine the apparent molecular weight (as the product of the asphaltene molecular weight and the apparent aggregation number), as suggested by Rogel.25 The tendency of the graph shown in Figure 14 is in accordance with those measurements of molecular weight versus temperature on asphaltene in aromatics that were reported by Espinat et al.14 Their experiments showed that aggregated asphaltene in different aromatic solvents changes to elementary units of asphaltene when the molecular weight decreases as the temperature increases. The variation of the temperature as the density changes at constant pressure was reported in Table 3. In this case, the density was calculated on the basis of the radius of gyration of the entire system, as obtained directly from our MD simulations. The tendency shown in Table 3 between temperature and density shows the effect of temperature on the density of the solution previously mentioned for a system of 96 asphaltene molecules under vacuum, after the simulations. The effect observed involves how the density increases as the temperature decreases, which was expected for one branch of a phase behavior diagram.26-28 (25) Rogel, E. Langmuir 2002, 18, 1928-1937. (26) Pacheco, J. H.; Mansoori, G. A. Pet. Sci. Technol. 1998, 16, (3&4), 377-395. (27) Pacheco, J. H. Rev. Mex. Fis. 2001, 47, (4), 324-338. (28) Pacheco, J. H.; Zaragoza, I. P.; Martıńez-Magadań, J. M. Memorias del XVII Congreso Nacional de Termodina´ mica; Sociedad Mexicana de Termodina´mica: D. F., Me´xico, 2002; pp 94-106.

The peaks that appear at

Asphaltene Aggregation under Vacuum at Different Temperatures by

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