Molecular View of the Asphaltene Aggregation Behavior in Asphaltene

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Molecular View of the Asphaltene Aggregation Behavior in Asphaltene-Resin Mixtures A. Ortega-Rodrı´guez,† S. A. Cruz,‡ A. Gil-Villegas,§ F. Guevara-Rodrı´guez,† and C. Lira-Galeana*,† Branch of Molecular Engineering, Instituto Mexicano del Petro´ leo, Apartado Postal 14-805,07730, Me´ xico, D.F, Me´ xico, Department of Physics, Universidad Auto´ noma Metropolitana-Iztapalapa, Apartado Postal 55-534,09340, Me´ xico, D.F., Me´ xico, and Institute of Physics, Universidad Auto´ noma de Guanajuato, Apartado Postal E-143, 37150, Leo´ n, Guanajuato, Me´ xico Received January 9, 2003. Revised Manuscript Received May 16, 2003

The aggregation behavior of asphaltenes in asphaltene-resin mixtures within different host media is studied on the basis of the asphaltene/resin molecular structures and considering the embedding medium as a uniform background field. The approach employs models of molecular structures for both asphaltenes and resins (as derived from characterization data), and uses Molecular Mechanics (MM)/Molecular Dynamics (MD) calculations to predict the effect of the intermolecular interactions on the aggregation process as a function of composition and embedding medium. The peptizing behavior of resins is analyzed as a function of the ratio of resin to asphaltene molecules in each host medium by constructing the corresponding MD-generated radial distribution functions as well as the associated potentials of mean force (PMF). In all cases, the PMF presents repulsive barriers characteristic of aggregate systems showing a strong aggregation effect in a highly precipitant medium such as heptane. For an intermediate precipitant, as toluene, the results indicate the formation of stable asphaltene cores peptized by resins with no further association. Finally, it is shown that for a highly dispersive mediumssuch as pyridinesthe system behaves as a typical solution. All calculations have been performed at T ) 273 K. The results of this study point to the usefulness of MM/MD simulations as a complementary tool to understand the behavior of asphaltene-resin mixtures embedded in different host media.

Introduction Asphaltenes are a complex solubility class of compounds whose tendency to precipitate from petroleum causes serious operational problems in all facets of oil production. Oil-flow blockage in producing wells, transport lines, and processing equipment are common and high-cost operational contingencies reported from asphaltenes in typical field cases.1 Asphaltenes are defined as the insoluble fraction of crude oil, which drops out after addition of amounts of low-molecular-weight nalkanes.2 In recent years the number of experimental studies regarding asphaltene structure and composition has increased considerably.3-10 A common feature in * Author to whom correspondence should be addressed. Phone: +5255-3003-6507. Fax: +52-55-3003-6239. E-mail: [email protected]. † Instituto Mexicano del Petro ´ leo. ‡ Universidad Auto ´ noma Metropolitana-Iztapalapa. § Universidad Auto ´ noma de Guanajuato. (1) Speight, J. G. The Chemistry and Technology of Petroleum; Marcel Dekker: New York, 1991. (2) ASTM D 4124, Standard Test Method for separation of asphalt into four fractions. American Society for Testing and Material: Philadelphia, 1988. (3) Groenzin, H.; Mullins, O. Energy Fuels 2000, 14, 677. (4) Murgich, J.; Rodriguez, M. J.; Aray, Y. Energy Fuels 1996, 10, 68. (5) Murgich, J.; Abanero, J. A.; Strausz, O. P. Energy Fuels 1999, 13, 278-286. (6) Burke, N. E.; Hobbs, R. E.; Kashou, S. F. J. Pet. Technol. 1990, 42, 1440.

these studies is that asphaltenes are composed of condensed aromatic structures of high molecular weight, having aliphatic side chains and heteroatoms. It has been well established that asphaltenes are stabilized in crude oils by natural resins (surfactantlike agents). The action of these peptizing agents on the asphaltene aggregation and precipitation processes is thought to be of paramount importance.11 Resins are thought to have less condensed structures, acidic endsites, and lower molecular weight. Resins and asphaltenes are known to constitute the polar fraction of crude oil.1 Due to their molecular constitution, asphaltenes and resins have a mutual intrinsic effect on the stability of molecular self-assembling, either in the form of asphaltene-resin micellar association (which promotes re-dispersion) or asphaltene-asphaltene association (which promotes precipitation). To date, the most practical approach to deal with asphaltene problems in field cases uses chemical sol(7) Zajac, G. W.; Sethi, N. K.; Joseph, J. T. Scanning Microsc. 1994, 8, 463. (8) Carnahan, N. F.; Quintero, L.; Pfund, D. M.; Fulton, J. L.; Smith, R. D.; Lapel, M.; Leontaritis, K. Langmuir 1993, 9, 2035. (9) Dickie, J. P.; Yen, T. F. Anal. Chem. 1967, 39, 1847. (10) Altamirano, J.; Flores, M. A.; Pie, O.; Panivino, N.; Arzate, C.; Kapellmann, G.; Lo´pez, M. T.; Espinosa, S.; Rosales, S. Rev. Inst. Mex. Pet. 1986, 18, 32. (11) Leontaritis, K. J.; Mansoori, G. A. J. Pet. Sci. Eng. 1989, 1, 229.

10.1021/ef030005s CCC: $25.00 © 2003 American Chemical Society Published on Web 06/18/2003

Asphaltene Aggregation in Asphaltene-Resin Mixtures

vents which prevent flocculation and subsequent precipitation from occurring when injected into the oil streams.12 Design of these chemicals is often performed by semiempirical analytical procedures andsin that regardsa predictive screening criterion prior to product injection is highly desirable. As a preliminary step to yield this goal, in this work we investigate the role of the molecular characteristics of asphaltenes and resins in the formation of aggregates when the collective interactions are accounted for within a given host medium. The results of this study will then allow us to infer on the possibility of predicting the macroscopic behavior of asphaltene aggregation starting from the molecular characteristics of both asphaltenes and peptizing agents. On the other hand, due to the complexity of the molecular structure of asphaltenes and resins, to generate molecular-based equations of state for these substances is not an easy task. Usually, a whole series of aspects must be taken into account in order to satisfactorily obtain an equation of state for its use in industrial applications, and a compromise has to be made among all of them: the simplifications of the molecular model, the approximations introduced in the theoretical approaches used, the accuracy of the equation of state obtained, and, finally, the capability of using the equation of state in numerical implementations for the determination of phase diagrams. The usefulness of molecular simulation studies as the one presented here can be assessed through the information provided to generate accurate equations of state. An example of important information provided by computer simulation is the potential of mean force (PMF). A useful theoretical approach for asphaltene precipitation has been proposed recently,13 which is based on the Statistical Associating Fluid Theory14 and the McMillanMayer theory for electrolyte solutions.15 The core of the McMillan-Mayer theory is the use of PMF to determine the thermodynamic properties of an asphaltene-resin system considered as a solution, where the solvent is formed by a continuum medium that represents mainly low-weight alkanes. Accordingly, the PMF derived from the molecular simulations is also presented in this paper and a discussion on their possible consequences in theoretical modeling of equations of state is given. The work is organized as follows. First, the molecular models for experimentally determined asphaltene and resin structures are constructed and the corresponding asphaltene-asphaltene (A-A), asphaltene-resin (A-R), resin-resin (R-R) intermolecular potential curves are calculated using molecular mechanics (MM). Subsequently, the details of the molecular dynamics (MD) calculations are given. Another section is devoted to the analysis of results of the MD simulations for asphaltene-resin mixtures in three different host media: n-heptane, toluene, and pyridine for different resin/ (12) Aquino-Olivos, M. A.; Buenrostro-Gonza´lez, E.; Andersen, S. I.; Lira-Galeana, C. Energy Fuels 2001, 15, 236. (13) Wu, J.; Prausnitz, J. M.; Firoozabadi, A. AIChE J. 1998, 44, 1188; AIChE J. 2000, 46, 197. (14) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Fluid Phase Equilib. 1989, 52, 31. Ind. Eng. Chem. Res. 1990, 29, 1709. (15) Lee, L. L. Molecular Thermodynamics of Nonideal Fluids; Butterworth Publishers: Boston, 1988.

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asphaltene relative concentrations. Also in this section, a discussion is presented on the characteristics of the corresponding PMF as derived from the MD simulations and their possible consequences on the generation of an associated equation of state. Finally, the conclusions of this work are given. Methods Molecular Mechanics (MM) Computation of Intermolecular Potentials. Recent experimental studies regarding the size of asphaltene moieties point to the existence of two possible molecular structures depending on the aggregation state of these entities in crude oil. One of these3 suggests that asphaltenes consist of relatively small molecules containing 4-9 fused aromatic rings with a few heteroatoms and attached aliphatic chains. Larger asphaltene structures are considered as being composed by the coalescence of these minimal structures. Here, we use a relatively small asphaltene structure reported experimentally,7 as well as a model resin structure reported in the literature.5 We point out at this stage that the method to be described in the following sections is equally applicable to larger structures. Figure 1 shows the molecular structure and composition of both the asphaltene and resin molecules used in this work. Both structures were constructed and optimized using molecular mechanics, as described in a previous contribution,16 where the corresponding asphaltene-asphaltene (A-A), resin-resin (R-R), and asphaltene-resin (A-R) interactions were computed using MM techniques considering different relative orientations between each pair of molecules. Due to the complicated structure of the interacting molecules, a detailed analysis of the orientational dependence of the interaction potential for each dimer was not pursued. Instead, a sampling of specific orientations and positions was performed. It was found there that the most favorable interaction takes place when the aromatic regions approach parallel to each other. Indeed, the most repulsive interactions take place when the aliphatic chains face the docking partner. Clearly, the interaction potential is fully anisotropic, and some simplifying assumptions have to be made in order to assess insight on the potentiality of the method before embarking in a more detailed calculation where the potential anisotropy is included as, for example, a GayBerne parametrization scheme.17 In light of the above discussion, we have considered the competing effect of the most favorable A-A, A-R, and R-R interactions in the aggregation process, keeping in mind that the mid and highly repulsive interactions will certainly act as potential barriers preventing association. Although this approximation might look too stringent, some important information may be extracted on the relative role of A-A, A-R, and R-R interactions by treating the whole set on the same footing. Accordingly, we have used the interaction potentials for the most favorable relative orientation of each dimer as an (16) Ortega-Rodriguez, A.; Cruz, S. A.; Ruiz-Morales, Y.; LiraGaleana, C. Pet. Sci. Technol. 2001, 19, 245. (17) Gay, J. G.; Berne, B. J. J. Chem. Phys. 1981, 74, 3316.

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Figure 2. Intermolecular potential curves in a vacuum for the most favorable relative orientation (see text) between asphaltene-asphaltene (A-A), asphaltene-resin (A-R), and resin-resin (R-R). Symbols correspond to MM calculations. Continuous curve: best fit using eq 1 according to ref 16.

Figure 1. Molecular models used in this work. (a) 3D diagram of the MM-optimized asphaltene structure (C57H63N1S1) reported in ref 7 showing an aromatic region (continuous lines) and its aliphatic chain (dashed lines). (b) Transverse view of the asphaltene structure showing the aromatic region in more detail. (c) Diagram showing the resin structure (C13H10S1) reported in ref 5.

effective spherical potential given by the following expression:16

V(r) )

Z1Z2 -Rr C2 4 + C1re-βr) - 2 6e-γ/r (e r r

(1)

where r is the distance between the centers of mass (CM) of each molecule with facing parallel aromatic regions, and Z1, Z2 are the number of atoms in each molecule. The parameters C1, C2, R, β, and γ were

obtained by fitting eq 1 to the corresponding MM numerical values (T ) 0 K, in vacuum). Figure 2 displays the A-A, A-R, and R-R intermolecular potentials generated according to the previous discussion.16 The symbols correspond to the MM numerical values and the continuous curves to the best over-all fit found with eq 1. Note that within this spherical approximation for the interactions, asphaltenes and resins are considered as entities without internal structure in the MD simulations described further below. Thus we shall be only concerned with the A-A, A-R, and R-R spatial distributions in terms of the molecular CM positions. The embedding medium is accounted for through a mean field approximation given by its dielectric constant, , affecting only the Coulomb and London contributions. The use of an effective medium through its dielectric constant is known to be questionable for intermolecular distances of the order of the molecular size, mainly because it is at these distances where atomic detail becomes important.18 However, it is still a valuable first exploratory means to account for the screening of Coulomb and London interactions due to the embedding medium for intermediate to large intermolecular distances. It is deemed that the initial stages of aggregation will correlate strongly with the longrange interactions. As the interacting molecules become closer to each other the molecular structure of the solvent is more apparent and local effects become important. These local interactions may be dominant in defining the structure of an aggregate, solvation free energies, possible chemical reactions, etc. Hence, the use of an effective medium in our case has its aim in looking at the evolution of aggregation from its initial stages and extrapolating the behavior of the system in its final “gross” equilibration (see further below). Molecular Dynamics Simulations. The intermolecular potentials described in the previous section were used in a canonical molecular dynamics (MD) simulation for mixtures of asphaltene/resin in different host media. Our model system consists of NAs and NRe (18) Smith, P. E.; Pettitt, M. B. J. Phys. Chem. 1994, 98, 9700.


asphaltene and resin moieties, respectively, contained in a cubic box and imposing periodic boundary conditions. The NVT-canonical ensemble simulation procedure was employed and the reversible Verlet algorithm was used throughout.19,20 The simulations were carried out considering the host medium as a background field with a dielectric constant equivalent to that experimentally observed for the solvent. Hence we shall only consider the effect of the favorable intermolecular interactions among the mixture components screened by the average reaction field of the medium represented by its dielectric constant. Three different solvents were considered, namely n-heptane ( ) 1.92), toluene ( ) 2.38), and pyridine ( ) 12.3). To introduce realistic conditions in the input quantities for the MD simulations, the asphaltene (A), resin (R), aromatic (a) and saturated (S) hydrocarbon concentrations in a sample of Maya crude oil (measured density: 1.12 g/cm3) were experimentally obtained by means of a sequential IP 14321,22 and S.a.R.A. fractionation analyses. First, the oil is subjected to asphaltene separation with the modified IP 143 method stated above, and the deasphalted fraction is subjected to a preparative S.a.R fractionation using an HPLC chromatographic technique. These measurements yielded a composition of 10 wt % for asphaltenes, 20 wt % for resins, 40 wt % for aromatic hydrocarbons, and 30 wt % for saturated hydrocarbons. Assuming the molecular structures for asphaltene and resin are those described in the previous section, their corresponding molecular weights are 794 g/mol and 198 g/mol, respectively. Hence, according to the experimental analysis a resin/ asphaltene number ratio ξ ) (NRe:NAs) ) (8:1) is required within the simulation cell. The simulation was performed by defining the unit cell as a cube of length L ≈ 79 Å with NAs ) 42 and NRe ) 336 asphaltene and resin moieties, respectively. The volume of the simulation cell is such that the same resin/asphaltene wt % ratio is kept as observed in the experiment. Also, to account for the importance of resin concentration in their peptizing behavior, we have considered two additional independent simulations with number ratios ξ ) (3:1) and (27:1) for each host medium. In the former case, the simulation cell has been kept with the same size (L ≈ 79 Å) as in the first study, with NAs ) 86 and NRe ) 257; while for the latter NAs ) 62 and N Re ) 1666 with L ≈ 136 Å. All simulations were performed at a temperature of 273 K, with a time step of 1.0 fs starting from a random distribution of positions for each asphaltene and resin moiety in a regular cubic array for each host medium as shown in Figure 3, as an example. The final equilibrium configuration was yielded after ∼ 5 × 106 steps. (19) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (20) Tuckerman, M.; Berne, B. J.; Marytna, G. J. J. Chem. Phys. 1992, 3, 1990. (21) IP 143 Procedure. Asphaltenes precipitation with normal heptane. British Standard BS 4696, 1971. (22) Buenrostro-Gonzalez, E. Characterization and Thermodynamic Modeling of Asphaltene Precipitation. Ph.D. Thesis, National University of Mexico, Mexico, 2002.


Figure 3. Sample snapshots of the initial configuration employed in the MD simulations for ξ ) (3:1) in (a) n-heptane, (b) toluene, and (c) pyridine. Dark dots: asphaltene molecules; light dots: resin molecules.

Results and Discussion Figures 4-6 show snapshots of the simulation cell for the final configurations of the asphaltene-resin mixture for ξ ) (3:1), (8:1), and (27:1), respectively, in the three host media [(a) n-heptane, (b) toluene, and (c) pyridine]. Looking at asphaltenes as the dark dots and resins as the light dots, the qualitative behavior of the aggregation process is similar for each medium despite the different number ratios, ξ. In an n-heptane host medium ( ) 1.92), which is characterized as a precipitant medium, asphaltenes tend to coalesce to form large asphaltene particles, while resins gather around an already formed asphaltene particle (Figures 4a, 5a, and 6a). The reduced number of asphaltenes used in this simulation prevents us from showing other clusters. However, we would expect that similar structures would be formed if the number of asphaltene/resin moieties is

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Figure 4. Snapshots of the final configuration of an asphaltene-resin mixture with ξ ) (3:1) in (a) n-heptane, (b) toluene, and (c) pyridine host media. Asphaltene molecules are represented by dark dots and resins by light dots.

increased keeping the same relative concentration. The tendency of asphaltenes to aggregate and the peptizing effect due to resins are apparent from these figures, taking into account that all particles evolved during the same time from initial aleatory conditions. Of course, care must be taken in making a definite statement at this stage, since we have considered only the favorable interactions among all mixture components. However, even in this situation, we observe that the competing behavior of the different interactions points to a synergistic effect leading to a structured fluid whereby asphaltene-asphaltene affinity seems stronger than asphaltene-resin affinity and the latter stronger than the resin-resin one. The low value of the dielectric constant of the host medium, n-heptane in this case, has a poor screening effect on the long-range interactions and hence promotes the correlated evolution of species in an order going from the highest to the lowest

Figure 5. Same as in Figure 4 with ξ ) (8:1).

affinity. This effect may be also deemed from a glance at the intermolecular potentials in a vacuum shown in Figure 2. In the case of toluene ( ) 2.38) as host medium, asphaltene aggregation is also observed and resins still show the tendency to surround asphaltenes although at a lower rate (Figures 4b, 5b, and 6b). In contrast with the case of n-heptane, this is clearly a consequence of the stronger dielectric screening on the long-range interactions so that the correlated evolution of the various molecular moieties is reduced. Interestingly, for the large resin/asphaltene ratio ξ ) (27:1) the formation of small dispersed peptized aggregates appears (see Figure 6b). In this case the large resin concentration might correspond to a cosolvent behavior. For pyridine ( ) 12.3) an almost homogeneous distribution of



Figure 7. Calculated radial distribution functions (RDF) for the asphaltene-asphaltene gAA(r), asphaltene-resin gAR(r), and resin-resin gRR(r) pairs in a n-heptane host medium for number ratios ξ ) (a) 3:1, (b) 8:1, and (c) 27:1.

Figure 6. Same as in Figure 4 with ξ ) (27:1).

asphaltene and resin moieties is observed (Figures 4c, 5c, and 6c). The large screening effect on the long-range intermolecular interactions due to the high dielectric function of the host medium is reflected in this simulation. Analysis of the Radial Distribution Functions. The radial distribution functions (RDF) for the pairs A-A, A-R, and R-R obtained from the simulation in the case of n-heptane as host medium for ξ ) (3:1), (8:1), and (27:1) are shown in Figure 7. For all ξ values, the radial distribution function gAA(r) exhibits three well distinguished peaks at r ∼ 7 Å, 10 Å, and between 13 and 14 Å, indicating a strong local density of asphaltenes evidencing the aggregation process observed in Figures 4a, 5a, and 6a. For the A-R distribution function we first observe for ξ ) (3:1) and ξ ) (8:1)

(Figures 7a and 7b) two well-differentiated peaks in gAR(r) centered at r ∼ 5.5 Å and 9.5 Å and a third peak at r ∼ 12 Å, whereas for ξ ) (27:1) (Figure 7c) only the first two peaks persist. The appearance of the first two peaks for all number ratios may be explained as follows. Since resins concentrate mainly around the asphaltene aggregate (see Figures 4a, 5a, and 6a), the radial positions of the peaks in gAR(r) may be correlated with the corresponding ones for the A-A distribution, indicating the peptizing tendency of resins around asphaltenes. As a matter of fact, if the dielectric constant for n-heptane is included in the corresponding intermolecular interactions16 the equilibrium A-R distance becomes ∼ 5 Å, whereas that for A-A becomes ∼ 7 Å. The first peak in gAR(r) appears at the position of this minimum indicating a close asphaltene-resin partnership. Furthermore, the position of the second peak in gAR(r)swhen compared with the corresponding one in gAA(r)sindicates a definite asphaltene-resin spatial correlation. We note here that the first peak in gAA(r) correlates well with equilibrium position in the A-A interaction curve, thus evidencing also the formation of a core of associated asphaltenes. On the other hand, the third peak appearing in gAR(r) for the lower number ratios coincides with a lowering in the gAA(r) curve, suggesting the penetration of resins in void spaces between asphaltenes. This observation might be in support of recent experimental reports on multilayer adsorption and penetration of resins in the microporous structure of asphaltene particles,23 namely, for low resin/asphaltene number ratios a competing effect between surface adsorption and void penetration takes place (see Figures 4a and 5a). As the number ratio increases, several layers of adsorbed resins form around the asphaltene particle not precluding the existence of (23) Leoń, O.; Contreras, E.; Rogel, E.; Dambakli, G.; Acevedo, S.; Carbognani, L.; Espidel, Y. Langmuir 2002, 18, 5106.

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Figure 8. Same as in Figure 7 for a toluene host medium.

resins already trapped within the structure of the asphaltene particle (see Figure 6a). Along the same line of arguments, the R-R radial distribution function gRR(r) shows two peaks at r ∼ 4.5 Å and r ∼ 8.5 Å. Again, the first peak correlates very well with the equilibrium R-R distance in heptane (∼ 4.5 Å) which may be explained by the compact association of resins around and within the aggregate (see below). Note, however, the slight increase in the amplitude of gRR(r) after dropping from the first peak for radial distances between 8 and 10 Å, indicating a relative increase of neighboring R-R pairs which is perhaps reflecting the effect of resin moieties grouping around asphaltene particles, hence increasing their local density as compared to the rest of the system. Figure 8 shows the radial distribution functions gAA(r), gAR(r), and gRR(r) for a toluene host medium for the ξ values discussed in this work. The RDF curves are quite similar in all cases, indicating a first peak located at about the equilibrium A-A, A-R, and R-R position in the corresponding intermolecular potentials when the dielectric constant of the host medium is introduced into eq 1. For instance, gAA(r) shows only a strong peak at this distance, suggesting the formation of small asphaltene particles (see Figures 4b, 5b, and 6b). The structure observed in gAA(r) for radial distances between 10 and 15 Å correlates with gAR(r) for these distances. This is consistent with the formation of smaller-size asphaltene particles with resins still grouping around them, as discussed before for the corresponding case for n-heptane. Interestingly, as the number ratio ξ increases, the gRR(r) curve tends to decrease in a practically monotonic fashion after the first correlation peak suggesting a lower tendency to increase the resin local density in the region surrounding already “peptized” asphaltene particles [compare with the gAR(r) curve]. Finally, for the pyridine case, the system behaves as a typical liquid as shown by the radial distribution functions gAA(r), gAR(r), and gRR(r) in Figure 9 for all


Figure 9. Same as in Figure 7 for a pyridine host medium.

cases. In general, a large dispersion in the gAA(r) values is observed and increases as the number ratio increases. This behavior points to the need for a better statistics for this case, i.e., a larger number of configurations since the number of asphaltene particles used in order to keep the asphaltene/resin ratio is very small. To test the reliability of the results for this case, a theoretical prediction was obtained for the system ξ ) (27:1), solving the Ornstein-Zernike equation (OZ)15 using the Reference Hypernetted Chain Equation closure (RHNC).24 For isotropic potentials, the RHNC predictions are within the same accuracy of the computer simulation results, as has been proved for a wide range of potential models.25 To obtain the OZ-RHNC prediction, we followed the same procedure and numerical technique reported in ref 26. Figure 9c shows the comparison between theory and the simulation results. The continuous curve corresponds to the theoretical curve for gAA(r) while the “+” signs are points obtained from the simulation. Similarly, the dotted and dashed curves represent the theoretical curves for gAR(r) and gRR(r), respectively, compared to their corresponding simulation results (crosses and open circles). A reasonable agreement is observed among all calculations, where the fluctuation of the gAA(r) simulation results around the corresponding theoretical curve is apparent. We may deem the “average” tendency of the RDF in pyridine as that of a solution behavior. Potential of the Mean Force. The MD simulation results already presented here provide information for analyzing the characteristics of the spatial distribution of the different species, on the basis of the approximation of considering only the favorable interactions among the different species. The question remains on whether this assumption yields to physically sound (24) Lado, F. Phys. Rev. A 1973, 8, 2548. Lado, F.; Folies, S.; Ashcroft, N. W. Phys. Rev. A 1983, 28, 2374. (25) Talbot, J.; Lebowitz, J. L.; Wasiman, E.; Levesque, D.; Weiss, J. J. J. Chem. Phys. 1986, 85, 2187.


conclusions regarding the dynamics of the collective interactions leading to the observed structures. Moreover, from the thermodynamic point of view, we would like to assess the usefulness of the information generated in order to develop molecular-based equations of state. We can address both issues considering the potential of the mean force (PMF), whereby the interactions between pairs of particles are estimated within the effective field created by the rest of the particles. A basic approximation used in solution theories is to consider the solvent as a continuum with a screening effect on the solute interactions. This approach has been successfully used, for example, in electrolyte solutions (primitive models). In this way, the solvent is described by continuous parameters, such as the dielectric constant. A rigorous theoretical treatment of this approximation is given by the McMillan-Mayer theory for solutions,15 which demonstrates that the statistical mechanics of solutions can be accomplished through the theory of mixtures without a solvent if and only if the intermolecular potential between solutes, V(ri,rj), is replaced by the corresponding mean-force potential, W(ri,rj). Both potentials are related by the following exact relationship obtained in the canonical ensemble:15

∫drN∇ijV(ri,rj) exp[-βU(rN)] -∇ijW(ri,rj) ) ∫drN exp[-βU(rN)]

(2)

where U(rN) is the total potential energy of the system, and β ) 1/kT, where k is the Boltzmann constant and T is the temperature. This equation states that the force between solute particles i and j in the presence of another N - 2 particles is given by the statistical average of the force derived from the pair intermolecular interaction. The mean-force potential is related exactly to the pair distribution function,15,27

W(ri,rj) ) - ln g(ri,rj) kT

(3)

Figures 10a, 10b, and 10c show the PMF for the various solvents discussed in the previous section and for the number ratio ξ ) (3:1), as an example. In the case of heptane (Figure 10a), the A-A PMF has defined minima separated by potential humps of height ∼1.5kT. The depth and positions of the minima suggest the formation of asphaltene core structures within the large clustered particle. The height of the potential hump between the cores is large enough to prevent coalescence due to an effective repulsive interaction appearing from resins still surrounding each core. The strong peptizing effect due to resins is apparent from the A-R curve in this figure, where a well-defined minimum is observed at equilibrium A-R separation and a high barrier hump prevents A-R separation. In the case of the R-R PMF, there is indication of resin association with a smaller activation energy to dissociate. In the toluene case (26) Gil-Villegas, A.; Vega, C.; del Rıó, F.; Malijevksy´, A. Mol. Phys. 1995, 86, 857. (27) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids, 2nd ed.; Academic Press: New York, 1986. (28) Mejıá-Rosales, S.; Gil-Villegas, A.; Ivlev, B.; Ruı´z-Garcıá, J. J. Phys. Condens. Matter 2002, 14, 4795.


Figure 10. Potential of mean force obtained from the RDF of the (A-A), (A-R), and (R-R) pairs in (a) n-heptane, (b) toluene, and (c) pyridine for ξ ) (3:1).

(Figure 10b), the A-A curve indicates more stable asphaltene cores, i.e., higher activation energy to dissociate. Hence, already formed asphaltene particles will remain as such, like a suspension. Moreover, the resin peptizing effect is apparent also from this curve, which means the asphaltene particles will remain peptized with no further association. In the case of pyridine (Figure 10c), the system behaves as a perfect solution. Notice that the main effect obtained by changing the solvent is observed in the A-A interaction, indicating that as the repulsive barriers disappear, the associating behavior of the asphaltene molecules is also reduced. These observations are common also for the other two values for ξ with regard to the stability of asphaltene particles peptized by resins. It is worth mentioning at this stage that similar results have been observed in other systems. For example, the formation of soap-froth aggregates of colloidal particles at the air/water interface has been explained as a consequence of an effective electrostatic-interaction potential with a repulsive barrier, which is also isotropic.28 The same type of interaction can also induce colloidal aggregation as chains. Then, we can expect that a simple but reliable approach to consider in the theoretical modeling of asphalteneresin mixtures, following the McMillan-Mayer approach, consists of using isotropic potentials of the mean force for the A-A, A-R, and R-R particles, with the basic features observed in the computer simulation study presented here. Conclusions The aggregation of asphaltenes in mixtures containing realistic asphaltene/resin concentrations and a dielectric host medium has been studied. Molecular dynamics simulation techniques were used introducing the most favorable A-A, A-R, and R-R intermolecular interactions, previously obtained through molecular

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mechanics and represented by an analytic effective spherical potential. Despite the oversimplification introduced in ignoringsin this first contributionsevident anisotropies in the intermolecular potentials, and the consideration of a uniform, static background field, the results reveal an important aspect regarding the relative competition among the various interacting partners in order to form aggregates. It is found that asphaltenes have the greatest affinity to form aggregates and resins clearly show a peptizing behavior. Moreover, the screening of long-range interactions due to the reaction field of the medium represented by its dielectric constant effectively reduces the correlated evolution of the different species. It is deemed here that the introduction of a fully anisotropic intermolecular potential will probably change the equilibration time for the formation of aggregates due to interfering repulsive interactions. However, the favorable interactions will certainly compete to lend a fraction of the system to schemes as the ones shown here. Despite the simple models of interaction used in this study, we have shown that the basic features observed for the potentials of mean force are consistent with the observation of cluster formation in other systems. Furthermore, since a basic assumption followed in molecular theories for the thermodynamic description of asphaltene-resin mixtures is to simplify the role played by the solvent and to take it into account


as a continuum media, in the spirit of the McMillanMayer theory for electrolytes, then we necessarily have to work with PMF. According to the computer simulation results shown in this article, an important feature observed in the PMF of aggregated systems is the presence of repulsive barriers. These results suggest that it would be desirable that a theory based on the McMillan-Mayer approach could include the effect of these repulsive barriers. Further work is necessary to test the ideas mentioned here, and also including the anisotropy in the interaction potential as well as the dynamical interactions with the molecules of the host medium. Such work is in progress. Acknowledgment. This work was supported by the Molecular Engineering Research Branch of the Mexican Instititue of Petroleum, under Contract D00337. The criticisms of the referee, which helped to enrich this work, are deeply appreciated. S. A. Cruz thanks the IMP for the inspiring atmosphere and facilities provided during the course of this research. A.O.-R. is indebted to the National Council of Science and Technology of Mexico (CONACyT) for a fellowship. Thanks are also given to Professor J. Murgich for various fruitful discussions. EF030005S

Molecular View of the Asphaltene Aggregation Behavior in Asphaltene

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